InP-based polarisation independent wavelength demultiplexers

InP-based polarisation independent
wavelength demultiplexers

The cover shows a microscope image of a
phased-array demultiplexer manufactured
in an erbium-implanted Al 2 O 3 waveguide
structure, see Chapter 6, section 6.4.
(photo: Eduard de Kam / Hollandse Hoogte)

InP-based polarisation independent
wavelength demultiplexers
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR
AAN DE TECHNISCHE UNIVERSITEIT DELFT,
OP GEZAG VAN DE RECTOR MAGNIFICUS PROF. DR. IR. J. BLAAUWENDRAAD,
IN HET OPENBAAR TE VERDEDIGEN TEN OVERSTAAN VAN EEN COMMISSIE,
DOOR HET COLLEGE VAN DEKANEN AANGEGEWEZEN,
OP DINSDAG 2 DECEMBER TE 13:30 UUR
DOOR
Cornelis van DAM
elektrotechnisch ingenieur,
geboren te ’s-Gravenhage.

Dit proefschrift is goedgekeurd door de promotor:
Prof. dr. ir. H. Blok
Samenstelling promotiecommissie:
Rector Magnificus, voorzitter
Prof. dr. ir. H. Blok, Technische Universiteit Delft, promotor
Dr. ir M.K. Smit, Technische Universiteit Delft, toegevoegd promotor
Prof. dr. G.A. Acket, Technische Universiteit Eindhoven
Prof. dr. ir. R.G.F. Baets, Universiteit Gent
Prof. dr. ir. W. van Etten, Universiteit Twente
Prof. dr. ir. H.J. Frankena, Technische Universiteit Delft
Prof. dr. B.H. Verbeek, Philips Optoelectronics
Part of this work was supported by the Dutch Ministry of Economic Affairs (IOP Electro-
Optics). Also parts of this work have been carried out in connection with the RACE 2070
MUNDI project and the ACTS AC 065 BLISS project.
The work described in Chapter 4 has been performed in close cooperation with Philips
Optoelectronics Centre, Eindhoven, The Netherlands.
The work described in Chapter 6, section 6.4, has been performed in close cooperation with the
FOM-Institute for Atomic and Molecular Physics, Amsterdam, The Netherlands.
van Dam, Cornelis
InP-based polarisation independent wavelength demultiplexers /
Cornelis van Dam. - [S.l. : s.n.] - Ill. -
Ph.D. Thesis Delft University of Technology. - With ref. - With summary in Dutch.
ISBN 90-9010798-3
NUGI 832
Keywords: Integrated optics / optoelectronics
Copyright © 1997 Cor van Dam
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system,
or transmitted in any form or by any means - optical, electronic, magnetic, mechanical, or any
other recording system - without the prior written permission from the publisher.
Typeset by FrameMaker 5; printed by Ponsen & Looijen, Wageningen, The Netherlands

Aan Renée

Contents
1 Introduction: WDM in optical communication networks 1
1.1 Optical communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Recent developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Phased-array demultiplexers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 About this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 PHASAR demultiplexers: a review 9
2.1 Basic operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Focusing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Dispersion and Free Spectral Range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 Insertion loss and non-uniformity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.4 Bandwidth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.5 Channel cross talk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.6 Polarisation dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Phased-array design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Demultiplexer design procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 Array geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.4 Design for polarisation independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.5 Design for flattened response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.6 Design for low loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.7 Device size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.8 Correction for bending effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.9 Waveguide junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.1 Wavelength routers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.2 Multi-wavelength receivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.3 Multi-wavelength lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.4 Wavelength-selective switches and add-drop multiplexers . . . . . . . . . . . . . . 31
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

viii Contents
3 Polarisation conversion in waveguide bends 35
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Computational methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.1 Effective index method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.2 Method of lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.3 Finite element method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.4 Conformal transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Attenuation in bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Tilting of the modal polarisation plane in bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 Polarisation dispersion in bends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.6 Polarisation conversion at junctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.7 A compact polarisation converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.8 Tolerance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.8.1 Layer thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.8.2 Waveguide width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.9 Avoiding polarisation conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4 Polarisation independent PHASAR demultiplexers
based on nonbirefringent waveguides 63
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2 Nonbirefringent waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.1 The embedded square waveguide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.2.2 The raised-strip waveguide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.4 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Loss reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.4 Ghost images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4.1 Ghost image mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.4.2 Verification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4.3 Junction optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.4 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4.5 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5 Demultiplexer integrated with detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 Polarisation independent PHASAR demultiplexers
based on birefringent waveguides 83
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2 Polarisation dispersion compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.2.1 Production tolerance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.2.2 Coupling between array waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.4 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3 Polarisation conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.1 Cross talk tolerance analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Contents ix
5.4 Polarisation splitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4.1 Cross talk tolerance analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6 MMI-based components 97
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 MMI-MZI demultiplexer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.1 Operation principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2.2 Tolerance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.2.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.3 Spatial mode filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.3.1 Operation principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3.2 Tolerance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.3.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.4 Optical imaging of MMI patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4.1 Upconversion mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4.2 Measurement principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.4.3 MMI-coupler simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.4.4 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7 Discussion and conclusions 127
A Overview of phased-array demultiplexers produced 129
B Dispersion of the phased array 133
C Waveguide mode effective width 135
D Cross talk penalty of the tunable laser 137
D.1 Measurement with a tunable laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
D.2 Measurement with an EDFA as source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
D.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
E Excitation coefficient of the first-order mode 141
F Phase correction in MMI-MZI demultiplexers 143
References 145
List of symbols and acronyms 157

x Contents
Summary 161
Samenvatting 163
Dankwoord 165
Biography 167

Chapter 1
Introduction: WDM in optical
communication networks
This chapter gives a brief overview of the development of optical communications and places
the subject of this thesis in the right context. Finally, an outline of the contents of this thesis is
presented.
1.1 Optical communication
Optical fibre communication provides a solution for the growing demand for bandwidth in
telecommunication systems. Two major developments - the laser and the fibre - triggered
optical communication. In 1960 the first laser (Light Amplification by Stimulated Emission of
Radiation) was developed by Theodore Maiman [79,85], using a pink ruby medium. In 1962
Robert Hall and others followed with the invention of the semiconductor laser [85], a device
now used in optical fibre communication systems, compact disk players and laser printers. The
usage of optical fibres as a suitable transmission medium for light was suggested by Kao and
Hockham in 1966 [72].
The first fibres, however, measured transmission losses in the order of 1000 dB/km. The breakthrough
took place in 1970, when Corning Glass scientists Robert Maurer, Donald Keck and
Peter Schultz developed an optical fibre [71,85], capable of carrying 65,000 times more information
than conventional copper wire, with optical losses of 20 dB/km - low enough for practical
use in telecommunication systems. Within nine years of intensive research, this loss was
narrowed to below 0.2 dB/km. By the mid-eighties fibres with attenuation minima of less than
0.4 dB/km at 1.3 μm wavelength and less than 0.25 dB/km at 1.55 μm were commercially
available. At that time reliable AlGaAs semiconductor lasers and Si detectors were already
available, and full-scale implementation of fibres in the telephone network started. The first
generation used graded-index multimode fibres with a core diameter of 50 μm in the
transmission window of around 850 nm, determined by the wavelength range accessible by
AlGaAs. The second generation uses the longer wavelengths (1.3 and 1.55 μm) in combination
with monomode fibre, in this way enabling higher transmission capacities. For these
wavelengths other semiconductor material was needed: In 1-x Ga x As 1-y P y . By varying the

2 1. Introduction: WDM in optical communication networks
material composition x and y, materials with wavelengths in the entire range from 0.92 μm to
1.65 μm and lattice-matched to InP can be obtained.
Nowadays, optical fibre is the foundation for global multimedia telecommunications networks.
More than 90 percent of the U.S. long-distance traffic is already carried via optical fibre, and
more than 25 million kilometres have been installed. In the Netherlands more than 18,000
kilometres fibre have been installed. Globally, over 40 million kilometres have been installed,
which, if strung together, could reach 28 times from the earth to the moon and back.
1.2 Recent developments
The reason which makes the fibre enormously attractive is the huge bandwidth it offers in
combination with high transmission speeds. At first, direct detection was used for point-topoint
links, a basic system consisting of a laser, a detector and optical fibre. A more advanced
principle is the coherent transmission scheme [49], in which the incoming (modulated) signal
is mixed with the signal of a local oscillator laser. The advantage of this transmission scheme is
the improved sensitivity and more efficient usage of bandwidth. However, the fabrication
complexity of coherent receivers and the tight requirements on the local oscillator laser,
restricted the attraction of this transmission scheme. Moreover, erbium-doped fibre amplifiers
(EDFA) [41,82] have been developed, which also provide these advantages.
The alternative is found in the concept of Wavelength Division Multiplexed (WDM) direct
detection, as shown schematically in its simplest form in figure 1.1. At the transmitter side a
wavelength multiplexer is used to combine the signals from lasers operating at different
wavelengths. The combined signals are launched into the fibre and at the receiver side a
wavelength demultiplexer is used to separate them again and to couple them to photodiodes.
The diagram depicted in figure 1.1 is a typical example of a simple point-to-point link. But the
most important advantage of WDM - apart from the huge transmission capacity (recently the
1 Tb/s barrier has been broken [97]) - is that it allows for novel network architectures which
offer much more flexibility than the current networks [23,24].
λ mux λ demux
fibre
transmitters receivers
Figure 1.1 Schematic diagram of a WDM link.
In present networks all switching functions are performed in the electrical domain, for which
opto-electronic conversion is required at each switch. This conversion can be avoided by
switching in the optical domain, based on wavelength, using wavelength routers. In this way a

1.2 Recent developments 3
passive transparent network can be created, of which an example is shown in figure 1.2. One
user can send data to the desired user(s) by selecting the wavelength to transmit on.
λ 1 ,λ 2
R
Wavelength routers, first reported by Dragone [44,45], provide an important additional
function as compared to multiplexers and demultiplexers. Figure 1.3 illustrates their function.
Wavelength routers have N input and N output ports. Each of the N input ports can carry N
different wavelengths. The N wavelengths carried by input channel 1 are distributed among
output channels 1 to N, in such a way that output channel 1 carries wavelength 1 and channel N
wavelength N. The N wavelengths carried by input 2 are distributed in the same way, but
cyclically rotated by one channel in such a way that wavelengths 2-4 are coupled to ports 1-3
and wavelength 1 to port 4. In this way each output channel receives N different wavelengths,
one from each input channel. To realise such an interconnectivity scheme in a strictly nonblocking
way using a single wavelength, a huge number of switches would be required. Using
a wavelength router this function can be achieved using only one single component.
For a passive network, one single wavelength is entirely dedicated over the whole network to a
point-to-point link between two users. More effective usage of wavelengths is offered by wavelength-selective
switches, or add-drop multiplexers (ADMs). Although a number
configurations are possible, they basically consist of a wavelength demultiplexer (not
necessarily a wavelength router) and switches, of which the number equals the number of
λ 1
λ 2 ,λ 3
Figure 1.2 Schematic diagram of a passive transparent network (R = router).
a 1 , a 2 , a 3 , a 4
b 1 , b 2 , b 3 , b 4
c 1 , c 2 , c 3 , c 4
d 1 , d 2 , d 3 , d 4
Wavelength
Router
a 1 , b 2 , c 3 , d 4
a 2 , b 3 , c 4 , d 1
a 3 , b 4 , c 1 , d 2
a 4 , b 1 , c 2 , d 3
transmission
(a) (b)
λ 3
a b c d a b c d
wavelength
Figure 1.3 Schematic diagram illustrating the operation of a wavelength router:
interconnectivity scheme (a), and wavelength response (b). It is noted that a i
denotes the signal at input port a with wavelength i.

4 1. Introduction: WDM in optical communication networks
wavelength channels. In figure 1.4 the configuration as produced by Tachikawa et al.
[144,146,149] is shown. The demultiplexer has one main input port and one main output port,
and the other outputs are routed back to the inputs of the demultiplexer using switches. By
feeding these switches, signals can either be tapped from the line (and simultaneously new
ones can be put on the line), or be passed through.
main input
mux/
demux
switch
switch
switch
switch
main output
λ4 . . λ1 λ1 . . λ4 drop ports add ports
Figure 1.4 Schematic diagram of an ADM.
Whereas the ADM acts as an access node to the network, there is also the need for connecting
local networks to other, possibly remote, networks. This can be achieved using an optical cross
connect (OCC). In a multi-wavelength network using N wavelengths, a local network can
transparently be connected to N-1 remote networks through such a cross connect. A schematic
diagram is shown in figure 1.5, in which the thick and thin lines denote the multiwavelength
and single-wavelength channels respectively. The OCC consists of N demultiplexers, N
multiplexers and N switching matrices of dimension N × N . In this example the OCC is also
equipped with integrated optical amplifiers to firstly compensate for the insertion losses of the
devices on chip, and to secondly balance the powers in the different wavelength channels.
demux
demux
demux
demux
optical
amplifiers
switching
matrix
Figure 1.5 Schematic diagram of an optical cross connect.
mux
mux
mux
mux

1.3 Phased-array demultiplexers 5
The future WDM communication network will consist of OCCs, ADMs and wavelength
routers, as depicted schematically in figure 1.6. By deploying more ADMs, the network can
handle an increasing number of users, which is an important advantage of such a network.
Another advantage is the enhanced reliability: a defect node can be “bypassed” by changing
the connectivity scheme. However, this strategy fails if the node serves a large number of users,
in which case other strategies are required such as e.g. dual homing on two nodes.
A
A
1.3 Phased-array demultiplexers
O
O
Figure 1.6 WDM communication network (A = ADM, R = Router, O = OCC).
It is obvious that wavelength (de)multiplexers are key components in WDM systems. Many
principles have been introduced and reported for the manufacture of multiplexers and
demultiplexers. Commercially available components are based on fibre-optic or micro-optic
techniques [106,107] and, recently, also fully integrated devices. Since the early nineties,
research on integrated-optic (de)multiplexers has increasingly been focused on grating-based
and phased-array (PHASAR) based devices (also called Arrayed-Waveguide Gratings) [165].
Both are imaging devices, i.e. they image the field of an input waveguide onto an array of
output waveguides in a dispersive way. In grating-based devices, a vertically etched reflection
grating provides the focusing and dispersive properties required for demultiplexing. In phasedarray
based devices these properties are provided by an array of waveguides, the length of
which has been carefully chosen to obtain the required imaging and dispersive properties. As
phased-array based devices are manufactured according to conventional waveguide technology
and do not require the vertical etching step needed in grating-based devices, they appear to be
more robust and production tolerant.
Phased-array demultiplexers were introduced in 1988 by Smit [116]. The first devices
operating at short wavelengths were reported by Vellekoop and Smit [161-163,117]. Takahashi
et al. reported the first devices operating in the long wavelength window [151,152]. Dragone
extended the phased-array concept from 1 × N to N ×
N devices - the so-called wavelength
routers [44,45] which play an important role in multiwavelength network applications. The
broad acceptance of the phased-array concept can be seen from the bargraph in figure 1.7. In
this graph the development of the phased-array demultiplexer is depicted by the number of
publications on single devices (including PHASAR-based system experiments, which started
A
O
A
A

6 1. Introduction: WDM in optical communication networks
in 1993 [144], leading to a more exponential growth of the number of publications). A
complete overview of realised phased-array demultiplexers can be found in Appendix A.
1
’89
1
’90
2
3
’91 ’92 ’93
’94 ’95
Figure 1.7 Development of phased-array demultiplexers, measured by the
number of publications on single devices.
Devices reported so far can be divided into two main classes: silica-based devices and InPbased
devices. Most of the silica-based devices use fibre-matched (low-contrast) waveguide
structures, which combine low propagation loss with a high fibre-coupling efficiency. More
recently silicon-based polymer devices [56,131] and lithiumniobate devices [95,96] were
reported which also used fibre-matched waveguide structures.
Silica-based devices have relatively large dimensions due to the low index contrast and the
corresponding large bending radii of the fibre-matched waveguides. This makes them less
suitable for integration of large numbers of components on a single chip. Furthermore, silica
has a limited potential for integration of active functions due to its passive character. The
feasibility of integration with switches, however, was demonstrated by Okamoto who reported
successful integration of thermo-optical switches with phased arrays in an integrated optical
add-drop multiplexer [89,90].
The first InP-based PHASAR-demultiplexer was reported in 1992 by Zirngibl et al. [176]. InPbased
devices have a better potential for integration of active functions. They exhibit
considerably higher propagation and fibre-coupling losses, the latter however due to the small
size of the waveguide cross section. Despite the higher propagation losses, the total on-chip
device loss can be kept within acceptable limits due to the small component size which is
possible because of the high index contrast and which also allows for integrating larger
numbers of components onto a chip. InP-based demultiplexers cannot compete with silica-,
lithiumniobate-, or polymer-based devices with respect to fibre coupling loss, which makes
them less suitable for production of low complexity circuits. Their main advantage is their
potential for monolithic integration of active components such as switches [167], detectors
[4,5,9,138-140,182], optical amplifiers and modulators [68-70,178-181,184], and their
potential to integrate large numbers of components onto a single chip.
In figure 1.8 the possible future development of opto-electronic chips for WDM applications is
depicted. At the moment micro-optic, fibre-optic or hybrid solutions are available, which in the
near future however will be complemented by integrated solutions. The drive for integration is
found in the reduction of packaging costs, mainly determined by the number of
interconnections, and in an increased reliability. Integrated devices are still in research stage
but promise to provide the higher feasability which will be required in future
telecommunication networks. The first silicon-based devices were recently introduced to the
market. These fibre-matched waveguide structures (silica, lithiumniobate and polymer) have
low coupling losses, but on the other hand also low index contrast, which limits the integration
4
7
17
17
’96

1.4 About this thesis 7
Integration scale
100
MSI
10
SSI
scale. These materials therefore will only reach the small-scale integration stage (SSI), or the
lower part of the medium-scale integration stage (MSI). Due to the large index contrast, InPbased
devices can be very compact, and therefore will be able to reach the MSI stage. The high
index contrast too is a cause for the high fibre-chip coupling losses, and therefore attention is
now focused on improving the coupling efficiency.
1.4 About this thesis
1
micro-optic
fibre-optic
hybrid
1995 2000 2005 2010
Year
As phased-array demultiplexers are key components in future WDM networks, a detailed
description of the operation and design of these components is described in Chapter 2, which
has been published in the Journal of Selected Topics in Quantum Electronics [118]. The design
strategy as described by Smit [117] has been followed, but as nowadays parameters such as
channel spacing are given in terms of frequency rather than wavelength, the equations
describing the PHASAR properties have been derived in the frequency domain. Also, elaborate
attention has been paid to a number of different design requirements, such as polarisation independence,
flattened wavelength response, low-loss operation, etc. Furthermore, an overview of
the most important applications is given.
The major part of this thesis is focused on methods for making PHASARs polarisation
independent. The state of polarisation of the transmitted light after propagation through a fibre
over a long distance is unknown and varies in time. It is therefore important that the transfer of
the demultiplexer to which the fibre is connected is insensitive to such variations. One way of
making a PHASAR polarisation independent is by inserting polarisation converters in the
middle of the array. It has been found that very short waveguide bends have polarisationconverting
properties, which can be applied in compact, low-loss polarisation converters. An
extensive discussion of the polarisation conversion phenomenon in waveguide bends is
presented in Chapter 3, using different computational methods. Also experimental results are
discussed, part of which have been presented elsewhere [34,35], and which have led to a patent
application [32].
There are several methods of making demultiplexers polarisation independent and the most
obvious one is to make use of polarisation independent waveguides. This method is discussed
in Chapter 4. The use of non-birefringent waveguides has been initiated by Amersfoort [7], and
has been extended with an elaborate analysis of the tolerances, and a discussion of
experimental results, part of which have been published [164]. These experiments clearly
demonstrate that polarisation independent behaviour can be achieved over a large wavelength
InP
silica lithiumniobate polymer
Figure 1.8 Future development of opto-electronic ICs for WDM.

8 1. Introduction: WDM in optical communication networks
range. This is an important advantage of these waveguides, together with low fibre-chip
coupling losses and compact device dimensions. Furthermore, a method for loss reduction has
been proposed and demonstrated [33], and the occurence of so-called “ghost” images has been
investigated [37]. Finally, a packaged device integrated with photodetectors is described.
Instead of making the waveguides polarisation independent, PHASAR demultiplexers can also
be made polarisation independent by adaptions of the device itself. An example of this is the
compensation of the polarisation dispersion of the array waveguides, as proposed by Takahashi
et al. [154]. This method is discussed extensively in Chapter 5, including a tolerance analysis,
and has been applied to our waveguide structure, of which experimental results are detailed.
Although this method is sensitive to width and layer thickness variations, the manufacture is
relatively simple, as a selective wet-chemical etchant can be used for the polarisation
dispersion compensating section in the PHASAR. Additionally, two methods which use
polarisation conversion and splitting respectively are discussed with emphasis on cross talk tolerance.
The order-matching method is discussed briefly, as a more comprehensive account of
this method including experiments is given by Spiekman [134].
Novel components based on Multimode Interference (MMI) are presented in Chapter 6. A
novel type of phased-array demultiplexer is one in which the free propagation regions are
replaced with multimode interference (MMI) couplers. Firstly in this chapter, the design of
such MMI-based demultiplexers is discussed, together with a tolerance analysis. Experimental
results are detailed, part of which have been published elsewhere [31]. Secondly a novel type
of spatial mode filter based on a single MMI coupler is discussed. The discussion includes a
tolerance analysis which reveals the advantages of this device - compact size, large optical
bandwidth, and tolerant to width variations. The experimental results, which have already been
presented [36], demonstrate the low-loss operation combined with a high first-order mode
rejection. Finally, the interference patterns in a MMI coupler with a high erbium concentration
are made visible by imaging the green light generated by upconversion of erbium atoms at high
pumping power levels. In this way, the field intensity of the infrared light can be imaged with a
resolution below the theoretical diffraction limit. This is demonstrated with a MMI-coupler
manufactured in an aluminum oxide ridge waveguide structure implanted with erbium. This
work has been carried out as a common project with the FOM-Institute for Atomic and
Molecular Physics, and has been presented earlier [30,59].
In Chapter 7 the results presented in this thesis are shortly highlighted and discussed.

Chapter 2
PHASAR demultiplexers: a review
Wavelength multiplexers, demultiplexers and routers based on optical phased arrays play a key
role in multiwavelength telecommunication links and networks. In this chapter a detailed
description of phased-array operation and design is presented and an overview is given of the
most important applications. Part of this work has also been published in the Journal of
Selected Topics in Quantum Electronics [118].
2.1 Basic operation
Figure 2.1a shows the schematic layout of a PHASAR-demultiplexer. The operation is
understood as follows. When the beam propagating through the transmitter waveguide enters
the Free Propagation Region (FPR), it is no longer laterally confined and becomes divergent.
On arriving at the input aperture, the beam is coupled into the waveguide array and propagates
through the individual array waveguides towards the output aperture. The length of the array
waveguides is chosen in such a way that the optical path length difference between adjacent
waveguides equals an integer multiple of the central wavelength of the demultiplexer. For this
wavelength the fields in the individual waveguides will arrive at the output aperture with equal
phase (apart from an integer multiple of 2π), and the field distribution at the input aperture will
be reproduced at the output aperture. The divergent beam at the input aperture is thus
transformed into a convergent one with equal amplitude and phase distribution, and an image
of the input field at the object plane will be formed at the centre of the image plane. The
dispersion of the PHASAR is due to the linearly increasing length of the array waveguides,
which will cause the phase change induced by a change in the wavelength to vary linearly
along the output aperture. As a consequence, the outgoing beam will be tilted and the focal
point will shift along the image plane. By placing receiver waveguides at proper positions
along the image plane, spatial separation of the different wavelength channels is obtained.
In the following subsections the most important properties of a PHASAR will be analysed.

10 2. PHASAR demultiplexers: a review
2.1.1 Focusing
array
waveguides
Δα
input
aperture
object
plane
transmitter
waveguide
FPR
R a
d a
output
aperture
(a)
output aperture
Focusing is obtained by choosing the length difference ΔL between adjacent array waveguides
equal to an integer number of wavelengths, measured inside the array waveguides:
whereby m is the order of the phased array, λ c (f c ) is the central wavelength (frequency) in
vacuo and N eff is the effective index of the waveguide mode. With this choice the array acts as
d r
image plane
(b)
image
plane
R a /2
Figure 2.1 a) Layout of the PHASAR demultiplexer
b) Geometry of the receiver side.
θ
FPR
focal line
s (measured along
the focal line)
receiver
waveguides
ΔL m λc mc
= ⋅ -------- = --------------
(2.1)
N eff N eff f c

2.1 Basic operation 11
a lens with image and object planes at a distance R a of the array apertures.
The input and output apertures of the phased array are typical examples of Rowland-type
mountings [81]. The focal line of such a mounting, which defines the image plane, follows a
circle with radius R a /2 as shown in figure 1b. Transmitter and receiver waveguides should be
positioned on this line.
α/αi starting angle/starting angle of array waveguide i
αr reference angle
β/βFPR propagation constant in waveguide/FPR
c speed of light
D dispersion
da pitch of the array waveguides in the array aperture
dr pitch of the receiver waveguides in the image plane
Δα divergence angle of the array waveguides in the array aperture
Δfch channel spacing
ΔfFSR free spectral range
Δfpol TE-TM shift
ΔfL L-dB bandwidth
ΔΦ phase shift between adjacent array waveguides
ΔL path length difference between adjacent array waveguides
Hi height of array waveguide i
k0 wave number in vacuo
L distance between the focal points
Lo central channel insertion loss
Lp propagation loss in the array
Lu non-uniformity
l(α) path length of array waveguide with respect to α
li path length of array waveguide i
λc /fc central (design) wavelength/frequency
m/m' order of the array/beam
N/Na number of channels/array waveguides
Neff /NFPR effective index in waveguide/FPR
Ng group index
NTE /NTM effective index for TE/TM polarisation
N1 /N2 transverse effective index in the ridge/in the region next to the ridge
Ra length of FPR
Ri radius of curvature of array waveguide i
Rr radius of curvature of reference array waveguide
Si Sr s
straigth section length (including Ra ) of array waveguide i
straigth section length (including Rr ) of reference array waveguide
position along image plane
θ dispersion angle
θa array aperture half angle
θο angular width of the far field
V lateral V-parameter (normalised film parameter)
w/we waveguide width/effective width
Table 2.1 List of symbols used in this chapter.

12 2. PHASAR demultiplexers: a review
2.1.2 Dispersion and Free Spectral Range
In figure 2.1b it can be seen that the dispersion angle θ resulting from a phase difference ΔΦ
between adjacent waveguides follows as:
whereby ΔΦ = βΔL , β and βFPR are the propagation constants in the array waveguide and
the Free Propagation Region (FPR) respectively, and da is the lateral spacing (on centre lines)
of the waveguides in the array aperture.
The dispersion D of the array is described as the lateral displacement ds of the focal spot along
the image plane per unit frequency change. From figure 2.1b it follows (after some
manipulation, see Appendix B) that:
whereby f c = c ⁄ λc is the central frequency, NFPR is the (slab) mode index in the Free
Propagation Region, ΔL is the length increment of the array waveguides as described before,
Δα = da ⁄ Ra is the divergence angle between the array waveguides in the fan-in and fan-out
sections and Ng is the group index of the waveguide mode:
It can be seen that R a does not occur in the right hand expression in equation 2.3 so that fillingin
of the space between the array waveguides near the apertures due to a finite lithographical
resolution does not affect the dispersive properties of the demultiplexer.
From equation 2.2 it can be seen that the response of the phased array is periodical. After each
change of 2π in ΔΦ, the field will be imaged at the same position. The period in the frequency
domain as shown in figure 2.2b is called the Free Spectral Range (FSR). It is found as the
frequency shift for which the phase shift ΔΦ equals 2π:
from which we derive:
ΔΦ m2π
θ arcsin – ( ) β ⎛
⁄ FPR
--------------------------------------------- ⎞ ΔΦ – m2π
=
≈ -------------------------
⎝ d ⎠
a
βFPRd a
D
with m' = ( N g ⁄ N eff)
⋅ m.
The rightmost identity, which is well known from grating theory, follows by substituting
N gΔL =
m'c ⁄ f c (see equation 2.1). It is noted that for phased arrays, different from gratings,
the Free Spectral Range is not related to the order m of the array, but to a modified order
number m', which can be interpreted as the order of the beam.
As the exact relation between θ and ΔΦ is non-linear (see equation 2.2), equation 2.6 is only
approximate and the FSR will be slightly dependent on the input and output ports. An accurate
analysis is given by Takahashi et al. [155].
(2.2)
ds dθ 1
----- R
d f a ⋅ ----- ---d
f
N g
----------- ΔL
= = = ⋅ ⋅ -------
(2.3)
Δα
f c
N g N eff f dN eff
= + -----------d
f
N FPR
2πΔ f FSR
---------------------N
c gΔL = 2π
Δf FSR
f c
(2.4)
(2.5)
c
= ------------- = ----
(2.6)
N gΔL m'

2.1 Basic operation 13
2.1.3 Insertion loss and non-uniformity
Figure 2.2a shows the field in the image plane for four different wavelengths. It is the sum field
of the far fields of all individual array waveguides. As the far-field intensity of the individual
waveguides reduces away from the centre of the image plane, as indicated in the figure, the
focal sum field will do the same. If the wavelength is changed, it will move through the image
plane and follow the envelope described by the far-field of the individual array waveguides. If
we approximate the modal field of the array waveguides as a Gaussian beam and neglect the
effects of coupling on the beam shape, we can derive some simple analytical equations for
estimating insertion loss, channel non-uniformity and bandwidth.
Using the Gaussian-beam approximation, the intensity of the far-field is found in:
I( θ)
Ioe 2
=
– θ2 2
⁄ θo whereby θ o is the width of the equivalent Gaussian far field
θ o
λ 1
= ----------- ⋅ ---------------we
2π
N FPR
with we being the effective width of the modal field in the transmitter waveguide (as described
in Appendix C). The non-uniformity Lu is defined as the intensity ratio (in dB) between the
outer and the central channel. Using equation 2.7, the insertion loss of the receiver relative to
the central channel is easily found by substituting the angle θmax ( θmax ≈ smax ⁄ Ra )
corresponding to the outer receiver waveguide:
L u
– θ 2
max
If the FSR is chosen as being equal to N times the channel spacing Δf, as in wavelength routers
(see section 2.3.1), the excess loss Lu of the outer channels will be close to 3 dB for reasons of
power conservation - as for large numbers of channels, receiver waveguide 1 and the virtual
receiver N+1 will experience approximately the same loss with each of them having at least
3 dB excess loss relative to the central channel. For small values of N the situation may be
slightly better. Thus minimising Lu will increase the FSR.
The insertion loss Lo of the central channel is mainly determined by diffraction of light into
undesired orders. The adjacent orders of the main focal spot will carry a fraction
2 2
exp( – 2Δθ FSR ⁄ θo) , with:
(2.7)
(2.8)
whereby D is the dispersion (equation 2.3). If we neglect the power coupled into other orders
the total loss L o can be estimated from:
L o
whereby it has been assumed that exp( – 2Δθ
FSR ⁄ θo) «
1 . The factor 4 is due to the fact that
2
θo – 10 e 2 ⎛ ⁄ ⎞ 2
= ⋅ log
≈ 8.7 ⋅ θ
⎝ ⎠ max ⁄
Δθ FSR
ΔsFSR -------------
Ra 2
θo (2.9)
D
= = (2.10)
2
2
θo -----Δf
R FSR
a
2 2
da
– 2Δθ
FSR ⁄
– 10 ⋅ log⎛1
– 4 ⋅ e ⎞ + L
⎝ ⎠ p 17 e 4π – we ⁄
≈ ≈ ⋅ + L (2.11)
p
2
2

14 2. PHASAR demultiplexers: a review
power is lost in two orders and that equal losses occur (because of reciprocity) at both the input
and the output side of the array. The term L p denotes the total propagation loss in the array and
both FPRs due to absorption and scattering. From this equation it can be seen that for low-loss
devices the waveguide spacing d a in the array apertures should be minimal. For semiconductorbased
devices, the best total loss reported is in the order of 2 dB [141]. It should be noted that
equation 2.11 is a worst-case guess - coupling between the array waveguides will reduce the
loss as discussed in section 2.2.6.
intensity
100%
order m-1
λ4 λ1 λ4 λ1 image plane
λ4 λ1 channel 4 1 4 1
frequency
4 1
(a) (b)
Figure 2.2 Central insertion loss, non-uniformity and free spectral range (FSR).
The 100% line denotes the peak intensity of the input field.
2.1.4 Bandwidth
central insertion loss L o
order m order m-1 order m order m+1
non-uniformity L u
far field
envelope
order m+1
If the wavelength is changed, the focal field of the PHASAR moves along the receiver
waveguides. The frequency response of the different channels follows from the overlap of this
field with the modal fields of the receiver waveguides. If we assume that the focal field is a
good replica of the modal field at the input, and that the input and output waveguides are
identical, the (logarithmic) transmission T(Δf) around the channel maximum T(fc ) follows as
the overlap of the modal field with itself, displaced over a distance Δs( Δf ) = DΔf :
whereby U(s) is the normalised modal field, D is the dispersion as defined in equation 2.3 and
T(f c ) is the transmission in dB at the channel maximum. For small values of Δs (smaller than
the effective mode width w e ) the overlap integral can be evaluated analytically by
+∞
FSR
T ( Δf ) = T ( f c)
+ 20log U( s)U
( s– DΔf
)ds
∫
-∞
(2.12)

2.1 Basic operation 15
approximating the modal fields as Gaussian fields:
⎛ ⎛ ⎞⎞
T ( Δf ) – T ( f c)
20 ⋅ log⎜
exp⎜–
------------ ⎟⎟
– 6.8 ⎛DΔf ---------- ⎞
2
⎝ ⎝ ⎠⎠
⎝ w ⎠
e
2
=
≈ ⋅
The L-dB bandwidth Δf L is twice the value Δf for which T ( Δf ) – T ( f c)
= L dB:
Δf L
The latter identity follows by substitution of D = dr ⁄ Δ f ch . If we substitute we ⁄ dr ≈ 0.4 as a
representative value (cross talk due to receiver waveguide spacing

16 2. PHASAR demultiplexers: a review
Truncation
Another source of cross talk results from truncation of the field due to the finite width of the
array aperture. This causes power to be lost at the input aperture, whilst at the output aperture
the side lobe level of the focal field will increase. For a proper PHASAR design, the array
aperture angle should be chosen in such a way that the corresponding cross talk is sufficiently
low. Figure 2.3b shows the transmitted power (solid line) and the cross talk versus the array
aperture half angle θ a , defined as:
θ a
( N a – 1)d
a
= -------------------------
normalised to the Gaussian width θ o as defined in equation 2.8, for different values of the
relative receiver waveguide spacing d r /w. As the estimate of figure 2.3a is rather pessimistic, it
is best to use the envelope depicted by the boldly dashed line. The values shown are calculated
for input and output waveguides with V = 3. The dependence on the V-parameter is small. The
envelope of the cross talk curves (boldly dashed line) can be used for estimating the maximum
cross talk level. It is seen that for θ a >2θ o the truncation cross talk is less than -35 dB.
Cross Crosstalk talk [dB]
0
-10
-20
-30
-40
-50
-60
V = 2
V = 3
V = 5
Crosstalk Cross talk [dB]
Mode conversion
If the array waveguides are not strictly single mode, a first order mode excited at the junctions
between straight and curved waveguides can propagate coherently through the array and cause
“ghost” images. Because of the difference in the propagation constant between the
fundamental and the first order mode, these images will occur at different locations and the
“ghost image” may couple to an undesired receiver waveguide thereby degrading the cross talk
performance. Mode conversion can be kept small by optimising the offset at the junctions for
minimal first-order mode excitation.
2R a
(a) (b)
(2.16)
-60
-10
1 2
d r r/w /w
3 4
0 1 2
θ a a /θ /θ0o 3 4
Figure 2.3 a) Cross talk resulting from the coupling between two adjacent
receiver waveguides for different values of the lateral V-parameter of the receiver
waveguides.
b) Transmitted power (solid line) and cross talk as a function of the
relative array aperture θ a /θ o , for different values of the relative receiver
waveguide spacing d r /w (d r /w = 2.5, 3.0, 3.5). The values shown are calculated for
input and output waveguides with V = 3. The boldly dashed line indicates the
envelope of the cross talk curves (maximum cross talk level).
0
-10
-20
-30
-40
-50
0
-2
-4
-6
-8
Transmitted power [dB]

2.1 Basic operation 17
Coupling within the array
Cross talk can also be incurred by phase distortion due to coupling in the input and output
sections in the arrays. It might be expected that this type of coupling will not greatly affect the
focusing and dispersive properties of the array on similar grounds as to those mentioned in
equations 2.3 and 2.4. The filling in of the gaps near the array apertures can be considered as
introducing an extremely strong coupling into the input and output region, which obviously
does not degrade the PHASAR performance [117]. Day et al. [38], however, observe a
degradation of the cross talk performance using BPM-simulation.
Phase transfer errors
A fifth source of cross talk results from phase transfer errors in the phased array due to
imperfections during the production process. The optical path length of the array guides is in
the order of several thousands of wavelengths. Deviations in the propagation constant may lead
to considerable errors in the phase transfer, and, consequently, to an increase of the cross talk
level. Takada et al. [150] and Yamada et al. [170,171] have shown that improved cross talk is
feasible by correcting the phase errors (e.g. by using thin-film heaters on top of the array
waveguides). Phase errors may be caused by small deviations in the effective index due to local
variations in composition, film thickness or waveguide width, or by inhomogeneous filling in
of the gap near the apertures of the phased array. Also more systematic errors (e.g. due to discretisation
in the mask pattern generation) may contribute to the cross talk [38].
Background radiation
As a last possible source of cross talk we mention background radiation due to light scattered
out of the waveguides at junctions or rough waveguide edges. This is especially important in
waveguide structures where the light is also guided besides the waveguides e.g. in shallow
etched ridge guides or in waveguide structures on a heavily doped substrate where the undoped
buffer layer may also act as a waveguide.
Cross talk in practical devices is not limited by design but by imperfections during the
production process. Typical cross talk values reported for PHASAR-demultiplexers are in the
order of -25 dB for InP-based devices to even less than -30 dB for silica-based devices. Recent
experiments in our laboratory, however, show cross talk levels less than -30 dB for good
semiconductor devices as well, which is outlined in Appendix D. Improvement on these
figures is mainly a matter of improving manufacturing technology.
2.1.6 Polarisation dependence
Phased arrays are polarisation independent if the array waveguides are polarisation
independent, i.e. the propagation constants for the fundamental TE- and TM-mode are equal.
Waveguide birefringence, i.e. a difference in propagation constants, will result in a shift Δf pol
of the spectral responses in respect of each other, which is called the polarisation dispersion. It
can be calculated when we consider the effective wavelengths in the waveguide. Light with
different wavelengths in vacuo will be coupled into the same receiver waveguide, when the
effective wavelengths λ TE and λ TM of the fundamental modes in the waveguide are equal:
λTM( f )
c
f ⋅ N TM f
c
--------------------------- λ
( ) TE( f – Δ f pol)
( f – Δ f pol)
⋅ N
TE f Δ f = = = --------------------------------------------------------------------- (2.17)
( – pol)
whereby N TE and N TM are the effective indices for both polarisations.

18 2. PHASAR demultiplexers: a review
By solving Δf pol from equation 2.17 we find:
whereby N g,TE is the group index. For InGaAsP/InP DH waveguide structures, Δf pol is
typically in the order of 4-5 nm. For silica-based and, more generally, for low-contrast
waveguides, it will be much smaller. Also, in waveguides structures which are designed for
polarisation independence, polarisation dependence may occur due to strain induced during the
manufacturing process. A number of methods to reduce polarisation dependence will be
mentioned briefly in section 2.2.4, and will be discussed more comprehensively in Chapter 4.
2.2 Phased-array design
2.2.1 Specification
( N TE – N TM)
Δ f pol ≈ f ⋅ -------------------------------
N g,TE
A PHASAR is specified by the following characteristics:
• Number of channels N.
• Central frequency f c and channel spacing Δf ch .
• L-dB Channel bandwidth Δf L .
• Free Spectral Range Δf FSR .
• Maximal insertion loss L o of the central channel.
• Maximal non-uniformity L u .
• Maximal cross talk level.
• Maximal polarisation dependence.
It is noted that the non-uniformity and the Free Spectral Range can not be chosen
independently from each other (see section 2.3.1)
2.2.2 Demultiplexer design procedure
(2.18)
PHASARs have many degrees of design freedom and many design approaches are possible.
The approach followed at TU Delft for designing multiplexers and demultiplexers is explained
below. It starts with a given waveguide structure (i.e. waveguide width w and lateral Vparameter
fixed). The design parameters of the PHASAR are derived subsequently from the
design specifications. The design procedure of a wavelength router is slightly different (see
section 2.3.1). For the reader’s convenience figure 2.1b is shown here again.
• Receiver waveguide spacing dr . We start with the cross talk specification, which puts a
lower limit on the receiver waveguide spacing dr . As with today’s technology cross talk
levels lower than -30 to -35 dB are difficult to realise, it does not make sense to design the
array for much lower cross talk. To be on the safe side, we take a margin of 5-10 dB and
read from figure 2.3a the ratio dr /w required for -40 dB cross talk level. It is noted that the
cross talk for TE- and TM-polarisation may be different as the lateral index contrast and,
consequently, the lateral V-parameter can differ substantially for the two polarisations.
• FPR length Ra . From the maximum acceptable excess loss for the outer channel (the nonuniformity
Lu ), we determine the maximum acceptable dispersion angle θmax using
equations 2.8 and 2.9. The minimal length Ra,min of the Free Propagation Region then
follows as Ra,min =
smax ⁄ θmax whereby smax is the s-coordinate of the outer receiver
waveguide (see figure 2.1b).

2.2 Phased-array design 19
array
waveguides
Δα
• Length increment ΔL. First we compute the required dispersion of the array from
D = ds ⁄ d f = dr ⁄ Δ f ch (see equation 2.3). The waveguide spacing da in the array
aperture should be chosen as small as possible (a large spacing will lead to high coupling
losses from the FPR to the array and vice versa). With da and Ra fixed, the divergence angle
Δα between the array waveguides is fixed as Δα = da ⁄ Ra (see figure 2.1b) and the length
increment ΔL of the array follows from equation 2.3.
• Aperture width θa . The angular half width θa of the array aperture should be determined
using a graph like figure 2.3b (adapted for the specific waveguide structure used).
• Number of array waveguides Na . The choice of θa fixes the number of array waveguides:
N a = 2θaR a ⁄ da + 1 (see equation 2.16).
This completes the determination of the most important geometrical parameters of the
PHASAR.
2.2.3 Array geometry
R a
d a
output aperture
For the array waveguides a number of different shapes can be applied to realise the length
increment ΔL. Takahashi et al. [152] used the geometry as depicted in figure 2.5a, which is
very simple from a design point of view, with a constant R for all array arms. Smit [117] and
Dragone [44] applied the geometry of figure 2.5b, which contains a minimum number of
waveguide junctions. This is especially important in semiconductor waveguides where
junction losses and mode conversion at junctions can degrade the PHASAR performance.
The freedom in the choice of array shape is bounded by the requirement that the array
waveguides should not come too close to each other. For extremely low dispersion values (e.g.
for duplexing 1.3 and 1.55 μm), the path length difference ΔL between adjacent waveguides
becomes very small and the shapes depicted in figure 2.5 are no longer suitable. Adar et al. [1]
applied S-bend-like arrays in which the dispersion of one curved section is reduced by a
second section with opposite curvature and, consequently, opposite ΔL. Mestric et al. [83,84]
recently also reported a S-bend shaped phased-array 1.31-1.55 μm duplexer with very low
cross talk (

20 2. PHASAR demultiplexers: a review
(a) (b)
Figure 2.5 Phased-array waveguide geometries.
The geometry as shown in figure 2.5b is also used for the design of the phased-array
demultiplexers discussed in this thesis and will be described below. According to this
geometry, an array guide consists of two straight waveguides connected to each other by a
curved waveguide, together forming a non-concentric set.
S i
R a
α i
input
aperture
α i
L
Each array guide is completely defined by the starting angle α i , the radius of curvature R i and
the straight section length S i , which includes the focal length R a for ease of calculation,
according to:
R i+1
R i
output
aperture
Figure 2.6 Geometry of the i-th guide of the phased-array.
S i
R i
L ⁄ 2 – Sicosαi = ---------------------------------sinαi
Lα i
1
-- ⎛l 2 i – ----------- ⎞ 1
⎝ sinα ⎠
i
αicosαi =
⁄ ⎛ – ------------------ ⎞
⎝ sinα
⎠
i
H i
Δα
(2.19)
(2.20)

2.2 Phased-array design 21
and:
αi = α1 + ( i – 1)Δα
whereby l i is the path length of the i-th array guide measured from transmitter to receiver:
li = l1 + ( i – 1)ΔL
In the above equations Δα is the divergence angle of the array waveguides in the array aperture
and ΔL is the path length difference between adjacent array waveguides.
2.2.4 Design for polarisation independence
(2.21)
(2.22)
Several methods can be used for eliminating the polarisation dependence of the response due
to waveguide birefringence. Five different methods will be briefly discussed here and more
comprehensively in Chapter 4.
Nonbirefringent waveguides
The most obvious way to make a PHASAR polarisation independent is by eliminating the
birefringence of the waveguide. This can be done by making the waveguide cross section
square if the index contrast is the same in both the vertical and lateral direction as, for example,
in buried waveguide structures. Bellcore [11,123] recently reported a polarisation independent
device based on a buried InGaAsP/InP waveguide structure with a low-contrast waveguide
core (small InGaAs-fraction). Philips and TU Delft, Bellcore, and Alcatel [9,19,20,21,122,
164] reported several devices based on a raised strip guide using similar material for the
waveguide core. An advantage of the raised strip guide is that, due to the high lateral index
contrast, it allows for very short bending radii and, consequently, for compact design. This
method will be discussed more comprehensively in Chapter 4.
Attempts have been made to compensate the birefringence of conventional “flat” waveguide
structures by applying strained MQW-waveguides. Bi-axial compressive strain, obtained by
decreasing the Ga-fraction, increases the birefringence, whereas bi-axial tensile strain reduces
it. First results of this method show that polarisation dispersion changes in the order of
7-12 nm are possible [166]. A complication of this approach is that the intrinsic birefringence
of MQW-structures is considerably higher than that of quaternary bulk material and requires
very high strains for it to be compensated. This makes the approach sensitive to well-width and
composition control.
The birefringence problem occurs also in silica-based waveguides, where it is due to strain
induced by the different thermal expansion coefficients of silica and silicon. It can be reduced
by using silica substrates instead of silicon substrates [142].
Order matching
The first attempt to make PHASARs polarisation independent was based on matching the FSR
to the polarisation dispersion as shown in figure 2.7 [127,133,162,163,177]. If the FSR is
chosen to be equal to the polarisation dispersion the m-th order beam for TE will overlap with
the TM-polarised beam of order m-1, which makes the response virtually polarisation
independent. From equation 2.6 it can be seen that this is obtained by choosing:
c
ΔL = -------------------
N gΔ f
(2.23)
pol

22 2. PHASAR demultiplexers: a review
TE m-1
TM m
TE m
TM m-1
TM m
TM m-1
wavelength
For this design, the procedure described in section 2.2.2 should be slightly changed. By fixing
the incremental length according to equation 2.23, the divergence angle Δα is fixed through
equation 2.3 and Ra through Ra =
da ⁄ Δα (see figure 2.1b). Ra being fixed in this way, the
non-uniformity Lu can no longer be freely chosen. One disadvantage of this method is that the
total wavelength span available for the WDM channels is limited by the polarisation
dispersion, which is in the order of 4-5 nm for conventional InGaAsP/InP DH structures.
Another disadvantage is that the exact value of the polarisation dispersion is very sensitive to
variations in layer composition and thickness, which makes it difficult to obtain a good match.
Half-wave plate
A very elegant method is the insertion of a λ/2-plate in the middle of the phased array. Light
entering the array in TE-polarised state will be converted by the λ/2-plate and will travel
through the second half of the array in TM-polarised state, and TM-polarised light will
similarly traverse half the array in TE-state. As a consequence TE- and TM-polarised input
signals will experience the same phase transfer regardless of the birefringence properties of the
waveguides applied. This method was introduced by Takahashi et al. [153] and using
polyimide half-wave plates, it has been successfully applied to silica-based [60,91] and
LiNbO 3 -based devices [95,96]. As the polyimide half-wave plates have a thickness of more
than 10 μm, they are only applicable to waveguide structures with a small NA which can
bridge this distance with small diffraction losses. With semiconductor waveguides, the method
is not practical due to the large NA of these waveguides. It could be applied successfully if a
compact and fabrication tolerant integrated polarisation converter could be developed.
Dispersion compensation
For semiconductor-based PHASARs, a broadband solution for the polarisation dependence
problem is found in compensation of the polarisation dispersion by inserting a waveguide
section with a different birefringence in the phased array. This method was suggested for
FSR
TE m
polarisation dispersion
TE m-1
Figure 2.7 Schematic diagram of the different diffraction orders at the receiver
side for both states of polarisation: polarisation dispersion. The diagram applies
to the demultiplexer’s state without order matching, because the orders TE m and
TM m-1 do not overlap.

2.2 Phased-array design 23
silica-based waveguides by Takahashi et al. [154] and successfully applied to InP-based
devices by Zirngibl et al. [183]. A more comprehensive account of this method can be found in
Chapter 4.
Polarisation splitter
Another method for obtaining polarisation independence is by applying a polarisation splitter
at the input, as shown in figure 2.8. Due to the polarisation dispersion, the position of the focal
spot in the image plane for TE polarisation is shifted relative to the TM-polarised one. If the
distance between the TE and the TM-polarised receiver waveguide in the object plane is
chosen equal to the polarisation dispersion in the image plane, the TE and TM-polarised
signals will focus on the same position and the response will become polarisation independent
over a broad wavelength range. This method does not apply to N × N devices.
TE-TM
splitter
TM
Figure 2.8 Application of a polarisation splitter at the input.
TE
2.2.5 Design for flattened response
TE+TM
In many applications a flattened passband is important in order to relax the requirements on
wavelength control. Three methods to achieve this goal will be discussed.
Multimode receiver waveguides
The simplest method is the use of broad (multimode) waveguides at the receiver side
[6,127,129,138,139]. If the focal spot moves along these broad receiver waveguides, almost
100% of the light will be coupled into the receiver waveguide over a considerable part of the
receiver waveguide aperture, thereby causing a flat region in the frequency response as shown
in figure 2.9a. In this way the 1-dB bandwidth can easily be increased from 31% of the channel
spacing, as shown in section 2.1.4 for a non-flattened PHASAR, to over 65%.
Due to the multimode character of the receiver waveguides, this method can only be applied at
the receiver side of a WDM-link, where the multimode waveguides can be coupled to a
detector without additional signal loss.

24 2. PHASAR demultiplexers: a review
Transmitted power [dB]
0
-2
-4
-6
-8
-10
-0.6 -0.4 -0.2 0.0
Δf/Δfch 0.2 0.4 0.6
MMI-flattening
A flattened response with single-mode outputs can be obtained by applying a short Multimode
Interference (MMI) power splitter at the end of the transmitter waveguide [10,124,125]. This
device converts the single waveguide mode at the input end of the coupler into a double image.
The resulting output field pattern has a “camel-like” shape and the depth of the central
depression can be controlled with the MMI width. If the image of this “camel-shaped” field
moves along the single mode receiver waveguides, the response will have a flat region as
shown in figure 2.9b. This method of flattening introduces insertion loss due to the mismatch
between the “camel-shaped” focal field and the receiver waveguide mode.
A similar effect can be obtained by applying a Y-junction and bringing the two output branches
close together in the transmitter aperture. This method, however, is less compact and less
robust.
Shaping the phase transfer
As the field in the image plane is the Fourier transform of the field at the output aperture, a field
which is more or less rectangular can be realised if the field at the output aperture has a sin(x)/
x distribution (x measured along the aperture). Such a sinc distribution can be approximated in
a discrete manner by multiplying the field at the array aperture with a function with alternating
sign in such a way that the Gaussian-like field is converted into a sin(x)/x-like field with
positive and negative side lobes. The multiplication can be realised by inserting an additional
half wavelength into the array waveguides terminating in the negative side lobe regions, or by
increasing the optical length using thermo-optic or photo-elastic effects [87].
2.2.6 Design for low loss
(a) (b)
-10
-0.6 -0.4 -0.2 0.0
Δf/Δfch 0.2 0.4 0.6
Figure 2.9 Flattening of the wavelength response by using multimode receiver
waveguides (a), and by applying an MMI-powersplitter at the transmitter side (b).
The dashed lines indicate the response without flattening.
For properly designed PHASARs realised with low-loss waveguides, the total loss is
dominated by the loss occurring at the junctions between the array and the Free Propagation
Region (FPR). Low losses can be obtained if the transition from the array to the FPR is
adiabatical, i.e. if the gap between the waveguides reduces linearly to zero. Due to the finite
Transmitted power [dB]
0
-2
-4
-6
-8

2.2 Phased-array design 25
resolution of the lithographical process, the gap between the waveguides, however, will stop
abruptly when the waveguides come too close together. At this discontinuity, the field coming
out of the array will show a modulation which is dependent on the width of the gap between
the array waveguides and on the confinement of the field in the guides. Figure 2.10 shows the
field for a large and a smaller gap. Due to the ripple in the field pattern, a considerable fraction
of the power will diffract into adjacent orders and be lost. On reciprocity grounds, an equal loss
will occur at the input aperture.
To reduce this loss, the ripple of the output field should be reduced. This can be obtained by
reducing the gap width (which requires better lithography) or by reducing the confinement of
the waveguides. A disadvantage of the latter approach is that lowering the confinement
increases the minimal bending radius and, consequently, increases the device size. Low
confinement can be combined with small bending radii by applying a local contrast reduction
near the array apertures using a double-etch process [33].
intensity
array aperture
2.2.7 Device size
intensity
array aperture
(a) (b)
Figure 2.10 Fields at the input (dashed) and the output aperture (solid) of the
phased array for a) a waveguide structure with strong confinement, and b) a
structure with moderate confinement. For efficient coupling to the receiver
waveguides, the output field should follow the dashed lines.
The relative dispersion D of the array is defined as the displacement ds of the focal spot in the
image plane with respect to the relative frequency variation
have the following value:
( ), and should
˜
δf δf = Δ f ch ⁄ f c
D ˜
d r
f
----- 1 -------δf
dN ⎛ eff
+ ⋅ ------------ ⎞
⎝ d f ⎠
1 –
= ⋅
(2.24)
whereby we have assumed that N eff ⁄ N FPR ≈ 1,
which is valid for most waveguide structures.
The relative dispersion therefore equals the derivative dl ⁄ dα of the array guide length with
respect to the starting angle α (see equation 2.3 and 2.22, and figure 2.6), resulting in the array
guide length to be written as:
The value l o is fixed by choosing a straight section length S r and a radius of curvature R r at an
arbitrary reference angle α r :
N eff
l( α)
lo αD˜ = +
(2.25)
lo 2Sr αrRr αrD˜ = + –
(2.26)

26 2. PHASAR demultiplexers: a review
This choice also determines the distance L between the focal points of the phased-array:
resulting in three degrees of freedom to be used for design optimisation.
Preferably, a phased-array design is made on the basis of graphs of R(α), S(α) and the guide
height H(α) over a range of 0 to 180 degrees for different combinations of S r and R r . R(α) and
S(α) follow directly from equations 2.19 and 2.20 by replacing α i with α, and H(α) is defined
as:
In figure 2.11 a design example is shown using representative values. It should be noted that
the phased array can only be realised if the following requirements are satisfied:
•
S( α)
> Ra,min • R( α)
> Rmin dH
• -------Δα > w ⋅ F with 2 < F < 3
dα
L = 2( Srcosαr + Rrsinαr) H( α)
= S( α)sinα
+ R( α)
( 1 – cosα)
(2.27)
(2.28)
The last requirement is imposed in order to avoid the gap between the array guides becoming
too small. The interval over which these requirements are satisfied must at least equal the array
aperture angle θa . In the presented example, a value of approximately 30 degrees is found for
the aperture angle θa (θa /θo = 4). In this case the required array aperture angle is larger than the
available interval, and a phased-array demultiplexer can be realised. If this is not the case,
either different combinations of Sr , Rr and αr have to be tried, or Ra has to be reduced at the
expense of a higher insertion loss for the outermost receiver waveguides ( Ra = smax ⁄ θmax combined with equation 2.9).
Size [μm]
2000
1500
1000
500
S
R
H
R min
f min
0
0 30 60 90
α [deg]
120 150 180
Figure 2.11 Design example for S r = 500 μm and R r = 500 μm at a reference
radius α r of 75 degrees.

2.2 Phased-array design 27
The variation of the bending radius as a function of α can be minimised if the curve R(α) is
flattened, which leads to a reduction of the dependence of the phased-array transfer on the
radius of curvature. Flattening of the curve is done by requiring dR ⁄ dα and d to be
zero at the (freely chosen) reference angle αr . The first requirement gives a local minimum in
the R(α) curve, whereas the latter results in a bending point in the curve, giving a larger region
of α over which the curve is flat. Both requirements lead to respectively:
2 R dα 2
⁄
and:
R r
S r
D˜ = ---------------
(2.29)
2tanα r
D˜ 1
--- 1
2 sin 2 ⎛ ⎞
= ⎜ + -------------- ⎟
(2.30)
⎝ α ⎠
r
Unfortunately, application of this concept leads to considerable device dimensions. In the best
case, Rr D is the smallest reference radius obtainable ( mm is a representative
value). If a concession to the flatness of the R(α) curve is allowed, the following empirical
requirement can be used:
˜ = D˜ = 2
R r
D˜ 2sin 2 = -----------------
(2.31)
αr With this condition the smallest possible reference radius is reduced by a factor two and,
consequently, the device size. As small device dimensions are preferred, an adaption of the
design strategy is still needed. The requirement for a flat R(α) curve is dropped, but in addition
to the requirement of dR/dα to be zero at the reference angle α r , a second requirement is
imposed:
R r
= Rmin (2.32)
with Rmin being the minimum allowed bending radius. In our case, this concept leads to the
smallest device dimensions, as the minimum bending radius is in the order of only a few
hundreds of microns.
The R(α) curve for each of the three proposed concepts is calculated using representative
values for D , αr and Rmin of 2 mm, 75 degrees and 500 μm respectively. The graph is depicted
˜
in figure 2.12. It can be clearly seen that concept (a) ensures flatness of the R(α) curve over a
long range of α (in this example even more than 70 degrees!), but additionally it results in the
highest values for the curvature radius. Concept (b) and (c) allow for use of smaller bending
radii at the cost of curve flatness. Corrections therefore have to be made in order to account for
the propagation constant in the bend which depends on the curvature radius.

28 2. PHASAR demultiplexers: a review
2.2.8 Correction for bending effects
In the present design concept, the curved waveguides are treated as straight waveguides with a
phase transfer of Φ = N effk02αR and the bending radius R defined in the centre of the
waveguide. With curved waveguides, however, the modal field distribution tends to shift
towards the outer edge of the bend, which effectively corresponds to an increase of the bending
radius. If bending radii are applied where the shift of the modal field cannot be neglected, a
correction to the bending radius is needed in order to avoid degradation of the array
performance. As the phase transfer of the bend with radius R seems to be caused by a bend
with radius R' = R + ΔR (see figure 2.13), the corrected bending radius R' is calculated as:
leading to:
R [μm]
3000
2500
2000
1500
1000
500
a: eqs. 2.29 & 2.30
b: eq. 2.31
c: eq. 2.32
0
0 30 60 90
α [deg]
120 150 180
Figure 2.12 Bending radii of the array guides as a function of array guide angle α
for the three proposed design concepts.
2αβ φ( R)
= Φ = 2αR'β s
(2.33)
ΔR
βφ( R)
= -------------- – R
(2.34)
with βs being the propagation constant of a straight waveguide. The apparent increase of the
bending radius can therefore be compensated for by a reduction of the bending radius by the
same amount, resulting in R'' =
R – ΔR for the actual bending radius.
As low-loss operation is favourable, the junction losses between the straight and curved
waveguides should be minimised by applying a lateral offset. The correction of the bending
radius corresponds to a lateral offset in the correct direction, but in most cases it amounts to
only half of the offset needed for minimum coupling loss. As the correction is in the order of a
tenth of micron, the loss penalty will be negligible. It may result, however, in unwanted
excitation of higher order modes, which causes “ghost” images (see section 2.1.5 and 4.4). The
optimisation of the offset, both for optimum phase transfer and minimum coupling loss (or
higher order mode excitation), will be explained in the next paragraph.
β s

2.3 Applications 29
2.2.9 Waveguide junctions
The correction for bending effects results in an offset at the junction of the straight and curved
array waveguides, which leads to undesired effects such as coupling loss, and, in case of
bimodal waveguides, also mode conversion causing “ghost” images (see section 2.1.5 and 4.4).
Usually, the bending radii are chosen in such a way that the fundamental orders for both TE
and TM polarisation are guided with negligible bending loss, and higher order modes with
high bending loss. However, if the higher order modes are still guided with low bending loss
(which is, for instance, the case for the polarisation independent raised-strip waveguides),
mode conversion is undesirable. Because of different propagation constants for the
fundamental and the first order mode, the resulting image will occur at a different position
along the image plane. This shift can be calculated in the same way as the TE-TM shift
according to equation 2.18. Mode conversion can be kept small by optimising the offset at the
junctions on minimal first-order mode excitation.
Each offset between the straight and curved waveguides can be optimised separately as
desired, either to maximum coupling efficiency of the fundamental mode or to minimum mode
conversion. This is done by rotating each i-th straight waveguide over a small angle δα i ,
additional to its original angle α i (see equation 2.21), according to:
whereby Δx is the desired lateral offset. It should be noted, that the lateral shift due to the
bending correction ΔR is included in this offset and should be substracted first to find the
additional rotation angle δα i . With the offset Δx in the order of a few tenths of a micron, and
the straight section length S i in the order of a few hundreds of microns, the additional angle δα i
will be very small. Additionally, in this way neither the corrected bending radius nor the length
of the straight section are changed, and therefore the phase transfer of the array is not
influenced.
2.3 Applications
ΔR
Figure 2.13 Schematic diagram of the bending correction.
δα i
= asin( Δx ⁄ Si) ≈ Δx ⁄ Si (2.35)
In addition to the basic functions of wavelength multiplexing and demultiplexing, PHASARs
are applied in wavelength routers and, in combination with other components such as

30 2. PHASAR demultiplexers: a review
amplifiers and switches, in more complex devices for use in multi-wavelength networks. In this
section a number of applications will be discussed further.
2.3.1 Wavelength routers
A wavelength router is obtained by designing the input and the output side of a PHASAR
symmetrically, i.e. with N input and N output ports. For the cyclical rotation of the input
frequencies along the output ports (as described in section 1.2), it is essential that the frequency
response is periodical (as shown in figure 1.3b), which implies that the FSR should
equal N times the channel spacing. From equation 2.6 it can be seen that this is obtained by
choosing:
ΔL
whereby Ng is the group index of the waveguide mode, N is the number of frequency channels
and Δfch is the channel spacing.
For this design, the procedure described in section 2.2.2 should be changed similarly to section
2.2.4 paragraph (ii). By fixing the incremental length according to equation 2.36 the
divergence angle Δα is fixed through equation 2.3 and Ra through Ra =
da ⁄ Δα (see figure
2.1b). With this choice of FSR, the non-uniformity L u is fixed and will be in the order of 3 dB,
which can be explained as follows. Channels at a frequency Δf FSR /2 away from the central
frequency will experience an excess loss L u of at least 3 dB, because the focal spot
corresponding to this frequency will be equally divided among two orders, which focus
symmetrically around the centre of the image plane. As in a periodical design the frequency
spacing between the outer channels comes close to the FSR, the outer channels will experience
an excess loss L u in the order of 3 dB.
Wavelength routers have been applied in various configurations in add-drop multiplexers and
wavelength selective switches [47,48,64,65,90,130,143-147] and in multi-wavelength
networks [54]. In combination with a DFB laser used as a wavelength converter, a wavelength
router has also been applied as a wavelength switch [130, 135].
2.3.2 Multi-wavelength receivers
A multi-wavelength receiver is obtained by integration of a demultiplexer with a photodiode
array. The first PHASAR receiver (reported in 1993 by Amersfoort et al. [4,5]), applied a twinguide
waveguide structure where the passive region was obtained by locally removing the
absorbing top layer. Integrated receivers have also been used in buried waveguide structures
[182] and in polarisation independent raised-strip waveguides [9,122]. A wavelength-flattened
receiver module, hybridly integrated with a silicon bipolar front-end array, has been discussed
by Steenbergen et al. [138,139,140]. Recently, a low-loss (3 dB on-chip loss) 8-channel WDM
receiver with 10 GHz bandwidth per channel has been reported [141].
2.3.3 Multi-wavelength lasers
c
= ----------------------
N gNΔ f
(2.36)
ch
Today’s WDM systems use wavelength-selected or tunable lasers as sources. Multiplexing of a
number of wavelengths into one fibre is done by using a power combiner or a wavelength
multiplexer. Integrated multi-wavelength lasers have been produced by combining a DFB-laser
array (with a linear frequency spacing) with a power combiner on a single chip [12,173,174].

2.3 Applications 31
Using a power combiner for multiplexing the different wavelengths into a single fibre is a very
tolerant method, but it introduces a loss of 10 ⋅ logN dB, with N being the number of
wavelength channels. The combination loss can be reduced by applying a wavelength
multiplexer, at the cost, however, of more stringent requirements on control of the laser
wavelengths.
An elegant solution to this problem is combining a broadband optical amplifier array with a
multiplexer into a Fabry-Perot cavity as depicted in figure 2.14. This principle was first
demonstrated in the MAGIC-laser [169] in a hybridly integrated form. If one of the
Semiconductor Optical Amplifiers (SOAs) is excited, the device will start lasing at the
passband maximum of the multiplexer channel to which the SOA is connected. In principle all
SOAs can be operated and (intensity) modulated simultaneously. An important advantage of
this component is that the wavelength channels are automatically tuned to the passbands of the
multiplexer and coupled to the single output port with low loss.
Mirror
SOA
SOA
SOA
SOA
MUX
Figure 2.14 Integrated multi-wavelength laser.
Mirror
Zirngibl and Joyner reported the first multi-wavelength lasers based on integration of a SOAarray
with a PHASAR [68,178,179] and demonstrated it with a 9 × 200 Mb/s transmission
experiment [180]. Despite their long cavity length, these lasers show single mode operation in
a wide range of operating conditions [181]. Direct modulation speeds in excess of 1 Gb/s were
reported recently [184]. Power coupled into a fibre is still low. Highest power reported so far is
0.15 mW [132,136].
Joyner et al. [70] reported integration of a MW-laser with an electro-absorption modulator.
They used the power, radiated into an adjacent order of the phased array, to couple light out of
the cavity into the modulator.
A problem in MW-lasers with a small FSR is that the laser may start lasing in a wrong order
and, consequently, at a wrong frequency. Doerr et al. [43] proposed and demonstrated a
method to suppress the transmission for undesired orders by chirping the incremental length
ΔL in the array.
Tachikawa et al. [147] reported a 32-channel discretely tunable laser based on a
PHASAR with SOAs, with one reflecting mirror connected to both the 4 input and the 8 output
ports. The 32 wavelengths are generated by powering the proper SOA pairs.
2.3.4 Wavelength-selective switches and add-drop multiplexers
Add-drop multiplexers (ADMs) form a special class of wavelength selective switches. They
are used for coupling one or more wavelength signals from a main input port into one or more
drop ports by operating the corresponding switches. The other signals are simultaneously
routed into the main output port, together with the signals applied at the proper add ports.
Figure 2.15a shows the configuration as produced by Tachikawa et al. [144,146,149]. The
fibre
4 ×
8

32 2. PHASAR demultiplexers: a review
device (hybridly integrated, whereby the switching was done by changing fibre connectors),
showed a fibre-to-fibre insertion loss of 3-4 dB for the add-drop signals and 6-8 dB for the
transmitted signals. Through a suitable arrangement of the loop-back optical paths, the
insertion loss difference between the transmitted signals can be minimised [62].
demux/mux
(a) RX TX
(b)
(c)
demux
TX RX
demux/mux
A disadvantage of this loop-back configuration is that the cross talk of the PHASAR is coupled
directly into the main output port. This problem can be reduced by applying the PHASAR in a
fold-back configuration as shown in figure 2.15b [47,64]. A third approach uses a separate
demultiplexer and multiplexer (figure 2.15c) as reported by Okamoto et al. [89,90,93]. The two
PHASAR used in this approach were placed close together in order to ensure that their channel
frequencies match.
In wavelength routed networks, spatial switching of arbitrary wavelength signals between
multiple channels allows for efficient use of the transmission capacity by using a fixed number
of wavelengths and by re-using them. For this approach a number of configurations using
silica-based waveguide structures have been reported [63,64,143].
The first InP-based ADM has been reported only recently [167]. The 400 GHz spaced
4-channel device (in loop-back configuration) has less than 10.7 dB on-chip loss for the pass
function (including switch losses, twice the demultiplexer loss, 7 waveguide crossings, and a
total of 2 cm waveguide loss). The on-chip loss for the add and drop function is less than
6.7 dB, and the cross talk is less than -20 dB for all paths. The device is extremely compact
( mm2 3 ×
6 ), which demonstrates the potential for InP integration of complex circuits on a
small chip area. This potential can be further developed by including optical amplifiers to
compensate the on-chip losses.
mux
Figure 2.15 Three different ADM configurations: a) loop-back, b) fold-back, and
c) cascaded demux/mux (TX = transmitter, RX = receiver, X = switch).
RX
TX

2.4 Conclusions 33
A configuration which does not require switches makes use of wavelength conversion and is
shown in figure 2.16 [130,135]. The modulated signal is fed into a continuously operating
DBR laser, of which the wavelength can be tuned by the current injection. The insertion of the
modulated signal will decrease the carrier concentration, leading to a decrease of the DBR
laser signal. The output signal of the DBR laser is therefore not only converted to the DBR
laser wavelength, but also inverted with respect to the input. Spatial switching can be achieved
by tuning the DBR injection current and by connecting the output to a phased-array
demultiplexer.
2.4 Conclusions
DBR
router
Figure 2.16 Schematic diagram of a wavelength switch employing a currentinjection
tunable DBR laser.
The range of applications of PHASAR-based devices is growing rapidly. PHASARs have
proven to be flexible components which support the possibility of a broad range of functions
for use in multi-wavelength networks. Silica-based devices offer the best performance and are
presently being applied most widely. They might get some competition from polymer-based
devices in the future. InP-based devices are most promising for manufacture of active MWdevices
such as MW-lasers and receivers and, in the longer term, for more complicated circuits
containing large numbers of components, such as add-drops and optical cross connects.

34 2. PHASAR demultiplexers: a review

Chapter 3
Polarisation conversion in waveguide bends
Very short waveguide bends appear to have polarisation-converting properties. For most
applications the bends should be designed in such a way to keep polarisation conversion
effects small. The polarisation converting properties can be applied especially in compact lowloss
polarisation converters. The polarisation conversion phenomenon is discussed in this
chapter and experimental results are presented. Part of these experiments have been presented
at the IPR’96 [34] and have been published in IEEE Photonics Technology Letters [35]. They
have also led to a patent application [32].
3.1 Introduction
As the state of polarisation is unknown at the receiver side, polarisation handling is of great
importance in optical communication systems. The most obvious way to deal with this
problem is the usage of polarisation independent devices, and, in particular, a polarisation
independent demultiplexer. A number of methods to obtain polarisation independent
demultiplexers have already been mentioned in Chapter 2 and are discussed more
comprehensively in Chapters 4 and 5. One of these methods uses a half-wave plate inserted in
the middle of a phased array and has successfully been applied to waveguide structures with a
small NA, such as silica and LiNbO 3 . As this method is not practical for InP-based devices,
because of the large NA of InP-based waveguides and the corresponding large diffraction of
the unguided beam, a solution may be found in a compact integrated polarisation converter.
Until recently research has been focused on a type of converter which uses a periodically
alternating, asymmetrically loaded waveguide [53,115,157]. Schematic cross sections of
produced devices are shown in figure 3.1a-c. These types of converter consist of a periodic
structure, as shown in figure 3.1d (topview), of which the period is chosen in such a way to
obtain constructive interference of the light, converted at a junction with light which has been
converted at previous junctions. The waveguide is made asymmetrical in order to achieve a
high conversion efficiency at the junctions, which results in a short device. This can be done
either by a partial top load on the waveguide [115], or by tilted side walls [53,157] as shown in
figure 3.1a-c. It is obvious that these types of converter require multiple masking steps,
combined reactive ion etching and selective chemical etching steps. Their performance is
summarised in table 3.1.

36 3. Polarisation conversion in waveguide bends
Table 3.1 Performance of the three types of converter using a periodically
alternating, asymmetrically loaded waveguide.
Author Reference Conversion
[%]
Excess loss
[dB]
Length
[μm]
Shani et al. 115 90-100 2-3 3700
Heidrich et al. 53 50 3 825
van der Tol et al. 157 93 9-11 990
(a) (b)
(c) (d)
Figure 3.1 Cross sections of the periodically alternating, asymmetrically loaded
waveguide as proposed by Shani et al. [115] (a), Heidrich et al. [53] (b), van der
Tol et al. [157] (c), and a schematic top view of Shani’s device (d).
In this chapter a novel type of polarisation converter is presented based on deeply etched
waveguides with a small bending radius as shown in figure 3.2. It has a potential for low loss
and compact device size, and it can be integrated with other devices. The operation principle
can be explained as follows. It has been found that the non-dominant field component (E x for
TE and E R for TM) of both the TE and TM mode strongly increases if the bending radius is
chosen sufficiently small, which means that the polarisation direction of these modes will be

3.2 Computational methods 37
1.4 μm
InP
InGaAsP
Q(1.3)
InP substrate
rotated. If a straight waveguide is connected to such a bend, both modes will be excited. As
these modes have different propagation constants, a phase difference is obtained after
propagation through a bend section. By placing a next bend section with opposite curvature,
polarisation conversion can be achieved. The conversion ratio can be optimised by a proper
choice of the section length. Apart from the fact that tilting of the modal polarisation plane is
achieved by a curved waveguide instead of an asymmetrically loaded waveguide, the operation
of this type of converter is similar to those depicted in figure 3.1.
The operation of such a polarisation converter has been analysed using three different
computational methods, which are discussed in section 3.2. The radiation mechanism in deeply
etched waveguides is discussed in section 3.3, and following that the polarisation rotation of
such bends in section 3.4. The polarisation dispersion and conversion are discussed in sections
3.5 and 3.6 respectively, whereafter the layout of a polarisation converter is described. Section
3.8 deals with the tolerance analysis of the converter and in section 3.9 it is explained how
conversion can be avoided.
For the calculations and experiments detailed in this chapter, the deeply etched waveguide
structure as shown in figure 3.2 is used unless otherwise stated. The wavelength was chosen at
1508 nm, determined by the operating wavelength of the Fabry-Pérot laser used for the
experiments. The refractive indices of InP and InGaAsP at this wavelength are 3.1745 and
3.4005 respectively [46].
3.2 Computational methods
A number of methods for calculating the propagation constants and modal fields in curved
waveguides are available in our laboratory, which will be discussed in the following sections.
An overview is given in table 3.2.
3.2.1 Effective index method
0.3 μm
0.6 μm
Figure 3.2 The deeply etched waveguide structure as used for the polarisation
converter.
The Effective Index Method (EIM) [73] is probably the most widely used method due to its
ease of use. The principle of this method is briefly explained as follows, using the x, y and z for
the vertical, horizontal and longitudional directions respectively. Firstly, the local effective
index N(y,z) is calculated for each point (y,z) as if the structure were y-z-invariant.
ϕ
X
R

38 3. Polarisation conversion in waveguide bends
Table 3.2 Overview of the computational methods for calculation of the effective
index N eff , the radiation loss α, and the modal field Ψ. (EIM = Effective Index
Method, MOL = Method of Lines, FEM = Finite Element Method, and Conf.
trans. = Conformal transformation)
Method N eff α Ψ Comments
EIM + + + 2 x 1D scalar + Conf. trans.
FEM ++ − ++ 2D vectorial + Conf. trans.
MOL ++ ++ ++ 2D vectorial
Then the modal effective index is calculated by computing the two-dimensional mode
solutions for the index profile N(y,z). This method actually transforms the 2D problem into two
1D problems. With the EIM, both the mode index and the two 1D field profiles can be
calculated.
3.2.2 Method of lines
A method suitable for analysing waveguide bends is the Method of Lines (MOL) [99]. We have
a full 2D vectorial method available which is capable of calculating the effective index, the
radiation loss as well as the X-, R- and ϕ-components of the waveguide mode. The program has
been developed by the University of Hagen. With this method the waveguide cross section is
divided into regions by horizontal lines. On these lines the vector potentials for the
electromagnetic fields are calculated. For a straight waveguide they satisfy the Helmholtz
equations and can be expressed analytically. For a curved waveguide, however, Bessel equations
are obtained, of which the solutions are cylinder functions of large and complex order. In the
transverse direction, the potentials are discretised and continuity conditions are applied on the
interfaces of the single layers. The result is a system of coupled ordinary differential equations,
which can be solved using standard methods.
3.2.3 Finite element method
The third mode solver is a vectorial Finite Element Method (FEM) [108] made available to us
by the ETH-Zürich. This method is particularly suitable for electromagnetic field problems, as
the general geometry of the waveguide can be quite complicated with an arbitrary refractive
index profile n(x,y) in the transverse directions. For this method, the entire waveguide cross
section is divided into a patchwork (or mesh) of sub-regions or elements, usually triangles or
quadrilaterals. Using many elements, any cross section can be accurately approximated. The
field in each element is represented by a polynomial and the field continuity conditions are
imposed on all interfaces between different elements. By employing a variational expression
for Maxwell’s equations, an eigenvalue matrix is obtained, which can be solved using standard
methods.
Figure 3.3 shows a mesh definition for a straight waveguide. It can be seen that the mesh size
should be small near interfaces and equal on both sides of the interface. Additionally, as the
field intensity decreases away from the waveguide core, the mesh size can be increased. The
solution depends on the mesh size and therefore an increasing refinement has to be tried until
the mesh dependence vanishes. It should be noted, however, that on the boundary of the

3.2 Computational methods 39
Figure 3.3 Mesh definition for a straight waveguide.
computation window the field is assumed to be zero, which implies that a sufficiently large
window has to be chosen. In this way it is avoided that solutions are obtained which actually do
not represent physical modes of the waveguide.
3.2.4 Conformal transformation
Using the EIM and the FEM, the complex angular propagation constant in the bend can be
calculated using the conformal transformation technique [52]. This technique transforms a
curved waveguide into an equivalent straight waveguide with a transformed index profile. The
transformation, which is shown schematically in figure 3.4, is written as
r = Rt ⋅ exp( u ⁄ Rt) , whereby Rt is an arbitrary reference radius. As the waveguide width is
much smaller than the reference radius, the transformation can be linearised around r = Rt as
r ≈ Rt + u.
This leads to the following transformed index profile:
nt( r)
= n( r)
⋅ r ⁄ Rt (3.1)
The transformation leads to a solution in the form of a propagation constant β t in the
transformed domain, from which the angular propagation constant β ϕ can be calculated as:
βϕ = βt ⋅ Rt = N eff,t ⋅ k0 ⋅ R (3.2)
t
This angular propagation constant has the dimension rad -1 , because the propagation through a
bend is described as exp( – jβϕϕ
) . The radiation loss can be calculated from the imaginary part
of the angular propagation constant according to:
β' ϕ
αϕ = 20 ⋅ log[ exp( 2 β' ϕ ⁄ π)
] [ dB/90° ] (3.3)
For the EIM it should be noted that, being a 2x1D scalar method, it cannot give a good
prediction for the radiation loss in deeply etched waveguide structures, as it does not take
radiation into the substrate into account. On the other hand, however, it is found that the modal
field solutions correspond very well to the ones calculated using the MOL or the FEM.

40 3. Polarisation conversion in waveguide bends
n
For the 2D-FEM-analysis of a curved waveguide, a step-wise approximation of the
transformed index distribution nt( x, y', z')
= n( x, r, ϕ)
⋅ r ⁄ Rt has to be implemented in the
mesh definition. As the bend goes to the left, the flux in the left part is reduced and therefore a
larger mesh can be taken than for a straight waveguide, which is shown in figure 3.5a.
Consequently, the mesh size at the right side should be taken smaller. It should be noted,
however, that the size of the window should be taken in such a way that the transformed index
profile does not exceed the effective index as shown schematically in figure 3.5b. Otherwise
the solutions will become complex which cannot be handled by our FEM mode solver.
Consequently, a complex solution for the propagation constant cannot be obtained and
therefore no estimation of the radiation loss can be made.
3.3 Attenuation in bends
ϕ
r
r
From the equation of the conformal transformation (equation 3.1) it can be seen that the
transformed index increases with increasing r. This gives three effects, which will be discussed
ϕ
n t
u = 0
r = Rt Figure 3.4 Schematic diagram of the conformal transformation.
N eff
(a) (b)
n t
u
u
r
upper limit
Figure 3.5 Mesh definition for a curved waveguide (a), and the step-wise
approximated transformed index profile showing the calculation window limit (b).

3.3 Attenuation in bends 41
briefly. Firstly, as the mode is guided strongest in the region with the highest index, the mode
profile will “move” to the high-index region. It is shifted to the outer edge of the waveguide
and will also be compressed, leading to a field mismatch at the transitions to straight
waveguides. Secondly, the transformed index will always exceed the effective index at a
certain value of r. At that point the mode will start radiating. The result is radiation loss, which
is inherent to waveguide bends. However, if this point lies far away from the waveguide, the
radiation loss is negligibly low. If the bending radius is decreased, this point comes closer to
the waveguide, giving higher radiation loss. These two effects are depicted in figure 3.6. And
finally, as the field intensity at the outer edge of the waveguide increases, the scattering losses
increase as well.
index profile
Figure 3.6 Mode profiles in a straight waveguide (dashed line) and in a leftoriented
curved waveguide (solid line), clearly showing an oscillatory behaviour,
which indicates that the mode is experiencing radiation loss.
For low-contrast waveguide structures, light radiates away from the waveguide bend in the
guiding film as shown in figure 3.7a. When a high-contrast bend is used, such as the deeply
etched waveguide structure of figure 3.2, light radiates into the substrate as shown in figure
3.7b. This is explained by the fact that when the bending radius is decreased, the mode index
decreases and phase-matching with substrate modes will occur, which in turn leads to coupling
to radiation modes and a corresponding increase of the radiation loss.
Transverse position [ μm]
3
2
1
0
-2 -1 0 1 2 3
Lateral position [μm]
(a)
0
-2 -1 0 1 2 3
Lateral position [μm]
Figure 3.7 Radiation loss in a low-contrast (a) and in a high-contrast (b) bend.
Transverse position [μm]
3
2
1
(b)

42 3. Polarisation conversion in waveguide bends
In most cases it is important for curved waveguides to find a value for the minimum usable
bending radius. Preferably this should be done in a simple and fast manner. Pennings [104]
found empirically that the phase-matching condition at the outer edge of the waveguide bend is
a practical criterion for radiation cut-off. Using the EIM, he derived a simple method for
estimating the minimal bending radii usable for deeply etched waveguide bends, based on the
width of the waveguide and on the effective index in the ridge, as well as on the mode index of
a straight waveguide with the same dimensions.
For the estimated cutoff radius R co he found:
R co
wN ridge
= -----------------------------------------
(3.4)
2( N straight – nsub) whereby Nridge and Nstraight are the effective index in the ridge region and the mode index in a
straight waveguide respectively and nsub is the substrate index. Although no magnitude of the
substrate leakage is given by this prediction, the excess bend loss at the cut-off radius was
found to be in the order of 1 dB/90° [104]. These experiments consisted of waveguide
structures with a low transverse index contrast. For the deeply etched waveguide bend a cut-off
radius of 23 μm is estimated.
Experiments on waveguide bends with very small bending radii (down to 30 μm) have been
reported earlier [126,128]. The results are depicted as squares in figure 3.8 and show that when
a deeply etched waveguide structure (as shown in figure 3.2) is used, low radiation loss can be
combined with very small bending radii - less than 0.2 dB/90° at a 30 μm radius. The
estimated measurement accuracy is ± 0.2 dB. It should be noted, however, that this graph
gives a slightly pessimistic view on the losses, as maximum loss values were taken from a
series of measurement data. However, measured bending losses still do not exceed 0.2 dB/90°.
The radiation losses as predicted by the MOL (figure 3.8, solid line) are below 0.2 dB/90° for
radii as small as 20 μm, which is confirmed by the measurements (figure 3.8 - squares). No
estimation for the waveguide losses could be obtained with the EIM due to the large lateral
index contrast ( Δn = 3.17 – 1 ).
Radiation loss [dB/90]
0.50
0.40
0.30
0.20
0.10
0.00
Measured
MOL
20 40 60 80 100
Radius [μm]
Figure 3.8 Radiation loss: measured [126,128] (squares), and predicted with the
MOL (solid line).

3.3 Attenuation in bends 43
It can be seen from figure 3.8 that although the radiation loss is still less than 1 dB/90° at the
estimated cut-off radius of 23 μm, the estimation gives a reasonable indication of the radius
where radiation loss becomes important.
As equation 3.4 was found empirically using low-contrast (both lateral and transverse)
waveguide structures, we decrease the transverse index contrast of the deeply etched
waveguide at a bending radius of 20 μm. For this purpose, the band-edge wavelength of the
quaternary guiding layer was decreased from 1.3 μm to 1.0 μm in steps of 0.1 μm. The mode
indices for TE polarisation are calculated using the MOL and it was found that the transverse
index contrast decreases from 0.23 to 0.05 in steps of approximately 0.06.
Transverse position [μm]
Transverse position [μm]
3
2
1
0
3
2
1
0
straight curved
0 1
0
Lateral position [μm]
1 2
(a) (b)
0 1
0
Lateral position [μm]
1 2
(c) (d)
0 1
0
Lateral position [μm]
1 2
In figure 3.9 contour plots of the dominant field component of the TE-polarised mode are
shown for the four different guiding layer compositions. As a reference, the dominant field
components for the corresponding straight waveguide are also shown in the same graphs. It has
been noted that when the transverse index contrast decreases, the mode confinement also
Transverse position [μm]
Transverse position [μm]
3
2
1
0
3
2
1
0
straight curved
Q(1.3) Q(1.2)
straight curved straight curved
Q(1.1)
Q(1.0)
0 1
0
Lateral position [μm]
1 2
Figure 3.9 Dominant lateral field component of the TE-polarised fundamental
mode in a straight (left part) and curved waveguide (right part) with a radius of
20 μm, for decreasing band-edge wavelengths of the guiding film: 1.3 μm (a),
1.2 μm (b), 1.1 μm (c), and 1.0 μm (d). The corresponding radiation losses are
0.15, 0.93, 4.4, and 15.9 dB/90° respectively and the corresponding cut-off radii
are 23, 43, 336, and 905 μm.

44 3. Polarisation conversion in waveguide bends
decreases and the mode leaks increasingly into the substrate. The corresponding cut-off radius
increases from 23 μm to 905 μm. Consequently, the (calculated) radiation loss increases by a
factor of 10 from 0.15 dB/90° (Q(1.3) guiding layer) to 15.9 dB/90° (Q(1.0) guiding layer).
3.4 Tilting of the modal polarisation plane in bends
As the non-dominant field component of both the TE and TM mode strongly increases if the
bending radius is chosen sufficiently small, the modal polarisation plane is tilted. If a straight
waveguide is connected to such a bend, both modes will be excited. These modes propagate
with different propagation constants, resulting in a phase difference after a bend section. If a
next bend section with opposite curvature is connected, polarisation conversion can be
achieved, the ratio of which can be optimised by a proper choice of the bend section length.
For investigation of the increase of the non-dominant field component, we consider figure 3.10
and 3.11. These figures show the surface and contour plots respectively of the intensity for the
E x (non-dominant) and the E r (dominant) field component of the TE-polarised fundamental
mode in a curved waveguide for decreasing bending radii as calculated with the MOL. Use of
the FEM mode solver yields similar results. These figures show that for TE polarisation the E x
field component increases strongly if the radius is chosen sufficiently small. (Simultaneously,
the E r field component for TM polarisation increases strongly.)
For a certain value of the radius, almost 100% of the total field power is present in the E x
component. This means that the polarisation angle, which is defined as:
ϕ pol
arctan Er,max = ⎛-------------- ⎞
(3.5)
⎝ ⎠
E x,max
is rotated by 90 degrees. This equation is valid if both field components have an (almost)
identical shape and if the peaks are located in the same position. From the graphs of figure 3.11
it may be concluded that this is indeed the case.

3.4 Tilting of the modal polarisation plane in bends 45
Figure 3.10 Surface plots of the intensity for the E x (left column) and the E r
(right column) field component of the TE-polarised fundamental mode in a
curved waveguide for decreasing bending radii: 100 μm (a), 50 μm (b), 40 μm
(c), and 20 μm (d).

46 3. Polarisation conversion in waveguide bends
Figure 3.11 Contour plots of the intensity for the E x (left column) and the E r
(right column) field component of the TE-polarised fundamental mode in a
curved waveguide for decreasing bending radii: 100 μm (a), 50 μm (b), 40 μm
(c), and 20 μm (d).

3.5 Polarisation dispersion in bends 47
Polarisation angle [deg]
80
60
40
20
0
10
50 100 150
Radius [μm]
Figure 3.12 Polarisation angle of the TE (solid line) and TM (dashed line) mode
versus the bending radius, calculated with the MOL. A polarisation angle of zero
(ninety) degrees indicates that the mode is horizontally (vertically) polarised.
Using equation 3.5, the polarisation angles for both TE and TM polarisation have been
calculated and are shown in figure 3.12. It has been noted that a polarisation angle of zero
degrees indicates that the mode is polarised horizontally. It can be seen that if the radius is
reduced, the TE- and TM-polarised modes evolve into hybridly polarised modes. If a straight
waveguide (or a bend with opposite curvature) is connected to such a bend, both modes will be
excited. The coupling efficiency is high as the intensity profiles of the hybrid modes match
very well, leading to low coupling losses.
3.5 Polarisation dispersion in bends
The mode index for TE and TM polarisation has been calculated with three different methods
and the results are shown in figure 3.13a-b. It is found that the indices obtained with the FEM
and the MOL, match very well for TE polarisation, but less for TM polarisation. The index
curve obtained with the EIM shows a different behaviour for small bending radii, which is due
to the fact that the EIM is known to give less accurate solutions when the mode is close to cutoff.
The best methods to use for these small radii are the MOL and the FEM, of which the
MOL is more favourable if radiation losses are to be calculated as well.
If we take a look at the index difference between the TE and TM polarisation (also denoted as
the polarisation dispersion ( ΔN pol =
N TE – N TM))
we can see that it is almost constant for the
large-radius region (80 to 100 μm) as depicted in figure 3.14. The index difference decreases
towards a minimum at a bending radius between 30 and 50 m, but the predicted position
depends however on the calculation method.
TE
TM

48 3. Polarisation conversion in waveguide bends
Mode index
3.40
3.35
3.30
3.25
FEM
MOL
EIM
20 40 60 80 100
Radius [um]
Mode index
20 40 60 80 100
Radius [um]
At this minimum, the power of both TE and TM mode is equally divided over the dominant
and non-dominant components (crossing of the curves in figure 3.12). When the radius is
decreased further, the index difference increases and the power is transferred completely to the
non-dominant component.
The two hybridly polarised modes propagate with different phase velocities and at a length
equal to the beat length L π , defined as:
whereby Δβ and ΔN are the propagation constant and the mode index difference between the
TE and TM mode, the combined field will show a polarisation rotation of 90 degrees, if both
modes are excited equally. The beat length is calculated with the three methods and is depicted
in figure 3.15.
3.40
3.35
3.30
3.25
(a) (b)
Figure 3.13 Calculated mode index in the bend for different methods - for TE
polarisation (a) and for TM polarisation (b).
Index difference
0.008
0.006
0.004
0.002
0.000
FEM
MOL
EIM
20 40 60 80 100
Radius [μm]
Figure 3.14 Mode index difference calculated with the three methods.
FEM
MOL
EIM
π λ
Lπ = ------ = ----------
(3.6)
Δβ 2ΔN

3.6 Polarisation conversion at junctions 49
Beat Beatlength length [μm] [μm]
2000
1500
1000
500
0
FEM
MOL
EIM
20 40 60 80 100
Radius [μm]
Figure 3.15 Calculated beat length versus bending radius for the FEM (solid
line), the MOL (dashed line) and the EIM (dotted line).
Apart from the fact that different values of the beat length are predicted, another problem arises
for realising a polarisation converter based on these deeply etched bends. As the converter
consists of a number of segments (see figure 3.1d), the length of which is chosen equal to the
beat length, rotation angles in excess of 10π radians are required. It is better therefore to
choose the radius in such a way that the beat length is small, and consequently the conversion
per junction lower. In this way, more segments are needed, but they are considerably shorter.
The best choice, therefore, may be found in using a large radius (>70 μm).
3.6 Polarisation conversion at junctions
Polarisation conversion takes place at junctions of waveguides with different curvatures, which
can be computed from the overlap of the modal fields in both waveguides. From the graphs of
figure 3.10 it can be seen that the dominant and non-dominant field components match very
well with the modal fields of a straight waveguide, and therefore a high coupling efficiency is
expected. Verification contour plots are drawn of both field components in a curved waveguide
with a bending radius of 50 μm (calculated with the MOL). These are shown in figure 3.16,
together with contour plots of the modal fields in a straight waveguide (calculated with the
FEM).

50 3. Polarisation conversion in waveguide bends
Transverse position [μm]
Transverse position [μm]
Transverse position [μm]
1
0
-1
-1 0 1 2
Lateral position [μm]
1
0
-1
-1 0 1 2
Lateral position [μm]
1
0
-1
-1 0 1 2
Lateral position [μm]
(a)
(b)
(c)
-1
-1 0 1 2
Lateral position [μm]
The coupling efficiency η between two fields U 1 and U 2 is calculated using the overlap
integral:
Transverse position [μm]
Transverse position [μm]
Transverse position [μm]
1
0
1
0
-1
-1 0 1 2
Lateral position [μm]
1
0
-1
-1 0 1 2
Lateral position [μm]
Figure 3.16 The E x (a) and E r (b) field components of the curved waveguide
mode for a radius of 50 μm, and the dominant field component of the straight
waveguide mode (c). The left column shows the TE polarisation and the right
column the TM polarisation.
∫
( U1U 2)
( U1, xU
2, x + U1, rU
2, r)
η = ------------------------------------------------------------ = ----------------------------------------------------------------------------- (3.7)
2
2
2
2
U1 ⋅ ∫ dxdr ∫ U1 dxdr ⋅ ∫ U2 dxdr
dxdr 2
∫ dxdr U 2
∫
dxdr 2

3.7 A compact polarisation converter 51
Using this equation, the coupling efficiency from a quasi 1 -TE mode to a quasi-TM mode has
been calculated (based on fields obtained with the MOL) and is shown in figure 3.17. At the
junction between two oppositely curved waveguides the coupling efficiency (depicted in figure
3.17a) is very low and such a junction will therefore not contribute to polarisation rotation. The
coupling efficiency at a junction between a straight and a curved waveguide on the other hand
is very high, as shown in figure 3.17b. This is a result of the high fraction of power that is
present in the non-dominant component, combined with the good match between the fields.
And because of this match, the curve of figure 3.17b may be considered as a measure for the
fraction of power carried by the non-dominant component.
Coupling efficiency [%]
10
8
6
4
2
0
20 40 60 80 100
Radius [μm]
(a) (b)
3.7 A compact polarisation converter
20 40 60 80 100
Radius [μm]
The polarisation conversion was analysed using the layout as shown in figure 3.18. Two Ubends,
consisting of four arc segments with a segment angle α and a waveguide width of
1.4 μm, are placed in series. This segment angle is varied between 10 and 80 degrees, allowing
for different beat lengths between two subsequent junctions. As the 1.4 μm wide waveguides
have propagation losses in the order of 8-10 dB/cm [126,128], waveguides of 3.0 μm width are
used to connect the U-bends to each other. They are also used for in- and output waveguides,
because they are known to have low propagation losses in the order of 1-2 dB/cm [126,128].
This is due to the fact that the field intensity at the (rough) etched side wall decreases when the
waveguide width increases, and therefore less scattering loss will occur for broad waveguides.
For the transition between these wide waveguides and the narrow bends, an adiabatic taper is
used with a length of 50 μm. The (maximum) total device size measures μm2 975 ×
83 .
1. Strictly taken, we cannot speak of TE- and TM-polarised modes because both types have a
strong orthogonal field component. For a deeply etched curved waveguide with a small
bending radius, the assignment to TE or TM polarisation of a modal solution found with
the 2D-solver is done on the basis of continuous evolution of the bending radius: the mode
type assignment is done according to the polarisation type of the mode when the bending
radius is increased to infinity.
Coupling efficiency [%]
Figure 3.17 Coupling efficiency from a quasi-TE to a quasi-TM mode between
two oppositely curved waveguides (a), and between a straight and a curved
waveguide (b).
100
80
60
40
20
0

52 3. Polarisation conversion in waveguide bends
The converter can be described as a number of curved and straight waveguides, connected to
each other by junctions, and is depicted schematically in figure 3.19.
This approach allows for a transmission matrix description, of which the complete transfer
from input to output can be described by a transmission matrix T:
with:
whereby u TE and u TM are the complex signal amplitudes of the quasi-TE and quasi-TM modes
respectively.
The transmission matrix T can be decomposed as follows (see figure 3.19):
with:
α
975 μm
83 μm
Figure 3.18 Layout of the polarisation converter, where the segment angle is
depicted as α.
in
+
Tsc T cc
T c
T c T c
T cc
T c
-
Tsc whereby T c and T s describe the transmission in a curved section with angle α and in a straight
+
Tsc T cc
T cc
α L α out
T s
T c
T c T c
Figure 3.19 Schematic diagram of the polarisation converter.
T u
=
U out
U
=
=
T U in
u TE
u TM
T = T uT sT u
- +
T scT
cT ccT cT cT ccT cT sc
T c
-
Tsc (3.8)
(3.9)
(3.10)
(3.11)

3.7 A compact polarisation converter 53
section with length L α respectively:
and:
T c
T s
=
=
exp( – jβϕ, TEα)
0
0 exp – jβϕ, TM
( α)
exp( – jβTELα ) 0
0 exp( – jβTMLα) (3.12)
(3.13)
whereby the exponential terms describe the phase transfer along the waveguide. The matrix T sc
describes the junction between a straight and a curved waveguide, and the matrix T cc describes
the junction between two oppositely curved waveguides. The matrix elements are calculated
using 2D vectorial overlap integrals according to:
+ ηTE,TE – ηTE,TM - ηTE,TE ηTE,TM = , T sc =
ηTM,TE ηTM,TM – ηTM,TE ηTM,TM T sc
T cc
=
η TE,TE η TE,TM
η TM,TE η TM,TM
(3.14)
whereby η B,A is the coupling coefficient between the field of polarisation A in the straight or
curved input waveguide, and the field of polarisation B in the curved output waveguide (A and
B equal TE or TM), calculated according to equation 3.7.
Results of the calculation of the transmission matrix T with the MOL are shown in figure
3.20a. Although the predicted conversion is very small, a beat can be clearly observed,
especially for the 150 μm bending radius. In any case, low losses in the order of 0.2-0.4 dB are
expected, as the radiation and the junction losses are both low. Based on these results, it is
anticipated that 100% polarisation conversion is obtained after ten U-bends with 75 μm
bending radius and with 55 degrees segment angle. The excess loss will then be approximately
1.5 dB.
Experimental results are also available: waveguides have been fabricated in a MOCVD-grown
InP/InGaAsP(λ g = 1.3 μm)/InP ridge waveguide structure. A 100 nm thick PE-CVD deposited
SiNx film was used as a masking layer and waveguides were etched completely through the
guiding layer into the substrate employing a CH 4 /H 2 reactive-ion etching (RIE) etch/descum
process to reduce the scattering losses [86]. Waveguide losses were measured at 1.0 dB/cm and
2.2 dB/cm for widths of 3.0 μm and 1.4 μm respectively both for TE and TM polarisation. The
side wall angle was measured to be approximately 10 degrees off verticality.
A Fabry-Perot laser, operating at a wavelength of 1508 nm, was used to measure the
performance of the polarisation converters. TM-polarised light was launched into the input
waveguide, and at the output a polarisation filter was used for separate measurement of the TE
and TM response. The measured performance of the polarisation converter is shown in figure
3.20b. The curves show the behaviour as expected, which indicates that the calculation of the
propagation constants is relatively accurate. The converters with a bending radius of 50 μm
show the most interesting measurement results: a polarisation conversion of 85% was
measured at a segment angle of 70 degrees.

54 3. Polarisation conversion in waveguide bends
Conversion [%]
20
15
10
5
R = 50 μm
R = 75 μm
R = 100 μm
R = 150 μm
0
0 20 40 60 80
Segment angle [deg]
Conversion [%]
(a) (b)
10 20 30 40 50 60 70 80
Segment angle [deg]
Low conversion values (

3.8 Tolerance analysis 55
3.8 Tolerance analysis
In this section, the dependence of polarisation conversion on variations in the manufacturing
process is described. These variations comprise the layer thickness, the waveguide width, and
also the angle of the etched side wall. Variations of the etch depth do not influence the
polarisation conversion as long as the guiding layer is etched through completely.
3.8.1 Layer thickness
The beat length between the TE- and TM-polarised modes is an important parameter of the
converter of figure 3.18. It is not very tolerant to variations of the layer thickness, as shown in
figure 3.22. As can be seen in this figure, the layer thickness has to be controlled accurately.
The guiding layer thickness variation has to be limited to a value of ± 1 % around the designed
thickness in order to keep the beat length variation below ± 10 %. The same beat length
variation limits the cladding layer variation to ± 2.5 %. These are very stringent requirements
on the layer thickness, which make the polarisation converter difficult to realise.
Beat Beatlength length deviation variation [%]
100
50
-50
3.8.2 Waveguide width
0
Guiding layer
Cladding layer
-100
-15 -10 -5 0 5 10 15
Thickness deviation [%]
Figure 3.22 Beat length deviation versus layer thickness deviation.
Coupling efficiency
Figure 3.23 shows the radius dependence of the coupling efficiency for different waveguide
widths. The efficiency for TE-polarised input and TM-polarised output fields is calculated
using a two-dimensional vectorial overlap integral. The efficiency for TM-polarised input
fields to TE-polarised output fields is quite similar and is not shown here. Equally, from the
point of power conservation, the efficiency for the coupling of TE-polarised input fields to TEpolarised
output fields is complementary to the curves shown in figure 3.23. In graph (a) the
efficiency is shown for a junction between two oppositely curved waveguides. It shows that the
coupling efficiency remains very low and is hardly influenced by the waveguide width.

56 3. Polarisation conversion in waveguide bends
Coupling efficiency [%]
10
8
6
4
2
0
W = 1.2 μm
W = 1.4 μm
W = 1.6 μm
20 40 60 80 100
Radius [μm]
(a) (b)
20 40 60 80 100
Radius [μm]
The junction efficiency from a straight to a curved waveguide depicted in figure 3.23b on the
other hand depends strongly on the waveguide width. But if the radius is decreased to
15-25 μm, the width dependence is greatly reduced. This small-radius region has been zoomed
in and is depicted in figure 3.24. The graph shows that high efficiencies can be obtained,
especially for small waveguide widths, which can be explained by the fact that for small radii
the modal field in the bend is guided by the outer edge alone, and becomes independent of the
inner edge. Such a mode is called a “whispering-gallery” (WG) mode after Lord Rayleigh
[109], who applied this term to acoustic waves guided by a single curved surface which he had
found in St. Paul’s cathedral. The field of such a WG mode is highly compressed and becomes
asymmetrical, leading to high coupling losses to the symmetrical field of the straight
waveguide. Pennings [103] presented an approximal formula for estimating the width and
Coupling efficiency [%]
100
80
60
40
20
0
W = 1.2 μm
W = 1.4 μm
W = 1.6 μm
Figure 3.23 TE to TM coupling efficiency versus bending radius for different
waveguide widths: curved to curved waveguide (a), and straight to curved
waveguide (b).
Coupling efficiency [%]
100
95
90
85
R = 15 μm
R = 20 μm
R = 25 μm
80
1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80
Waveguide width [μm]
Figure 3.24 TE to TM coupling efficiency versus bending radius for different
waveguide widths.

3.8 Tolerance analysis 57
radius at which this occurs. For the very small radii (15 to 25 μm) the width is found to be
between 1.5 and 1.6 μm.
Another interesting feature of figure 3.23b is the curve for the 1.2 μm waveguide width. This
curve shows a different behaviour than the ones for a width of 1.4 and 1.6 μm, which is due to
the fact that the assignment to TE or TM polarisation of a modal solution found with the 2Dsolver
is done on the basis of continuous evolution of the mode index (see note on page 51).
The problem arising from the 1.2 μm waveguides is that for a straight waveguide the mode
index for TE polarisation is lower than that of the TM polarisated mode. This is shown in
figure 3.25, in which the mode indices (calculated with the vectorial FEM) are depicted as a
function of the waveguide width.
Mode index
3.285
3.280
3.275
3.270
3.265
3.260
TE
TM
3.255
1.20 1.30 1.40 1.50 1.60
Waveguide width [μm]
Figure 3.25 Effective index of the fundamental TE- and TM-polarised mode in a
straight waveguide as a function of the width.
Beat length
Figure 3.26 shows the beat length between the TE- and TM-polarised mode versus the bending
radius at different waveguide widths. From this figure it can be seen that the waveguide width
does not only have a large impact on the coupling efficiencies at the junctions but also on the
beat length. Two areas are of major interest for the application of polarisation conversion.
Firstly the region with radii in the order of 15-25 μm is of interest as the beat length is very
short (100-200 μm) and the dependence on the waveguide width vanishes. The disadvantage of
this region, however, is that to obtain a curved waveguide with a propagation length equal to
the beat length, the rotation angle must be higher than 360 degrees. Additionally, the radiation
losses, which are listed in table 3.3, increase with decreasing radius and width, leading to
(calculated) losses in the order of 1.2-1.8 dB for a bend with a 360-degree rotation angle.
The second interesting region is the one with bending radii in the range from 70 to 100 μm. In
this range the beat length is almost independent of the bending radius if the waveguide width
equals 1.2 or 1.6 μm. In this case the beat length will be around 265 μm, leading to a rotation
angle of approximately 150 degrees and therefore the design of a polarisation converter is
feasible. In addition, as the radiation loss is negligible, low-loss operation is expected.

58 3. Polarisation conversion in waveguide bends
Beat Beatlength length [μm]
2000
1500
1000
500
0
W = 1.2 μm
W = 1.4 μm
W = 1.6 μm
20 40 60 80 100
Radius [μm]
Figure 3.26 Beat length versus bending radius for different waveguide widths.
Table 3.3 Calculated radiation losses for TE/TM polarisation at different
waveguide widths.
W [μm] R = 15 μm R = 20 μm R = 25 μm
1.2 0.34 / 0.46 0.18 / 0.24 0.10 / 0.12
1.4 0.31 / 0.38 0.15 / 0.17 0.08 / 0.08
1.6 0.30 / 0.36 0.14 / 0.15 0.07 / 0.06
The performance of the polarisation converter (see figure 3.19) has been calculated for the
nominal width of 1.4 μm and a width deviation ΔW of ±
0.2 μm. For the bending radius a
value of 75 μm has been chosen. The results are depicted in figure 3.27, which shows that the
polarisation converter is very sensitive to width deviations.
Side wall angle
During the etching of the waveguide using a CH 4 /H 2 -plasma, polymer deposition occurs on
top of the masking material, which results in broadening of the mask. The polymer can be
removed by descumming with oxygen after a limited time of etching. The etching process
therefore consists of a number of alternating descumming and etching steps. The ratio of the
etching and descumming time influences the side wall angle, which has been investigated by
our laboratory and is presented elsewhere [86].
If a short descumming time is used, the etched side wall will be close to vertical, as well as
being very rough. In order to obtain a smooth side wall and, consequently, low propagation
losses, a longer descumming time is required. This, however, results in a less steep side wall
and therefore a compromise has to be made.

3.8 Tolerance analysis 59
Conversion [%]
100
80
60
40
20
ΔW = -0.2 μm
ΔW = 0.0 μm
ΔW = +0.2 μm
0
0 20 40 60 80
Segment angle [deg]
Figure 3.27 Calculation of the polarisation converter performance with a 75 μm
bending radius for different waveguide width deviations ΔW.
Figure 3.28 shows a scanning electron microscope (SEM) picture of the cross section of a
deeply etched waveguide (1.2 μm deep). The etched side wall of the waveguide shows a
deviation from the vertical of 8 to 10 degrees. As a result, the field in the waveguide will follow
this interface, an effect which is used by other types of polarisation converter (see, e.g., [157]).
The effect of a non-vertical side wall has been analysed by making a staircase approximation
of the angled side wall using a small number of steps (3). In order to obtain the effective width
deviation, the overlap to a field of a waveguide with vertical side walls has been calculated. It
has been found that a side wall angle of 8 to 10 degrees has the same effect as a width deviation
of 0.1 to 0.2 μm for bending radii in the range of 50-100 μm. This is shown schematically in
figure 3.29.
Figure 3.28 SEM picture of the waveguide.

60 3. Polarisation conversion in waveguide bends
W W+ΔW
(a) (b)
Figure 3.29 Schematic diagram of width increase due to a non-vertical side wall:
the width of the mode in (a) is equal to the mode width of (b)
The performance of the polarisation converter has been calculated 1 with a side wall angle of
10 degrees taken into account, by using a width deviation of +0.2 μm. The results are shown as
lines in figure 3.30 for different radii of curvature. The measurement data are also depicted in
the figure as symbols (see also figure 3.20). The measurements and calculations correspond,
indicating that a non-vertical side wall angle has a large impact on the polarisation conversion.
Conversion [%]
100
80
60
40
20
R = 50 μm
R = 75 μm
R = 100 μm
R = 150 μm
0
0 20 40 60 80
Segment angle [deg]
Figure 3.30 Calculated polarisation converter performance for an increased
waveguide width of 0.2 μm (lines), together with measurement results (symbols).
The polarisation converters presented in this chapter have also been analysed by Lui et al. [78].
He solved the wave equations with a transformed index profile with a 2D mode solver. By
using the coupled-mode theory in combination with the initial field conditions and their first
derivatives in the direction of propagation, a solution can be obtained for the propagation
constant and the corresponding field. By taking the side wall angle into account, Lui obtained
1. By using the fact that a width deviation has the same effect as a non-vertical side wall
angle, the calculations can also be done with the MOL, as with the version available in our
laboratory only three lateral regions can be taken into account and therefore no staircase
approximation of the side wall angle can be used.

3.9 Avoiding polarisation conversion 61
beat length values of 100, 120 and 130 μm for bending radii of 50, 75 and 100 μm respectively
(measured values: 120,130, and 140 μm). In addition, his method also predicts a high
polarisation conversion. The values increase almost linearly from 65% to 85% when the
segment angle increases from 70 to 80 degrees. The bending radii at which these values are
obtained are slightly less than measured (40-60 μm). The predictions obtained with this
method are in the line with experimental data.
In view of the above results, it has been established that a variation of the side wall angle has a
large impact on the performance of the polarisation converter. The angle therefore should be
controlled accurately in order to be able to manufacture repetitively devices with a high degree
of polarisation conversion.
3.9 Avoiding polarisation conversion
To date design has been aimed at optimum polarisation conversion. In many cases, however,
polarisation conversion is highly undesirable. As the graphs of figure 3.23 suggest, large radii
provide a solution to this problem, but then the advantage of a deeply etched waveguide
structure is lost completely, so a solution for small radii must be found. The graph in figure
3.24 shows that the coupling efficiency from a TE- to a TM-polarised field at the junction
between a straight and a curved waveguide decreases with increasing waveguide width.
Further investigation reveals that the earlier mentioned WG modes show a negligible coupling
efficiency, even at very small radii. This is depicted in figure 3.31 for different waveguide
widths of the curved waveguide. The graph in figure 3.31a shows that even radii down to
40 μm can be applied with coupling efficiencies below -20 dB. This low TE-TM coupling is
obtained at the expense of rather high coupling losses for TE-TE coupling, which is the result
of the strong asymmetry of the WG mode (figure 3.31b). They can be minimised, however, to
values well below 0.5 dB, while still using very small bending radii. For instance, at a radius of
50 μm only 0.3 dB coupling loss is obtained with a curved waveguide width of 2.5 μm.
The fact that WG bends show negligible polarisation conversion is an important and newly
discovered feature of the deeply etched waveguide bends. This paves the way for
miniaturisation of components without having to cope with problems arising from polarisation
conversion. Furthermore, the polarisation conversion shows a negligible dependence on the
waveguide width (see figure 3.31a), which makes it very tolerant to variations in the
Coupling loss [dB]
0
-10
-20
-30
W = 2.5 μm
W = 3.0 μm
W = 3.5 μm
W = 4.0 μm
-40
20 40 60
Radius [μm]
80 100
-3
20 40 60
Radius [μm]
80 100
(a) (b)
Coupling loss [dB]
0
-1
-2
W = 2.5 μm
W = 3.0 μm
W = 3.5 μm
W = 4.0 μm
Figure 3.31 Coupling efficiency between a straight and a curved waveguide for
different widths of the curved waveguide: TE to TM (a), and TE to TE (b).

62 3. Polarisation conversion in waveguide bends
production process (e.g. side wall angle), and the coupling losses can be made sufficiently low
(see figure 3.31b) even at very small bending radii.
3.10 Conclusion
In this chapter the polarisation conversion occuring in deeply etched waveguide bends has
been discussed. Aiming at high conversion, a novel type of polarisation converter using deeply
etched narrow InP/InGaAsP ridge waveguide bends with small bending radii has been
analysed. The device has been produced and combines high polarisation conversion (>85%)
with low loss (2.7 dB) and compact device size ( μm2 975 ×
83 ). However, this type of
converter is difficult to produce repetitively because it is very sensitive to variations in the
waveguide structure.
On the other hand, in many cases polarisation conversion is not desirable. Calculations have
shown that the usage of whispering gallery bends can solve this problem. It has been shown
that when this type of bends is used even at very small bending radii (down to 40 μm), the
polarisation conversion is negligibly low. These bends are also tolerant to variations in the
width and, consequently, the side wall angle. Additionally, the coupling losses at junctions to
straight waveguides remain sufficiently low (a few tenths of dB’s). Therefore, they provide a
good solution to the miniaturisation of integrated optical components, without having to cope
with undesired polarisation conversion.

Chapter 4
Polarisation independent PHASAR
demultiplexers based on
nonbirefringent waveguides
A low-loss PHASAR demultiplexer based on raised-strip waveguides is described which has
been made polarisation independent by properly shaping the array waveguides in such a way
as to eliminate their birefringence. Furthermore, a method for further reducing the PHASAR
loss is presented and the influence of mode conversion on the cross talk of the device is
analysed. Finally, a packaged device integrated with photodetectors is described.
4.1 Introduction
In general, a waveguide produced in a semiconductor material has different propagation
constants for TE and TM polarisation. The result is a shift of the spectral responses with
respect to each other which is called polarisation dispersion. This is shown schematically in
figure 4.1 (see also section 2.2.4).
TMm+1 TMm+1 TMm TEm TMm-1 TEm-1 polarisation dispersion
wavelength
Figure 4.1 Schematic diagram of the periodic wavelength response of a phasedarray
demultiplexer with the polarisation dispersion indicated.

64 4. A polarisation independent PHASAR based on nonbirefringent waveguides
In order to eliminate the polarisation dispersion, it is obvious that the attention should be
focused on the waveguide itself. If the array waveguides are polarisation independent, the total
response of the array will be polarisation independent too. Waveguides can be made
polarisation independent by using a burried waveguide structure [11,123], or a raised-strip
waveguide [9,19,20,21,122, 164]. A comprehensive discussion of both structures with respect
to the tolerances is presented, together with experimental results of devices using the raisedstrip
waveguide (part of which have already been presented [164]). This can be found in
section 4.2. The experiments clearly demonstrate that polarisation independent behaviour can
be achieved over a large wavelength range. This is an important advantage of these
waveguides, together with low fibre-chip coupling losses and compact device dimensions.
The insertion loss of a phased-array demultiplexer is mainly determined by the fibre-chip
coupling losses and the losses at the transition between the array waveguides and the Free
Propagation Region (FPR) as described in section 2.2.6. An optical microscope image of the
transition is shown in figure 4.2. The fibre-chip coupling loss can be minimised by applying a
fibre-matched waveguide structure. The losses at the transition, however, are not reduced
easily.
Free
Propagation
Region
Array
Waveguides
Figure 4.2 Optical microscope image of the transition between the array
waveguides and the Free Propagation Region.
In theory, the best solution is to make the transition adiabatical, which means that the gap
between the array waveguides reduces gradually to zero. Due to the finite resolution of the
lithographic process, the gaps will not, however, be etched open completely leaving us with an
abrupt transition, which will introduce transition loss. Additionally, the gap obtained in this
way is not uniformly distributed along the array aperture (which can be seen clearly in figure
4.2), resulting in an increased cross talk level due to phase errors. The transition loss can also
be reduced by decreasing the confinement of the waveguides. At the transition, the fields of
adjacent array waveguides will overlap and the resulting sum field will have a smaller ripple,
leading to an increased overlap with the field in the FPR. However, as a decreased confinement
of the waveguide requires an increase of the minimum bending radius (and thus an increase of
the device size), this should be done locally at the transition using a two-step etching process.
We applied this method and demonstrated its effectiveness [33]. The method is discussed in
section 4.3.

4.2 Nonbirefringent waveguides 65
Usually, waveguides used in phased-array demultiplexers are monomode. If the first-order
mode is not cut-off, the cross talk performance of the demultiplexer can be deteriorated. At the
junction between a straight and a curved waveguide, a fraction of the fundamental mode will
couple to the first-order mode. Constructive interference of first-order modes in the array
waveguides can lead to the occurence of so-called “ghost” images at a different position in the
image plane. This shift in position corresponds to the difference in propagation constants
between the fundamental and first-order mode, the mechanism being equal to polarisation
dispersion. We will therefore denote this shift as the modal dispersion shift. We identified that
“ghost” images may contribute significantly to the cross talk of experimental devices. The
occurence of these “ghost” images is discussed in section 4.4. Also a method is suggested in
order to avoid them and experimental results are included.
Additionally, a waveguide detector structure for the raised-strip waveguide has been designed,
based on evanescent field coupling. Detectors of this type have been integrated with a
PHASAR demultiplexer and the resulting optical receiver has been packaged in an industrystandard
butterfly package. It is the first compact packaged InP PHASAR-based demultiplexer
with integrated detectors. This work has been presented at the ECOC’97 [137] and is described
in section 4.5.
It has been noted that the use of the raised-strip waveguide structures was proposed by
Amersfoort [7]. His work has been extended here with an elaborate analysis of the tolerances
and the performing of experiments, which include insertion loss [33] and cross talk decrease
(due to “ghost” images) [37], and the design and integration of detectors [137].
The work presented in this chapter has been carried out in cooperation with Philips
Optoelectronics Centre (POC) within the framework of the RACE 2070 MUNDI (Multiplexed
Network for Distributive and Interactive Services) project, and in the framework of the ACTS
AC028 TOBASCO (Towards Broadband Access Systems for CATV Optical networks) project.
4.2 Nonbirefringent waveguides
The most straightforward way to obtain polarisation independence is to make the array
waveguides polarisation independent by eliminating birefringence. Clearly, a square
waveguide embedded in a homogeneous medium with a constant refractive index, as shown in
figure 4.3a, is polarisation independent, as the index contrast is the same in both the transverse
and the lateral direction. But rectangular raised-strip waveguides, depicted in figure 4.3b, can
also be made polarisation independent by a proper choice of the aspect ratio (height/width) of
the waveguide core. The embedded square waveguide will be discussed in section 4.2.1, and
the raised-strip waveguide in sections 4.2.2 to 4.2.3.
InGaAsP
InP
W
(a)
Figure 4.3 The buried waveguide (a), and the raised-strip waveguide (b)
W
W
(b)
D

66 4. A polarisation independent PHASAR based on nonbirefringent waveguides
4.2.1 The embedded square waveguide
As monomode waveguides are preferred, we first look at the waveguide dimensions and the
composition of the quaternary layer in more detail. In figure 4.4 the V-parameter
2
2 1 2
( V k0W ( nInGaAsP – nInP) ) is depicted as a function of the waveguide width (and
thickness) and the composition of the quaternary layer. As can be seen in the picture, small
waveguide dimensions are needed for monomode operation (i.e. ): for quaternary
material with a band-edge wavelength higher than 1.12 μm the dimensions move into the
submicron range.
This puts rather stringent demands on the manufacturing feasibility of the photolithographic
process. In order to relax these demands, the index contrast between the quaternary layer and
the InP substrate can be minimised, which, on the other hand, will increase the radiation losses
in the bends.
⁄
=
V ≤ π
Band-edge Bandgap wavelength [μm]
1.30
1.25
1.20
1.15
1.10
1.05
1.00
0.95
π
2π
3π
1 2 3 4 5
Waveguide width [μm]
Figure 4.4 Contour plot denoting the V-parameter for a square waveguide, as a
function of the width (thickness) and the composition of the quaternary layer.
The radiation losses are depicted in figure 4.5 for different compositions of the quaternary
layer, the waveguide dimensions for each of which have been adjusted according to figure 4.4
to obtain monomode operation. The graph shows that small bending radii are possible if a high
index contrast is applied, but, consequently, with small waveguide dimensions. On the other
hand, a low index contrast leads to an increase of the waveguide dimensions, and, additionally,
the bending radius. Although this waveguide is tolerant to dimensional variations as
demonstrated by Soole et al. [123], it requires accurate control of the composition of the
quaternary layer and an increased complexity of the fabrication process due to an additional
epitaxial growth step, during which small gaps between relatively thick and wide waveguides
have to be filled completely (for instance at the junction between the FPR and the array
waveguides).
4π
5π
2π
6π
4π
7π
5π
3π

4.2 Nonbirefringent waveguides 67
Radiation loss [dB/90]
100.000
10.000
1.000
0.100
0.010
0.001
4.2.2 The raised-strip waveguide
Q(0.95)
Q(1.00)
Q(1.05)
Q(1.10)
200 400 600 800 1000
Bending radius [μm]
Figure 4.5 Radiation loss versus bending radius for monomode square
waveguide for different compositions of the quaternary layer. (Q(0.95) denotes
quaternary material with a band-edge wavelength of 0.95 μm.)
The rectangular raised-strip waveguide, which is shown in figure 4.3b, does not require an
epitaxial regrowth and has the advantage that it allows for small bending radii and,
consequently, compact design, due to the high lateral index contrast, even with a small GaAsfraction
in the quaternary layer (low contrast). Additionally, it can be made relatively wide and
thick (ideal for small fibre-chip coupling loss) and still maintain its monomode nature.
The basic principle is that the birefringence induced by the asymmetry in lateral and transverse
index contrast is compensated by a small correction of the aspect ratio (height/width) of the
waveguide core. As the penetration depth of the field is larger for TE polarisation than for TM
polarisation, the waveguide should be made slightly wider than high in order to obtain identical
field distributions and propagation constants. This was demonstrated by Chiang [26], who presented
a simple equation for the correct width of the waveguide core needed to obtain polarisation
independence, which is based on the fact that the modal field distributions in a waveguide
with high index contrast can be approximated by a sine function:
2
nQ 2 2
2πn Q N TE
– 1
W = λ ---------------------------------------------
2
( – )
whereby n Q is the refractive index of the quaternary layer, and N TE and N TM are the transverse
effective indices in the centre region for TE and TM polarisation respectively. Due to the high
lateral index contrast, a mode close to cut-off will radiate into the substrate, which can be
examined by using Marcatili’s approximation for the propagation constant [80]:
β 2
2 2
konQ 2
kx with N x being the effective index in the centre region, and k o , k x and k y the wave numbers in
vacuum in the transverse and the lateral direction respectively. Due to the high lateral index
2
N TM
2 2
N x
1 ⁄ 3
(4.1)
= – – ky = ko – k (4.2)
y
2

68 4. A polarisation independent PHASAR based on nonbirefringent waveguides
contrast, the lateral field distribution may be approximated by a sine function, with which we
find for the lateral wavenumber:
k y
( m + 1)π
= ---------------------
whereby m is the lateral mode number. Using the above equations, combined with the fact that
the cut-off condition occurs when the mode index becomes less than the substrate index n InP ,
we find for the cut-off width W m of the lateral mode m:
W m
According to this equation, for each mode that propagates in the waveguide, a relation between
waveguide width and thickness can be calculated for which the mode index equals the
substrate index. This relation is called the cut-off condition, and the cut-off conditions of the
three lowest-order modes are shown in figure 4.6 for a Q(0.97) and a Q(1.02) waveguide layer.
The cut-off conditions are almost identical for TE and TM polarisation. Monomode operation
is possible for a wide range of waveguide widths, as depicted by the hatched area in the figure.
Also shown in the graph is the zero birefringence condition denoted by Δλ pol = 0. A proper
choice for the waveguide width and thickness is one close to the maximum allowed value for
monomode operation [39]. The field at the side walls will then be minimal, which will reduce
the scattering losses.
Width Q(0.97) [μm]
5
4
3
2
TE TE/TM 00 /TM 00
TE TE/TM 10 /TM 10
TE TE/TM 01 /TM 01
1
1 2 3
Thickness Q(0.97) [μm]
4 5
The dependence of the zero-birefringence condition on the composition of the quaternary
material is shown in figure 4.7. It has been calculated for the correct aspect ratios for a Q(0.97)
and a Q(1.02) guiding layer (because both types have been used for experiments), which are of
3.4 μm and 3.0 μm width respectively with a 2.2 μm waveguide thickness. In this figure it can
be seen that the raised-strip waveguide is rather insensitive to variations in the composition of
the quaternary layer.
W m
( m + 1)λ
= -----------------------------
2 2
2 N x – nInP
Width Q(1.02) [μm]
(a) (b)
5
Δλ Δf pol = 0 Δλ Δf pol = 00
4
3
2
(4.3)
(4.4)
TE TE/TM 00 /TM 00
TE TE/TM 10 /TM 10
TE TE/TM 01 /TM 01
1
1 2 3
Thickness Q(1.02) [μm]
4 5
Figure 4.6 Raised-strip waveguide cut-off conditions for a Q(0.97) layer (a) and
a Q(1.02) layer (b). The hatched area denotes the monomode region. The line
with TE ij /TM ij denotes as a function of the thickness the width, for smaller values
of which the i-th transverse and j-th lateral TE and TM mode are cut-off.

4.2 Nonbirefringent waveguides 69
A good strategy for designing a tolerant waveguide structure (from a production feasibility
point of view) is to choose the InGaAs-fraction of the quaternary layer as low as possible (i.e.
low band-edge wavelength). This follows directly from the graphs (a) and (b) of figure 4.8,
where it can be seen that the sensitivity of the birefringence to width and thickness variations
increases rapidly with increasing InGaAs-fraction. For each composition of the quaternary
layer, the calculations have been performed on waveguides with dimensions close to the
maximum allowed values for monomode operation.
Δλ pol [nm]
Δλ pol [nm]
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
4.2.3 Experimental results
W/D = 3.4/2.2
W/D = 3.0/2.2
Q(0.97)
Q(1.02)
-0.25
0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30
Band-edge Bandgap wavelength wavelength [μm]
Figure 4.7 Composition dependence of the zero-birefringence condition.
1.0
0.5
0.0
-0.5
-1.0
Q(0.95)
Q(1.00)
Q(1.05)
Q(1.10)
-0.4 -0.2 0.0 0.2 0.4
ΔW [μm]
(a) (b)
-0.4 -0.2 0.0 0.2 0.4
ΔD [μm]
Figure 4.8 Waveguide width (a) and thickness (b) dependence of the zerobirefringence
condition.
A 8-channel raised-strip-waveguide-based PHASAR has been designed and produced in
cooperation with Philips Optoelectronics Centre (POC) [164]. The raised-strip waveguide was
designed for polarisation independence for a Q(0.97) guiding layer, and therefore the width
and thickness were chosen at 3.4 μm and 2.2 μm respectively. Additionally, due to its large
Δλ pol [nm]
1.0
0.5
0.0
-0.5
-1.0
Q(0.95)
Q(1.00)
Q(1.05)
Q(1.10)

70 4. A polarisation independent PHASAR based on nonbirefringent waveguides
core dimensions, this strip waveguide allows for a high coupling efficiency (loss dB) to a
lensed fibre. The channel spacing was designed at 2.0 nm (250 GHz) at a centre wavelength of
1536 nm, determined by the specifications of the RACE 2070 MUNDI project. The gap
between the array waveguides was chosen at 0.8 μm (da = 4.2 μm), the smallest feasible gap
size in order to minimise device dimensions. The gap between the receiver waveguides was
chosen at 1.5 μm (dr = 4.9 μm), which is sufficient to achieve a theoretical channel isolation
better than -40 dB. The resulting array size is mm2 , measured between object and
image plane, and the overall device size is mm2 ± 1
1.4 × 1.7
2.6 × 2.3 . A microscope photograph of the
device is shown in figure 4.9.
Figure 4.9 Microscope photograph of the realised PHASAR with raised-strip
waveguides.
Low-pressure OMVPE (Organo-Metallic Vapour Phase Epitaxy) has been used to grow the
undoped guiding layer and RIE (Reactive Ion Etching) using Cl 2 has been applied to etch the
waveguides with smooth side walls for low propagation loss. This loss is 2-3 dB/cm for both
TE and TM polarisation and no radiation loss could be measured on curved waveguides using
a Fabry-Pérot measurement technique [168] on uncoated waveguides.
The measured response is depicted in figure 4.10a for both TE (solid lines) and TM
polarisation (dashed lines). The cross talk is better than -25 dB and the on-chip loss is 4-5 dB.
The figure clearly shows a polarisation independent behaviour and a polarisation independent
on-chip loss. To demonstrate the large bandwidth of polarisation independence, the response of
a single channel was measured in different wavelenght windows, corresponding with different
orders (43, 44, and 45). The measured FSR of 32 nm corresponds with the design value of
33 nm. Polarisation independence was measured over a wavelength span of 64 nm, determined
by the maximum wavelenght span of the tunable laser. From these measurements, as depicted
in figure 4.10b, another important feature of this PHASAR becomes evident, which is the
wavelength independent insertion loss.

4.3 Loss reduction 71
On-chip loss [dB]
0
-10
-20
-30
-40
1510 1515 1520 1525 1530
Wavelength [nm]
4.2.4 Conclusions
In this section the method for obtaining polarisation independence by using nonbirefringent
waveguides has been presented. Two waveguide structures were analysed: the embedded
square waveguide and the raised-strip waveguide. The first has the advantage that it is
inherently polarisation independent, due to the identical lateral and transverse index contrast.
For low-contrast waveguides, however, the bending radius becomes unpractically large,
whereas the size of high-contrast waveguides gets into the submicron range, which puts
stringent demands on the lithography. Additionally, an expitaxial regrowth is needed. The
raised-strip waveguides at the other hand only need one single etching step for the production.
Furthermore, they can be made relatively wide and thick, while maintaining their monomode
nature. Also small bending radii can be used (even with a small GaAs-fraction in the guiding
layer) due to the high lateral index contrast. Both structures have low fibre-chip coupling losses
due to the circular mode profile, which gives a good match to the fibre mode. The raised-strip
waveguide, however, has a higher potential for application because compact devices can be
produced with a relatively simple manufacturing process.
4.3 Loss reduction
(a) (b)
A significant part of the phased-array loss occurs at the junction between the array waveguides
and the FPR. At this junction the field in the waveguide section shows a very deep modulation
(figure 2.10a, solid line) caused by the trenches between the array waveguides. Due to the
ripple in the field pattern, a considerable fraction of the power is diffracted into adjacent
orders. As the coupling efficiency is found from the overlap of the sum field of the array
waveguides and the far field (dashed line), filling the zeros between the individual waveguide
modes (figure 2.10b, solid line) allows for an increase of the coupling efficiency. This can be
obtained by the insertion of a shallowly etched transition region (TR) between the deeply
etched array waveguides and the FPR [33]. This method has successfully been applied earlier
to waveguide bends in order to reduce the bending and scattering losses [102].
On-chip loss [dB]
0
-10
-20
-30
-40
1480 1482 1511 1513
Wavelength [nm]
1544 1546
Figure 4.10 Measured wavelength response of all channels (a), and of a single
channel for different orders of operation (b), both for TE (solid lines) and TM
polarisation (dashed lines).

72 4. A polarisation independent PHASAR based on nonbirefringent waveguides
AW
TR
FPR
3.0 μm 1.0 μm
The coupling from the FPR to the array waveguides and vice versa now takes place in two
steps: (1) at the junction between the TR and the array waveguides (AW), and (2) at the
junction between the TR and the FPR. Clearly, the first coupling becomes less efficient when
the TR thickness t is increased, whereas at the same time the second one becomes more
efficient, and therefore an optimum in the combined coupling efficiency can be found as shown
in figure 4.12a (solid line).
In this graph the calculated coupling losses (for TE polarisation) are depicted for a 2.2 μm
thick, 3.0 μm wide polarisation independent raised strip waveguide [164] with a band-edge
wavelength of the quaternary (InGaAsP) layer of 1.02 μm. The dashed line denotes the
coupling loss between the FPR and the TR (FPR-TR), and decreases to zero with increasing t.
The coupling loss between the TR and the array waveguides (TR-AW) on the other hand,
increases with increasing t as depicted by the dotted line. The combined coupling loss is
denoted by the solid line. The total coupling loss without TR (i.e. t = 0 μm) is 3.5 dB.
Coupling loss [dB]
2.5
2.0
1.5
1.0
0.5
2.2 μm
Figure 4.11 Schematic topview (left) and cross section (right) including fields of
the transition region (TR) between the FPR and the array guides (AW).
FPR-TR
TR-AW
Total
0.0
0.5 1.0 1.5 2.0
TR thickness t [μm]
Coupling loss reduction [dB]
2.5
2.0
1.5
1.0
0.5
t
TE
TM
0.0
0.5 1.0 1.5 2.0
TR thickness t [μm]
(a) (b)
Figure 4.12 Coupling losses versus TR film thickness t for TE-polarisation (a),
and the total predicted loss reduction (b) for TE (solid line) and TM polarisation
(dashed line). The experimentally measured reduction is depicted by a diamond
(TE) and a triangle (TM).

4.4 Ghost images 73
In figure 4.12b the total loss reduction is shown for both TE and TM polarisation. The
optimum predicted loss reduction is 2.2 dB for TE polarisation, and 1.9 dB for TM polarisation
with t = 1.1 μm. Two PHASAR demultiplexers have been produced, one of which was used for
the double etch experiment [33]. The length of the TR was chosen at 10 μm, which is - according
to BPM simulations - sufficiently short to get rid of the radiation modes excited at the first
junction. The waveguide has a propagation loss of 2 dB/cm, both for TE and TM polarisation.
Due to the high lateral index contrast, small bending radii (200 to 500 μm) can be used, giving
an array size of mm2 1.0 × 1.3 , measured between object and image plane. The overall device
size is mm2 1.2 × 3.2 as the input and output waveguides are positioned with a 250 μm pitch
for tapered fibre ribbon coupling. The measured improvement of the insertion loss is shown in
the graph: 1.7 dB for TE polarisation and 1.3 dB for TM polarisation, which is only 0.6 dB less
than predicted.
4.4 Ghost images
The measured response of the second PHASAR demultiplexer produced as depicted in figure
4.13, shows considerably high peaks at unexpected positions. These peaks are denoted by
circles in the figure and are further referred to a “ghost” images. As these “ghost” images
contribute significantly to the cross talk of the device, it is of crucial importance to find and
eliminate the cause. After rejecting several possibilities (such as multiple reflections within the
device), we came to the conclusion that the ghost images are caused by mode conversion
within the phased array. During the first experiments with the epitaxial growth of the wafer at
POC, it was found that the band-edge wavelength of the quaternary material was 1.02 μm
instead of the requested 0.97 μm. Together with the used (design) thickness of 2.2 μm, the
width had to be fixed to 3.0 μm in order to make the waveguides polarisation independent. The
resulting waveguide structure turned out to carry three modes (see figure 4.6b). In this section
we will first discuss how mode conversion may cause ghost images. Then the experiments will
be described which we carried out to verify this hypothesis.
Transmission [dB]
-30
-40
-50
-60
-70
1520 1525 1530 1535
Wavelength [nm]
Figure 4.13 Ghost images (circles) in the response for TE (solid) and TM
polarisation (dashed).

74 4. A polarisation independent PHASAR based on nonbirefringent waveguides
4.4.1 Ghost image mechanism
Due to the high lateral contrast, the first-order mode experiences low radiation loss in the
curved waveguides. This first-order mode can be excited at discontinuities along the path of
propagation through the phased array. As the group index (see equation 2.4) is different for the
first-order mode, the dispersion will be different as well. The result is a “ghost” image, shifted
in position along the image plane with respect to the original image. These ghost images,
marked by a circle in figure 4.13, may couple into an undesired receiver waveguide, resulting
in an increased cross talk level. This shift in position along the image plane corresponds to a
shift in the wavelength response and is due to the difference in propagation constants between
the fundamental and first order mode, analogous to what is found for polarisation dispersion.
This wavelength shift will therefore be denoted as modal dispersion shift and can be calculated
in exactly the same manner as for the polarisation dispersion shift according to equation 2.18.
As the index of the first-order mode is smaller than the index of the fundamental mode, a
positive modal dispersion shift is obtained, which means that the ghost image occurs at a
shorter wavelength with respect to the original image. Furthermore, the index difference
between the first-order mode and the fundamental mode is smaller for TM polarisation than for
TE polarisation. The result is that the modal dispersion shift for TM polarisation is smaller
than for TE polarisation.
transmitter
waveguide
input
aperture
FPR
4
3
object
image
5 plane
plane 1
For a more comprehensive analysis of the occurrence of these ghost images, a path through the
phased array is considered as shown in figure 4.14. In this schematic diagram the positions at
which excitation of the first-order mode (through mode conversion) may occur are marked
with a circle. The positions will be discussed consecutively, the numbering of which follows
those of figure 4.14.
1. At this position the cross talk performance is not degraded. The first order mode may distort
further signal operations.
2. In this case the signal traverses the array almost completely as a fundamental mode, except
for the small straight section, where a fraction is converted to a first-order mode. Therefore,
only over a small part the phase transfer is disturbed and the image will remain almost in its
original place along the image plane.
3. In the same way as above, the phased array has now only traversed over a small straight
section length as a fundamental mode and almost completely as a first-order mode. The
2
output
aperture
FPR
receiver
waveguide
Figure 4.14 Schematic diagram of a path through the phased array, with the
positions (marked by a circle) where first order mode excitation is expected.

4.4 Ghost images 75
phase transfer, therefore, is determined by the first-order mode and the image will be shifted
in position along the image plane with respect to the original one.
4. At this position it is very unlikely that mode conversion will occur, as the far-field of the
transmitter waveguide can be treated locally as a uniform field. However, an estimation of
the excitation coefficient of the first-order mode can be made using a Gaussian
approximation. This is discussed in Appendix E. The result is that the first-order excitation
at this position is well below -50 dB and may therefore be neglected.
5. Excitation of the first-order mode at this point (or at the fibre-chip junction, the effect being
the same) will result in a mixed field (consisting of the fundamental and first-order mode) at
the object plane. As the PHASAR is an imaging device, this field will be reproduced at the
image plane at the position of the original image without affecting the dispersion properties
of the array.
4.4.2 Verification
The assumption that the occurrence of ghost images is caused by excitation of first-order
modes in the phased array has been verified by two experiments. Firstly, as the response of the
demultiplexer is periodical, so should the occurrence of the ghost images. This can be seen
clearly in figure 4.15. In this graph the response of a PHASAR demultiplexer (the same device
of which the response is shown in figure 4.13) is shown over the full wavelength span available
by the tunable laser source. The modal dispersion shift is denoted as Δλ 01,TE and Δλ 01,TM for
TE and TM polarisation respectively. (The non-constant cross talk level is due to the increased
spontaneous emission of the tunable laser, occurring when operating near the limits of its tuning
range.) The predicted modal dispersion shift is 13.5 nm for TE polarisation and 12.2 nm
for TM polarisation, which compares well to the measured modal dispersion shift of
Δλ 01,TE = 16.0 and Δλ 01,TM = 10.8 nm.
Transmission [dB]
-25
-30
-35
-40
-45
-50
-55
-60
-65
Δλ 01,TM
Δλ 01,TE
1460 1480 1500 1520 1540 1560 1580
Wavelength [nm]
Figure 4.15 Response over the full wavelength span of the tunable laser for TE
(solid line) and TM (dashed line) polarisation.
The second verification is described as follows. The field obtained at the image plane is the
sum field of the far fields of all individual array waveguides (see section 2.1.3). Therefore, if
the wavelength is changed, the image will move through the image plane and follow the

76 4. A polarisation independent PHASAR based on nonbirefringent waveguides
envelope described by the far field of the individual array waveguides. In the case of a ghost
image, this envelope has the shape of the far field of the first-order mode. Figure 4.16a
schematically shows the far field of the first-order mode, which has a similar shape as the
modal field: two maxima with a minimum in the centre.
array
waveguides
minimum
maximum
receiver
output
waveguides
aperture free
propagation
region
image
plane
field
intensity
The assumption that ghost images originate from the presence of a first-order mode can
therefore be verified by measuring the peak power in the ghost image in relation with the
power in the original peak for all receiver waveguides. For the receiver waveguides placed in
the centre of the image plane, the ghost peak level should have a minimum, whereas the level
should increase quadratically towards the outer receiver waveguides. Figure 4.16b shows the
measured ghost peak level for TE polarisation versus receiver waveguide number. The
quadratic behaviour of the ghost peak level can be clearly observed.
4.4.3 Junction optimisation
(a) (b)
1 2 3 4 5 6 7 8
Receiver waveguide number
Figure 4.16 The far-field intensity distribution of a first-order mode (a), and the
ghost peak level with respect to the passband peak level for the eight output
waveguides (b).
From the analysis presented in the previous section it is apparent, that mode conversion must
be minimised. This can be done by optimising the offset at the junctions not on maximal
coupling for the fundamental mode, but on minimal first-order mode excitation according to
the strategy presented in section 2.2.9 (equation 2.35). The bending radius nor the length of the
straight section have changed, and therefore the phase transfer of the array is not influenced.
As an example the strategy is applied to the raised-strip waveguide, at a thickness of 2.2 μm
and a width of 3.0 μm especially designed for polarisation independence of a Q(1.02) guiding
layer. The bending radius was chosen at 500 μm. In figure 4.17 the efficiency of the coupling
between the fundamental mode of the straight waveguide to the fundamental and first-order
mode in the curved waveguide is shown.
From this graph it can be seen that a first-order coupling efficiency to a TM-polarised mode of
-25 dB is obtained if the offset is optimised to optimum coupling for the fundamental TEpolarised
mode. An optimum offset cannot be found for both polarisations simultaneously, so
that a compromise has to be made. This compromise can be found between the optimum
offsets for each polarisation (120-150 nm), i.e. 135 nm. In any case the maximum excitation of
the first-order mode is below -30 dB and the coupling loss for the fundamental order remains
Ghost peak level [dB]
-14
-16
-18
-20
-22
-24
-26

4.4 Ghost images 77
negligibly low. Figure 4.18 shows the sensitivity of the coupling efficiency to the waveguide
width. If width variations of ± 0.2 μm are taken into account, which is a realistic value for
high-quality lithographic techniques, it shows that the first-order coupling efficiency increases
rapidly, but it remains below an acceptable level of -25 dB.
Offset [nm]
250
200
150
100
Zero-order coupling efficiency [dB]
0.00
-0.05
-0.10
-0.15
4.4.4 Experimental results
-0.20
-50
0 50 100
Offset [nm]
150 200
Figure 4.17 Zero and first-order coupling efficiencies for TE (solid lines) and
TM polarisation (dashed lines).
-20
-30
-40
-50
-50
-30
50
-0.2 -0.1 0.0
ΔW [μm]
0.1 0.2
-30
-40
-50
-40
-30
-40-50
(a) (b)
A 8-channel raised-strip-waveguide-based PHASAR-demultiplexer with optimised junctions
has been designed and produced in cooperation with POC [37]. The device is identical to the
one used in a previous experiment (see section 4.3). The response was measured using a
tunable laser for both TE (solid lines) and TM (dashed lines) polarisation, and is depicted in
figure 4.19. The cross talk is better than -23 dB and the insertion loss is 8-10 dB (including
fibre-chip coupling loss of ±
1 dB), 1.5 dB of which due to waveguide losses. As can be seen in
the graph, no ghost images are observed.
Offset [nm]
250
200
150
100
-20
-30
-40
-50
-50
-30
0
-10
-20
-30
-40
First-order coupling efficiency [dB]
50
-0.2 -0.1 0.0
ΔW [μm]
0.1 0.2
-30
-40
-50
-40
-30
-40-50
Figure 4.18 Sensitivity of the first-order coupling efficiency to the waveguide
width for TE (a) and TM polarisation (b).
-20

78 4. A polarisation independent PHASAR based on nonbirefringent waveguides
Insertion loss [dB]
4.4.5 Conclusions
0
-10
-20
-30
-40
-50
1510 1515 1520
Wavelength [nm]
1525 1530
Figure 4.19 Measured response of a phased-array demultiplexer with optimised
junctions for TE (solid) and TM (dashed) polarisation (channel 8 defect). The
graph shows an increasing TE-TM shift (from zero to 0.4 nm) to lower
wavelengths. This is due to an increasing temperature during measurements, as
first the TE response was measured from left to right and consecutively the TM
response from right to left.
The occurence of ghost images in the response of phased-array demultiplexers has been
analysed. Measurement results confirm that they originate from first-order modes excited at
junctions between straight and curved waveguides in the array. It has been experimentally
demonstrated that ghost images can be reduced by optimising the waveguide junctions.
4.5 Demultiplexer integrated with detectors
This section describes the integration of a raised-strip-guide-based PHASAR demultiplexer
with detectors. A detector based on evanescent field coupling is used, based on our experience
with this type of detector [7]. It is relative easy to produce as no expitaxial regrowth is required
and only an additional wet-chemical etching step is required to define the detector mesas. A
schematic diagram of the detector is shown in figure 4.20. In this detector, the InGaAs
absorption layer is sandwiched between n- and p-type layers, thereby forming a p-i-n
configuration. The light from the waveguide is coupled into the absorption layer, where
electron-hole pairs are created. The coupling efficiency between the guiding and the absorbing
layer is improved by inserting an InGaAsP(1.3) layer in between them, which acts as an antireflection
layer. For the optimisation of the layer thickness, modal propagation analysis has
been used. Figure 4.21 shows the field propagation in the xz-plane for TE polarisation. From
this figure it can be seen that at a detector length of 200 μm, more than 90% of the optical
power is absorbed.

4.5 Demultiplexer integrated with detectors 79
X
Z
p-InGaAsP(1.3)
p-InP
InGaAs(1.67)
InGaAsP(1.3)
InGaAsP(1.0)
n-InP substrate
0.4 μm
0.1 μm
0.3 μm
A 8-channel raised-strip-waveguide-based PHASAR with integrated detectors has been
designed and produced in cooperation with POC [137]. The width and thickness were chosen
at 3.0 μm and 2.2 μm respectively in order to obtain polarisation indepent waveguides using a
Q(1.02) guiding layer. The channel spacing was designed at 200 GHz at a centre wavelength of
1535 nm, determined by the specifications of the ACTS AC028 TOBASCO project. The array
size is mm 2 1.4 ×
1.3 , measured between object and image plane. The detectors are 8 μm wide
and 200 μm long and use a common n-type bottom contact. On top of the detectors a 6 μm
wide p-type contact is placed prior to which a Si 3 N 4 isolation layer is deposited. A microscope
photograph of the device produced is shown in figure 4.22.
Au
Pt
0.5 μm
0.4 μm
0.3 μm
2.2 μm
Figure 4.20 Schematic representation of the layer structure which has been used
for the integrated waveguide detector.
x-direction [μm]
4
2
0
0.60
0.50
0.40
0.30
0.20
0.10
0.50
0.50
0.300.40
0.10
0.10
0.20 0.20
0.60 0.70
0.40
0.40
0.30
0.20
0.30
0.10
0.20
0.20
0.10
0.10 0.10
0.10
-2
0 50 100
z-direction [μm]
150 200
Air
Au
InP
Pt
InGaAsP(1.3)
InP
InGaAs
InGaAsP(1.3)
InGaAsP(1.0)
Figure 4.21 Field distribution in the detector structure for TE polarisation.

80 4. A polarisation independent PHASAR based on nonbirefringent waveguides
Figure 4.22 Microscope photograph of PHASAR demultiplexer integrated with
detectors.
The response at 1 mW unpolarised input power was measured and is shown in figure 4.23a.
Problems with the Si 3 N 4 isolation layer are the cause of the low external efficiency of the
detectors (-13 dB, leading to an overall insertion loss of -21 dB including the 8 dB insertion
loss of the PHASAR) and the large background of one of the channels.
Photo current [μA]
10.00
1.00
0.10
0.01
1520 1525 1530
Wavelength [nm]
1535 1540
(a) (b)
1525 1530 1535 1540
Wavelength [nm]
Figure 4.23 Measured photo current versus wavelength before (a) and after (b)
packaging.
Subsequently, the wafer was cleaved into dies of mm 2 , an AR coating was applied to
the front facet and the device was mounted on a Si submount and a mm 2 3, 5 × 3
6 ×
6 carrier. The
fibre was aligned and fixed by soldering it on a base plate mounted stud in front of the carrier.
Finally, the assembly has been mounted on a Peltier cooler inside a 14-pin industry-standard
butterfly package. The device is shown in figure 4.24. It is the first compact packaged InP
PHASAR-based demultiplexer with integrated detectors. The response measured after
Photo current [μA]
10.00
1.00
0.10
0.01

4.6 Discussion 81
packaging is depicted in figure 4.23b and is only 1 dB below that of the unpackaged device,
which is due to a slighlty larger coupling loss. Using the Peltier cooler, the temperature has
been set at 55° C in order to shift the wavelength response to the required TOBASCO
specifications.
Figure 4.24 First 8-channel butterfly-type PHASAR module.
4.6 Discussion
In this chapter the design and experiments of PHASAR demultiplexers based on raised-strip
waveguides is described. The device has been made polarisation independent by properly
shaping the array waveguides in such a way as to eliminate their birefringence. It is
demonstrated that with this waveguide structure polarisation independence over a wide
wavelength range can be obtained. Further, a method for further reducing the PHASAR loss is
presented. With this method, for which only an additional etching step is required, a loss
reduction in the order of 1.5 dB is possible. The influence of mode conversion on the cross talk
of the device is analysed. It is demonstrated that mode conversion is the cause of the occurence
of so-called “ghost” images in the response, which leads to increased cross talk. However, the
mode conversion can easily be minimised by properly designing the junctions between the
straight and curved array waveguides. Finally, the integration of a PHASAR demultiplexer
with detectors in a raised-strip waveguide structure has been demonstrated. In addition, the
device has been packaged, resulting in the first compact packaged InP PHASAR-based
demultiplexer with integrated detectors in a 14-pin industry-standard butterfly package.

82 4. A polarisation independent PHASAR based on nonbirefringent waveguides

Chapter 5
Polarisation independent PHASAR
demultiplexers based on
birefringent waveguides
A PHASAR demultiplexer produced in a conventional double-hetero structure, which has been
made polarisation independent by inserting a polarisation dispersion compensating section, is
described in this Chapter. In addition, two other methods for making PHASAR demultiplexers
polarisation independent are introduced and analysed.
5.1 Introduction
A number of methods can be applied in order to eliminate polarisation dispersion and will be
discussed in this Chapter. The first attempt to do this was based on matching the Free Spectral
Range (FSR) to the polarisation dispersion (see figure 5.1). It was suggested by Vellekoop and
Smit [127,133], and also applied by Spiekman et al. [162,163] and Zirngibl et al. [177]. This
method, also known as the so-called “order trick”, is simple from a design point of view. If the
FSR is chosen equal to the polarisation dispersion as shown in figure 5.1, the m-th order beam
for TE polarisation overlaps with the TM-polarised beam of order m-1, and the device will
therefore be virtually polarisation independent. The disadvantage of this method lies in the fact
that the total wavelength range available for the WDM channels is restricted by the polarisation
dispersion, which is for conventional InGaAsP/InP DH waveguide structures in the order of 4-
5 nm. Additionally, Spiekman [134] showed that this method, although very tolerant to etch
depth variations, is very sensitive to waveguide width and layer thickness variations: a layer
thickness variation of 3% or a waveguide width variation of ±
0.2 μm will cause a shift of
0.2 μm between the TE and TM responses. These tolerances, however, can be relaxed if the
wavelength response is flattened.
In section 5.2 and 5.4 two alternative approaches for obtaining polarisation independence
based on polarisation conversion and polarisation splitting respectively are briefly discussed.

84 5. Polarisation independent PHASARs based on birefringent waveguides
TMm+1 TMm+1 TMm TEm TMm-1 TEm-1 polarisation dispersion
FSR
wavelength
Figure 5.1 Schematic diagram of the periodic wavelength response of a phasedarray
demultiplexer with the FSR and polarisation dispersion depicted.
5.2 Polarisation dispersion compensation
In the previous chapter it has been demonstrated that polarisation independent behaviour can
be achieved over a large wavelength range for compact PHASAR demultiplexers emplyoing a
raised-strip waveguide structure (see section 4.2.3). Another broad-band solution to obtain
polarisation independence is found in compensation of the polarisation dispersion. This can be
done by inserting a waveguide section with a different birefringence in the phased array as
shown in figure 5.2. If the waveguides in the shaded area have a polarisation dispersion
different from the dispersion in the unshaded region, the total polarisation dispersion of the
device can be cancelled, provided that the shape of the shaded area has been properly chosen.
Figure 5.2 Schematic diagram of a PHASAR demultiplexer with polarisation
dispersion compensation.

5.2 Polarisation dispersion compensation 85
The operation can be explained by considering the phase transfer difference ΔΦ between two
adjacent waveguides, where at one of which a section with length δL and a different
birefringence has been inserted (see figure 5.3):
whereby N eff and n eff are the effective mode indices of the original waveguide and the
compensation section respectively. It can be easily verified that ΔΦ becomes polarisation
independent if δL is chosen according to:
with:
i+1
i
δL
The whole array can be made polarisation independent by inserting a section with length δL in
the first waveguide, 2δL in the second one, 3δL in the third one, and so on. The compensation
section will thus obtain a triangular shape and its total length will amount to NaδL whereby Na is the number of array waveguides. The method applies for both positive and negative values of
Δn/ΔN. For values close to 1, the compensation section will become excessively long. A
disadvantage is that ΔN and Δn are very sensitive to film thickness and waveguide width, so the
compensation requires tight control of these parameters. This will be discussed in the next section.
Absolute compensation of the polarisation dispersion (as demonstrated by Steenbergen et al.
[141]) can be achieved if the following design and production stategy is used. First, a
PHASAR demultiplexer is produced without the dispersion correction and the TE-TM shift is
measured. From the measured TE-TM shift, the compensation section length is calculated and
the correction is applied. In this way, effects of layer thickness variations from one wafer to
another can be eliminated.
Additionally, the insertion of a waveguide section gives rise to a shift of the centre wavelength.
This can be seen by taking ΔΦ = 2πm in equation 5.1. The resulting centre wavelength λc' is
then found as:
whereby the first term denotes the original centre wavelength, and the second term the shift. It
is noted that this shift depends on the polarisation, just as the original centre wavelength.
L i
L i +ΔL
Figure 5.3 Schematic diagram of the polarisation dispersion compensation
principle.
ΔΦ = ko[ N effΔL + δL( N eff – neff) ]
Δn
δL = ΔL ⁄ ⎛------- – 1⎞
⎝ΔN ⎠
ΔN = N eff,TE – N eff,TM
Δn = neff,TE – neff,TM ΔL
λc' N eff ⋅ ------ ( N
m eff – neff) δL
= +
⋅ ----m
(5.1)
(5.2)
(5.3)
(5.4)

86 5. Polarisation independent PHASARs based on birefringent waveguides
5.2.1 Production tolerance analysis
For the tolerance analysis of the polarisation dispersion compensation method, we use the
ridge waveguide structure as depicted in figure 5.4a. It consists of a 600 nm thick InGaAsP
guiding layer on an InP substrate with a 300 nm thick InP cladding layer. The ridge width is
2 μm and the etch depth is chosen at 400 nm, i.e. 100 nm into the guiding layer. This allows for
the usage of sufficiently short bending radii (500 μm) and, therefore, compact device
dimensions.
100 nm
2 μm
InP
InGaAsP(λ g = 1.3 μm)
InP substrate
300 nm
600 nm
2 μm
InGaAsP(λ g = 1.3 μm)
InP substrate
(a) (b)
Figure 5.4 Waveguide structures as used for the polarisation dispersion
compensation: the original waveguide structure (a) and the waveguide structure in
the compensation section.
As the polarisation dispersion can be enlarged by removing the InP cladding layer, we used the
structure as depicted in figure 5.4b for the dispersion compensation section. The advantage of
this method is that a tolerant selective wet-chemical etchant can be applied to remove the
cladding layer. The disadvantage, however, is a reduction of the lateral index contrast, by
which coupling between array waveguides may become a problem. Furthermore, due to the
reduced index contrast, this method cannot be applied to curved waveguides as the radiation
losses will then become excessively high. The result is that an additional straight section length
is needed in the centre of the phased array, which leads to a longer device.
As an example, we use a PHASAR of which the design parameters are given in table 5.1. As
can be seen in this table, the channel spacing was chosen at 3.2 nm (400 GHz). For lower
channel spacings, the device will become less tolerant wih respect to production deviations.
Figure 5.5a shows a contour plot of the TE-TM shift after polarisation dispersion
compensation for different thicknesses of the Q(1.3) guiding layer and the InP cladding layer.
The values are calculated using the design parameters listed in table 5.1. From this figure it
becomes clear that the demands on the layer thickness are very stringent. A guiding layer
thickness variation of ± 15 nm (2.5%) leads to a TE-TM shift of approximately 0.2 nm. A
cladding layer thickness variation of ± 15 nm (5%) even leads to a TE-TM shift of 0.5 nm.
Therefore, it is important that the layer thicknesses are accurately known before the design is
made.
In figure 5.5b the TE-TM shift dependence with respect to etch depth and waveguide width are
shown. The standard lithographic process has to be pushed to its limits to obtain a waveguide
width deviation of ± 0.1 μm. If the etch depth variation can be controlled within ±
10 nm
(10%), the TE-TM shift can be limited to 0.2 nm.
It can, therefore, be concluded that due to the rather tight - but not unrealistic - demands on the

5.2 Polarisation dispersion compensation 87
processing, this method appeals to the controllability of the production process and to the skills
of the persons who actually manufacture the devices.
InP layer thickness [nm]
400
350
300
250
Table 5.1 Design parameters of the demultiplexer.
-4.0
-3.6
-3.2
-2.8
-2.4
-2.0
-1.6
-0.4
0.0
1.2
2.0
2.4
2.8
3.6
4.0
4.4
0.8
1.6
3.2
4.8
-1.2
-0.8
0.4
Parameter Value
centre wavelength λ c
1534 nm
number of channels N 8
channel spacing Δλ ch (Δf ch ) 3.2 nm (400 GHz)
array order m 37
free spectral range Δλ FSR
number of array waveguides N a
41.5 nm
62
array length 1.6 mm
array height 1.1 mm
TE-TM shift Δλ pol
4.0 nm
correction length δL 12.48 μm
centre wavelength shift Δλ c
index contrast ΔN
index contrast Δn
200
500 550 600 650 700
Q(1.3) layer thickness [nm]
-2.0
-1.6
-0.4
0.0
1.2
2.0
2.4
2.8
3.6
4.0
4.4
-1.2
-0.8
0.4
0.8
1.6
3.2
4.8
Etch depth into Q(1.3) layer [nm]
200
180
160
140
120
100
7.4 nm
– 9.8 10 3 –
⋅
– 2.3 10 2 –
⋅
(a) (b)
80
60
40
20
1.2
1.6
2.0
2.4
3.0
3.2
2.8
2.2
1.8
1.4
1.6 1.8 2.0 2.2 2.4
Waveguide width [μm]
Figure 5.5 TE-TM shift (nm) as a function of the guiding layer and the cladding
layer thickness (a) and as a function of waveguide width and etch depth into the
guiding layer (b).
0.4
0.8
2.6
1.0
-0.2
0.6
-0.4
0.2
-0.6
0.0
0.4
0.8
-0.8
1.0
-0.2
-0.4
0.6
-1.0
-0.6
0.0
0.2

88 5. Polarisation independent PHASARs based on birefringent waveguides
5.2.2 Coupling between array waveguides
By removing the InP cladding of the array waveguides, the lateral index contrast Δn decreases
by approximately 50% from 0.051 (0.071) to 0.027 (0.033) for TE (TM) polarisation, which
results in a decrease of the confinement of the waveguide field. The field will therefore extend
further into the film next to the waveguide and coupling between waveguides will increase.
This is shown in figure 5.6 for TE polarisation.
Transverse position [μm]
1.0
0.5
0.0
-0.5
-1.0
-2 0 2 4
Lateral position [μm]
-1.0
-2 0 2 4
Lateral position [μm]
(a) (b)
Figure 5.6 Field profile in the original waveguide structure (a) and in the
waveguide structure where the InP cladding has been removed (b).
Assuming that each waveguide only couples to its neighbouring waveguides, we use the
system-mode concept for an estimate of the coupling. We consider the fundamental (even) and
first-order (odd) mode of two coupled waveguides (the “system”). Light propagating in a
single waveguide can be decomposed into the even and odd system mode, as depicted
schematically in figure 5.7.
single
mode
=
even
mode
+
After propagation over a certain length, both system mode have opposite phases (i.e. phase
difference equals π radians) and light will be transferred completely to the other waveguide.
The length L at which this occurs, is defined as:
whereby β 0 and β 1 are the propagation constants of the fundamental and first-order system
Transverse position [μm]
1.0
0.5
0.0
-0.5
odd
mode
waveguide a
waveguide b
Figure 5.7 Decomposition of a single mode into the even and odd system mode.
L( β0 – β1) = π
(5.5)

5.2 Polarisation dispersion compensation 89
modes of the coupled waveguides. The value of L for which this occurs equals the coupling
length Lc . The coupling length is defined as Lc = π ⁄ 2C (using coupled-mode theory [160])
with C being the coupling coefficient. The coupling coefficient C is thus found as:
The fraction of power coupled to the other waveguide after propagation over a length L can be
estimated by:
We consider the worst-case coupling by using the longest side of the compensation triangle
( L = N a ⋅ δL ) as the length over which coupling occurs. Figure 5.8 shows the power coupled
from one waveguide to its neighbour. It shows that if the gap is chosen sufficiently large
(> 5 μm), coupling effects are negligible. For the PHASAR, the parameters of which are listed
in table 5.1, the gap equals 5 μm at the shortest side of the triangle, ( L
than 10 μm at the longest side.
= δL ) and is even more
Coupled power [%]
100.00
10.00
1.00
0.10
5.2.3 Experimental results
C = ( β0 – β1) ⁄ 2
The approach described above has been applied to a phased-array demultiplexer with a
waveguide structure as designed and depicted in figure 5.4. The design parameters are listed in
table 5.1 and the device has been produced in cooperation with Kees Steenbergen [141]. The
etching of the waveguides was done by employing a RIE etch/descum process for low-loss
waveguides [86], resulting in an optical loss of 1.4 dB/cm for both TE and TM polarisation.
The removal of the InP cladding was performed by selective chemical etching with HCl/
H3PO4 . The calculated index differences ΔN and Δn of the waveguide structure used are
– 9.8 10 and respectively. Together with the measured TE-TM shift of 4.2 nm
without correction, an incremental length δL of 12.48 μm was calculated. The number of array
3 –
⋅ – 2.3 10 2 –
⋅
(5.6)
2 CL
P sin ⎛------ ⎞ sin
⎝ 2 ⎠
2 β0 β ( – 1)L
= = ⎛------------------------- ⎞
(5.7)
⎝ 2 ⎠
0.01
1 2 3 4 5 6
Gap [μm]
Figure 5.8 Coupled power over the longest side of the compensation triangle
versus gap size.

90 5. Polarisation independent PHASARs based on birefringent waveguides
2.4 mm
0.8 mm
Figure 5.9 Microscope photograph of the realised demultiplexer.
1.1 mm
guides Na equals 62, leading to an increase of the device length of slightly less than 800 μm,
giving an overall array size of mm2 2.4 × 1.1 . A microscope photograph of the device is
shown in figure 5.9, in which the triangularly shaped polarisation dispersion compensation
section can be clearly distinguished.
The device, which has been integrated with photodetectors [141], has 8 wavelength channels
spaced at 400 GHz frequency (3.2 nm wavelength) with a centre wavelength of 1534 nm.
Figure 5.10 shows the measured response of the demultiplexer for both TE and TM
polarisation. It is seen that the response curves for both polarisations match very well. As can
be seen from the figure, the on-chip losses for TE polarisation are 3 dB and 5 dB for TM
polarisation. The cross talk is better than -25 dB for the lower wavelength range, increasing to
better than -20 dB to the higher wavelength range, which is due to the increased spontaneous
emission of the laser occurring when operating near its wavelength limit.
For TM polarisation, an additional loss was measured of about 2 dB, as can be seen in figure
5.10. This is the result of the excess propagation loss of the waveguide with the etched InP
cladding layer. Test structures were included and consisted of straight waveguides of which the
cladding layer was etched away over different section lengths. The excess propagation loss was
measured for TE and TM polarisation and is shown in the graph of figure 5.11. For TE
polarisation, the field does not suffer from the absence of the cladding layer, as the excess loss
is independent of the section length. Only a coupling loss of 0.5 dB over two junctions was
measured. TM polarised fields, on the other hand, do suffer from the absence of the cladding
layer and an excess loss of 2.1 dB/mm was observed. This loss can be minimised by only
partly etching the InP cladding layer, which leads to a longer section length δL and,
consequently, to a longer device. In turn this may be compensated by a decreased waveguide
width in the correction section [110].

5.2 Polarisation dispersion compensation 91
On-chip loss [dB]
5.2.4 Conclusions
0
-10
-20
-30
-40
1525 1530 1535 1540 1545 1550 1555 1560
Wavelength [nm]
Figure 5.10 Response of the phased-array demultiplexer: solid and dashed lines
denote TE and TM polarisation respectively.
Excess loss [dB]
10
8
6
4
2
L
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Length [mm]
Figure 5.11 Loss versus section length for TE (squares) and TM (triangles)
polarisation.
By locally removing the InP cladding layer of a conventional semiconductor waveguide
structure as shown in figure 5.4, a tolerant selective wet-chemical etchant can be used to define
the polarisation dispersion compensation section. Even though the production is relatively
simple, this method is very sensitive to layer thickness and width variations. Therefore, a twostep
production strategy is needed, in which the compensation section is based on an
intermediate characterisation of the component. Although full polarisation dispersion
compensation is obtained using this strategy, it makes this method less attractive for large-scale
application.

92 5. Polarisation independent PHASARs based on birefringent waveguides
5.3 Polarisation conversion
As mentioned earlier in paragraph 2.2.4, a good method to obtain polarisation independence
for silica-based and LiNbO 3 -based phased-array demultiplexers is the insertion of a λ/2-plate
in the middle of the phased array. Using this method, light will always traverse half of the
phased array in one state of polarisation, and the other half in the orthogonal state, regardless
of the birefringence properties of the waveguides. However, as stated in section 2.2.4, it is not
practical to apply this method to semiconductor waveguide structures due to their large
numerical aperture, which leads to high diffraction losses when traversing the half-wave plate.
Figure 5.12 Schematic diagram of a PHASAR demultiplexer with integrated
polarisation converters inserted in the centre.
An integrated polarisation converter, such as the one presented in section 3.7, might be an
alternative for semiconductor waveguide structures. This is shown in figure 5.12. In this case
the additional length of the demultiplexer will be in the order of less than 1 mm. Either the
complete demultiplexer can be produced in the deeply etched waveguide structure needed for
the ultra-compact bends, or only the converter part of the device can be etched deeply in a
second etching step. The first option has the additonal advantage of applying small radii for the
array guide bends, which leads to sub-millimeter device dimensions.
5.3.1 Cross talk tolerance analysis
The tolerance of this solution to deviations in the production process can be analysed as
follows. The amount of light which is not converted to its orthogonal polarisation state will be
imaged at the image plane, shifted in position (with respect to the original image) as
determined by the polarisation dispersion. In the worst case, this light will directly couple into
one of the other receiver waveguides and will cause cross talk. The cross talk CT is found as:
CT 10 log PTE = ⋅ ⎛--------- ⎞
⎝ ⎠
(5.8)
whereby P TE and P TM denote the power in the TE- and TM-polarised field respectively. The
converter presented in Chapter 3 measures a conversion ratio of more than 85%, which, in this
case, results in a cross talk value of -7.5 dB. Using equation 5.8, it is easily verified that for
P TM
output

5.4 Polarisation splitter 93
cross talk levels better than -30 dB, the conversion ratio must be even at least 99.9%, which is
a rather stringent demand.
5.4 Polarisation splitter
In the following section we introduce a novel method for obtaining polarisation independence
using a polarisation splitter at the input. Due to the polarisation dispersion, the focal spot
position along the image plane is differerent for both TE and TM polarisation. This is shown
schematically in figure 5.13a. This shift in position Δspol can be compensated by shifting the
original input field of the corresponding polarisation in the opposite direction along the object
plane as shown in figure 5.13b. A polarisation splitter is then needed to spatially separate both
polarisations. This method is best applicable to 1 × N demultiplexers and a sample layout is
depicted in figure 5.14. However, it can also be applied to N × N demultiplexers with channel
spacings larger than the TE-TM shift (determined by the receiver spacing d r ). In this way,
crossings are avoided or transmitter waveguides coming too close to each other, which is
shown schematically in figure 5.15. This is the case, for instance, for the PHASAR of section
5.2, the design parameters of which are listed in table 5.1. This device has a TE-TM shift of
4.0 nm and a channel spacing of 3.2 nm. In combination with a receiver spacing d r of 5.5 μm
and a waveguide width of 2 μm, the transmitter waveguides will overlap over 0.6 μm.
ΤΕ+ΤΜ
Δs pol
ΤΜ
ΤΕ
object
plane
object
plane
phased
array
(a)
phased
array
(b)
image
plane
ΤΜ
ΤΕ
image
plane
Δs pol
ΤΕ+ΤΜ
Figure 5.13 Schematic diagram showing the polarisation dispersion: without
compensation gives shifted images (a) and with compensation by proper
positioning of the transmitter waveguides gives a single image.

94 5. Polarisation independent PHASARs based on birefringent waveguides
TE+TM
TE-TM
splitter
TM
Figure 5.14 Application of a polarisation splitter at the input.
TE+TM
TE-TM
splitter
TE+TM TE-TM
splitter
crossing
TE
Δs pol
object
plane
5.4.1 Cross talk tolerance analysis
d r
image
plane
The cross talk arising from the application of this method depends on the positioning of the TE
and TM-polarised input fields with respect to each other. If proper positioning is not achieved,
the TE and TM pass-bands will be shifted relative to each other and in the worst case, the light
will couple into an adjacent receiver waveguide giving opportunity for cross talk. The effect of
proper positioning of the two input fields can be disturbed either by a deviation of the
polarisation dispersion Δs pol , or by insufficient discrimination of the polarisation splitter.
The first cause can be circumvented in the same way as for the “order trick” - by flattening of
the wavelength response. For the latter cause, however, a fraction of the unwanted polarisation
TM
TM
TE
TE
TE+TM
d r
TE+TM
Figure 5.15 Schematic diagram of the problems occurring when the polarisation
dispersion shift Δs pol is larger than the receiver spacing d r .

5.5 Discussion 95
may be coupled into the wrong output of the splitter. The power level of this fraction is called
the splitting ratio (in dB). In a worst case situation, this power is coupled into a different
receiver waveguide, resulting in an increased cross talk level. Polarisation splitters are known
from literature. They have been produced in LiNbO 3 [172], silicon-based [114] and Al 2 O 3 -on-
SiO 2 waveguide structures [161] (PHASAR-based). If we restrict ourselves to the InP-based
ones [2,101,120,156,158], we note that the splitting ratio is in the order of -20 dB for both
polarisations. As this is not sufficient to obtain cross talk levels better than -30 dB, they should
be cascaded as suggested by Shani et. al. [114]. In this way, splitting ratios in the order of -35
to -45 dB can be achieved.
5.5 Discussion
In this Chapter four methods to obtain polarisation independence have been discussed. They all
have their own specific advantages and disadvantages. The compensation of polarisation dispersion
provides a good solution. In this way, however, due to the high sensitivity to layer
thickness and waveguide width, an intermediate characterisation of the device is required in
order to obtain a fully polarisation independent device.
From the design point of view, the insertion of a half-wave plate is the most simple method for
obtaining polarisation independence and, in principle, it can be applied to any waveguide structure.
For semiconductor structures, the half-wave plate takes the form of an integrated polarisation
converter. The bandwidth of this method only depends on the bandwidth of the converter.
The conversion ratio, however, must be at least 99.9% in order to maintain a cross talk level
better than -30 dB.
Finally, a novel method has been introduced for obtaining polarisation independence by using
polarisation splitters at the input of the PHASAR. The method is best suited for 1 × N devices,
but can also can be applied to N ×
N devices if the polarisation dispersion is smaller than the
channel spacing. In order to maintain a high cross talk level, polarisation splitters should be
cascaded. Additionally, the response of the PHASAR should be flattened in order to relax the
polarisation dispersion tolerances with respect to the production process.

96 5. Polarisation independent PHASARs based on birefringent waveguides

Chapter 6
MMI-based components
A special type of phased-array demultiplexer is one in which the free propagation regions are
replaced with multimode interference (MMI) couplers. In this Chapter the design of such MMIbased
demultiplexers is discussed. A tolerance analysis is given together with experimental
results, part of which have been presented at the ECIO’95 [31]. Also, a MMI-based mode filter
is discussed and experimental results are given, part of which have been presented at the
IEEE-LEOS Annual Meeting [36]. Finally, the interference patterns in a MMI coupler have
been made visible. This is done using a MMI-coupler, produced in an aluminium oxide ridge
waveguide structure implanted with erbium, and by imaging the green light generated by
upconversion at high pumping power levels. This work has been carried out in cooperation
with the FOM-Institute for Atomic and Molecular Physics and has been presented earlier
[30,59].
6.1 Introduction
Multimode Interference (MMI) couplers are broad waveguides which support a high number
of modes, determined by the waveguide width and the lateral index contrast. These waveguides
have the so-called “self-imaging” property, which means that a replica of an arbitrary field
applied at the input is reproduced at periodic positions along the direction of propagation. At
fixed positions in between these intervals, multiple images of the input field are obtained with
the input power equally distributed over all images.
A significant advantage of MMI couplers over directional couplers is their tolerance with
respect to polarisation, wavelength and etch depth variations [121]. A drawback of these
couplers is their sensitivity to the waveguide width. This restriction has not, however, been an
obstacle for wide usage of MMI couplers for splitting and combining functions [51], in
interferometric switches [67], phase-diversity optical receivers [40,105] and in ring lasers
[111].
The derivation of general analytical expressions for the phases of the images in MMI couplers
has led to the design and production of MMI-based wavelength demultiplexers [8,31,76]. The
design and experiments of such a MMI-based demultiplexer are discussed in section 6.2 and
special attention is paid to tolerance analysis.
Another application of MMI couplers is a spatial mode filter. This device uses a single MMI

98 6. MMI-based components
coupler to spatially separate the fundamental mode from the first-order mode. The design and
experimental results of a MMI-based spatial mode filter are presented in section 6.3.
Finally, the interference patterns in a MMI coupler operating at 1485 nm wavelength are made
visible in green light. This has been done for an erbium-doped aluminium oxide ridge
waveguide structure by imaging the green light generated by upconversion at high pumping
power levels. This work, carried out in cooperation with the FOM-Institute for Atomic and
Molecular Physics, is presented in section 6.4.
6.2 MMI-MZI demultiplexer
MMI-based demultiplexers reported so far were produced for duplexing 980 nm and 1550 nm
light, and were produced by using a single MMI coupler in silica-based [50,66,98] and LiNbO3 waveguide structures [112]. This is possible due to the high ratio of the beat lengths at both
wavelengths ( Lπ, λ1 ⁄ Lπ, λ2 ≈ λ2 ⁄ λ1 ≈ 1.5 ). For smaller wavelength spacings, the MMI
coupler will become excessively long, which makes it less tolerant. In this case, a Mach-
Zehnder Interferometer (MZI) configuration should be used, consisting of two 2 × 2 MMI-
couplers connected to each other by two waveguides, the optical path lengths of which are
different. This concept has been used for switches [67,159], polarisation splitters [113,120]
and duplexers [58].
If MMI couplers are used to replace the FPR’s of the PHASAR, the demultiplexer acts as a
MMI demultiplexer in a MZI configuration, a so-called MMI-MZI demultiplexer. A sample
layout of such a demultiplexer is shown in figure 6.1. In this figure, it can be seen that the
number of array guides is equal to the number of input waveguides, or, in the sense of
demultiplexing, to the number of waveguide channels. This is a feature by which the MMI-
MZI demultiplexer can be distinguished from a conventional PHASAR demultiplexer.
MMI
section
input
waveguides
Array
waveguides
MMI
section
output
waveguides
Figure 6.1 Novel type phased-array demultiplexer: MMI-MZI demultiplexer.

6.2 MMI-MZI demultiplexer 99
A significant advantage of the MMI-MZI demultiplexer with respect to the “classical” phasedarray
demultiplexer becomes apparent when deeply etched waveguides are applied, either for
miniaturisation or for polarisation independence purposes. In this case, a problem arises with
phased-array demultiplexers: increased junction loss at the interface between the array
waveguides and the free propagation region (FPR). The lithographic resolution of the
production process limits the minimum spacing of the array waveguides and therefore also the
insertion loss. These problems can be avoided by using a MMI-MZI demultiplexer.
6.2.1 Operation principle
A N × N MMI-MZI demultiplexer consists of two identical N × N MMI couplers connected to
each other by N array waveguides, the lengths of which are properly chosen. A schematic
layout is depicted in figure 6.2, in which the notation of Besse et al. has been followed [13,14].
i=
N
...
2
a
1
2W/N
W/N
W
L MMI
Figure 6.2 Schematic layout of a generalised MMI-MZI demultiplexer.
j=
1
2
...
N
Both MMI couplers act as N × N power splitter-combiners if the length LMMI is properly
chosen: LMMI = 3Lπ ⁄ N , with Lπ = π ⁄ ( β0 – β1) , whereby β0 and β1 are the propagation
constants of the fundamental and the first order mode in the MMI coupler respectively. This
means, that a N-fold image of a field applied at any input i is obtained at the outputs j, when the
inputs and outputs are positioned as depicted in figure 6.2 (the parameter a can be chosen
freely [13,14]). The phase relations ϕj,i from input i to output j of the N × N imaging MMI
coupler have been calculated by Besse et al. [13,14]:
ϕ j, i
=
⎧
⎪
⎪
⎨
⎪
⎪
⎩
ϕ 0
whereby ϕ0 is a constant phase. Due to reciprocity, light will constructively interfere into
output i' of the second MMI-coupler if ϕ j', i' =
– ϕ j, i.
The phase relations calculated using
equation 6.1 are listed in table 6.1 with N = 4. These phases can be produced by adjusting the
path lengths of the array waveguides. It has been shown that a specific set of lengths meets
these requirements.
j'=
π
+ ------- ( 2N + 1 – j – i)
( j + i – 1)
4N
π
ϕ0 π
4N
------- + 2N – j i + ( ) j i – ( )
+
i+j odd
i+j even
i'=
N
...
2
1
(6.1)

100 6. MMI-based components
Table 6.1 The phase relations for a single 4 × 4 MMI-coupler.
Because of the constant phase factor ϕ0 , not the absolute phases are important for the
demultiplexer, but the phase differences between adjacent inputs of the second MMI-coupler
= – ( – ) in order the constituent waves at a certain output to be in phase:
Δϕ j', i' ϕ j' + 1, i'
Δϕ j', i'
=
⎧
⎪
⎪
⎨
⎪
⎪
⎩
Thiscan be simplified to:
ϕ j,i i = 1 i = 2 i = 3 i = 4
ϕ 1,i π 3π/4 −π/4 π
ϕ 2,i 3π/4 π π −π/4
ϕ 3,i −π/4 π π 3π/4
ϕ 4,i π −π/4 3π/4 π
ϕ j', i'
π
– π + ------- [ ( 2N + 1 – j' – i')
( j' + i' – 1)
– ( 2N – 1 – j' + i')
( j' + 1 – i')
]
4N
π
π
4N
------- + 2N – j' i' + ( ) j' i' – ( ) 2N – j' i' – ( ) j' i' + ( )
–
i'+j' odd
(6.2)
[ ]
i'+j' even
Δϕ j', i'
=
⎧
⎪
⎪
⎨
⎪
⎪
⎩
j'
– π + π( i' – 1)
⎛1 – --- ⎞
⎝ N⎠
π – πi'⎛
j'
1 – --- ⎞
⎝ N⎠
Δϕ j',i' i' = 1 i' = 2 i' = 3 i' = 4 ΔΦ j'
Δϕ 1',i' π/4 −π/4 3π/4 −3π/4 −π/2
Δϕ 2',i' π 0 0 π −π
Δϕ 3',i' 3π/4 −3π/4 π/4 −π/4 −3π/2
λ 1 λ 2 λ 4 λ 3
i'+j' odd
i'+j' even
Table 6.2 The required phase differences at the second MMI-coupler, calculated
between adjacent array guides for N = 4.
(6.3)
These phases are spaced at a distance of ΔΦ j' =
– j'2π
⁄ N between adjacent points. The
complete set of required phase differences is listed in table 6.2. The columns denoted by i' = 1

6.2 MMI-MZI demultiplexer 101
to i' = 4 from table 6.2 show the differences Δϕj',i' which are required in order to couple all the
power to output i' of the 4 × 4 demultiplexer. Investigation of the table shows that going from
output i' = 1 to output i' = 2, from output i' = 2 to output i' = 4, from output i' = 4 to output
i' = 3, and from output i' = 3 back to output i' = 1, the required phase difference Δϕj',i' increases
with a constant amount ΔΦj' , which is listed in the far right column. This can be made clear
when they are drawn in a phase diagram as a function of i', as shown in figure 6.3 with N = 4 as
an example.
i' = 3
i' = 4
j' = 1
i' = 1
i' = 2
j' = 2
i' = 1 i' = 2
i' = 4
i' = 3
i' = 1
i' = 2
j' = 3
Figure 6.3 Required phase differences ΔΦ j' at the input of the second MMI
coupler with N = 4.
i' = 3
i' = 4
From the values ΔΦ j' it becomes clear that, if we connect the output ports j of the first MMI
coupler to the input ports j' of the second MMI coupler by waveguides with lengths L j which
satisfy:
ΔL j L j + 1 – L j ---------- j
Δβ
2π
= = = -----------
(6.4)
NΔβ
with Δβ being the channel spacing Δβ = β (λi'+1 ) - β (λi' ), then the light will shift from output i'
to i'+1 if the wavelength changes from λi' to λi'+1 , according to the sequence listed in the
bottom row of table 6.2.
With the array guide lengths chosen according to equation 6.4, the correct absolute phase
distribution is not matched at the input of the second MMI-coupler for the design wavelength.
The correct phase distribution can be obtained by a small correction on the lengths, which does
not affect the dispersive properties of the array. This correction is discussed in Appendix F.
ΔΦ j'
The spectral response of a 4 ×
4 MMI-MZI demultiplexer has been calculated using a modal
propagation analysis implemented in a microwave CAD tool [29,75] - Hewlett-Packard’s
Microwave Desing System (MDS) - and is shown in figure 6.4. The demultiplexer has high
uniformity of the output intensity of the different channels, which is inherently due to the
uniform splitting ratio of the MMI-couplers. Low insertion loss in the order of 0.5 dB, and
cross talk values as low as -30 dB can be obtained. The practically usable bandwidth is not
determined by the 1-dB pass-band of the desired output channel, which is approximately
1.1 nm, but by the cross talk level of the undesired output channels. This low cross talk passband
is in the order of 0.19 nm for a -25 dB cross talk level (and only 0.11 nm for -30 dB),
which leads to high demands on the wavelength accuracy of the laser sources used.
Furthermore, the bandwidth of the MMI couplers, which determines the bandwidth of the
demultiplexer, is inversely proportional to the number of input and output channels N [15].
This is a major restriction for this type of demultiplexer and is discussed in the next section.

102 6. MMI-based components
Transmission [dB]
0
-5
-10
-15
-20
-25
1 3 4 2
-30
1510 1515 1520
Wavelength [nm]
1525 1530
Figure 6.4 Calculated spectral response of a 4x4 MMI-MZI demultiplexer.
A layout of how the required length differences ΔLj could be made is shown in figure 6.1. It
can be seen, that the length difference monotonically increases with array guide number j,
which agrees with the values of ΔΦj' listed in the last column of table 6.2. However, these
values denote the phase difference between adjacent array guides. If we consider the phase
difference with respect to a reference guide, we find a quadratical increase in stead of a linear
increase ( – ( – ) = π ⁄ 2,
3π ⁄ 2,
6π ⁄ 2 for j' = 2, 3, 4 respectively). As for a proper
ϕ j', i'
ϕ1', i'
phased-array design the phase difference between adjacent array guides should linearly
increase with respect to a reference array guide, it means that the phase transfer will be
disturbed. This causes considerably high sideobes, as can be seen in the graph of figure 6.4.
This can be avoided if we consider the phase difference Δϕj',i' with respect to a - arbitrarily
chosen - reference guide. As an example we take guide j' = 1 to be the reference guide, leading
to the phase differences Δϕ j', i' = – ( ϕ j', i' – ϕ1', i')
, which are listed in table 6.3, again with
N = 4 as an example.
Table 6.3 The required phase differences at the second MMI-coupler, calculated
with N = 4 and with respect to reference array guide j' = 1.
Δϕ j',i' i' = 1 i' = 2 i' = 3 i' = 4 ΔΦ j'
Δϕ 1',i' 0 0 0 0 0⋅π/2
Δϕ 2',i' π/4 −π/4 3π/4 −3π/4 −1⋅π/2
Δϕ 3',i' −3π/4 −π/4 3π/4 π/4 +1⋅π/2
Δϕ 4',i' 0 π π 0 −2⋅π/2
With this approach the simple layout as shown in figure 6.1 can no longer be used, because the
array guides would intersect at small angles as depicted in figure 6.5a. These crossings can be
circumvented if the path length differences are made by U-bends. This geometry, presented for

6.2 MMI-MZI demultiplexer 103
the first time at the ECIO’95 conference [31], has a decreased width at the expense of an
increased length as depicted in figure 6.5b.
Later another geometry was proposed by Lierstuen and Sudbø [76] and by Herben et al. [55]
(who proposed to use it in a multi-wavelength laser). In this geometry, depicted in figure 6.5c,
the crossings are circumvented by arranging the phase differences ΔΦ j' in such a way that they
increase monotonically in both directions from a reference array guide towards the outer array
guides. The advantage of this geometry is that all array guides have identically shaped arms,
except for the pathlength difference which is obtained by inserting extra lengths of straight
waveguides. On the other hand, the device has an increased height, which limits the integration
scale.
The number of U-bends needed in array guide j (configuration of figure 6.5b) can directly be
read from the far right column of table 6.3, when the path length difference between a U-bend
and a straight waveguide is calculated according to:
ΔL U-bend
( π ⁄ 2)
= --------------
Δβ
(6.5)
whereby R is the bending radius of the curved waveguide section, and L the horizontal length
of the U-bend.
(a)
(b)
(c)
crossings
Figure 6.5 Schematic layout of 4x4 MMI-MZI demultiplexer: with waveguide
crossings (a), with U-bends (b), and without waveguide crossings but with
increased height (c).

104 6. MMI-based components
Because the U-bend consists of four curved waveguide sections with an angle α, the path
length along the U-bend equals 4αR. If the length L of the U-bend is substituted with 4Rsin(α),
we end up with:
α – sin( α)
π
-------------
8RΔβ
which can be solved for any value of R.
According to the above approach, the spectral response of a 4 × 4 MMI-MZI demultiplexer
with U-bends (configuration of figure 6.5b) has been calculated and is shown in figure 6.6. If
we compare the graph in this figure with the one of figure 6.4, various items catch the eye:
• 100% bandwidth increase. The -1 dB band is increased from 1.1 nm to 2.2 nm and the
-25 dB cross talk bandwidth is increased from 0.19 nm to 0.42 nm (the -30 dB bandwidth
is increased from 0.11 nm to 0.23 nm).
• Side lobe level reduction. The level of the side lobes, which lie between the channel
maxima, reduces from -4 dB to -12 dB.
• Side lobe reduction. A number of side lobes seem to have disappeared and the side
lobes now overlap better.
Still, the bandwidth is small compared to that of a conventional phased-array demultiplexer. In
contrast with the PHASAR demultiplexer, it is not possible for MMI-MZI demultiplexers to
flatten the wavelength response without changing the channel spacing. This is due to the fact
that there is no scanning bundle in the MMI couplers as in the FPR of a PHASAR
demultiplexer and can be explained as follows. In order to flatten the response, a specific phase
distribution at the input of the second MMI coupler, which results in constructive interference
into one of the outputs, has to be maintained over a longer wavelength range. The result will be
that any phase distribution will be maintained over a longer wavelength range (including the
ones that do not result in constructive interference into one of the outputs), leading to a larger
channel spacing.
Transmission [dB]
0
-5
-10
-15
-20
-25
In contrast with the first structure proposed (figure 6.1), in which the path length differences
were obtained by length differences between straight waveguides (of which the propagation
=
1 3 4 2
-30
1510 1515 1520
Wavelength [nm]
1525 1530
Figure 6.6 Calculated spectral response of a 4x4 MMI-MZI demultiplexer with
U-bends.
(6.6)

6.2 MMI-MZI demultiplexer 105
loss can be kept negligibly low), now each array guide has a different number of U-bends. As
the propagation loss of a curved waveguide is higher than that of a straight waveguide, an
unequal power distribution is expected at the input of the second MMI coupler. This will result
in a higher cross talk and will be discussed in the next section.
6.2.2 Tolerance analysis
For the tolerance analysis we will consider the definition of the length L of a N × N MMI
coupler more closely. If we assume a strongly guided structure, it may be approximated by
[15]:
L
=
2
4 nW
--- ⋅ ----------
N λ
whereby n is the (transverse) effective index in the MMI coupler region. Small changes of the
wavelength, the width and effective index (through layer thickness variations) cause a change
in the beat length L π and, consequently, performance degradation. Hence using equation 6.7,
the variations of the wavelength, width, index and length of the MMI coupler are related by:
It now becomes apparent that all relative changes in these parameters have the same effect,
which is a change in the length at which the image is obtained. The imaging is not performed
properly, leading, in case of a very small change, to defocusing of the light into the output
waveguides and the result is an increased insertion loss. In more severe cases, increased cross
talk is also the result.
Using the relative changes of equation 6.8, particular tolerance windows for a single MMI
(6.7)
∂Lπ
∂L
∂n
----------- -------- -------- 2
Lπ L n
W ∂ ∂λ
= = = ---------- = --------
(6.8)
W λ
coupler can be calculated (e.g. the 1-dB bandwidth). These windows should be divided by
in order to obtain the tolerance windows for a MMI-MZI demultiplexer, which consists of two
MMI couplers.
For the analysis, the tolerance windows will be calculated and be compared with results of
simulations performed with MDS. We consider the following structure: the MMI-MZI uses
two MMI couplers which are 14 μm wide and 423 μm long, designed for application in a
deeply etched waveguide structure, consisting of a 600 nm thick InGaAsP guiding layer and a
300 nm thick InP cladding layer. The advantage of such a waveguide structure is not only that
small bending radii can be applied, but also that the tolerance to etch depth variations is greatly
relaxed. The input and output waveguides are 2 μm wide, which allows for a relaxed length
tolerance [127,134] and on the other hand, also limits the width of the MMI coupler. The
channel spacing is 3.2 nm (400 GHz) with a central wavelength of 1520 nm.
Bandwidth
Besse et al. [15] have shown that in order to limit the excess loss of a single MMI coupler to α
(in dB), the wavelength should be limited to a range
wavelength λc :
2 δλ centred around the centre
2 δλ Z( α)
Nπd 2
0
≅ (6.9)
-----------------λ
2 c
4W MMI
2

106 6. MMI-based components
whereby d 0 is the waist of the Gaussian field describing the input field. The exact form of Z(α)
can be found elsewhere [15], only a few values are given here: Z(α) ≈ 0.8, 0.5 for α = 1 and
0.5 dB respectively. According to equation 6.9, a 1-dB bandwidth of 28 nm is expected for a
single MMI coupler and 20 nm for the MMI-MZI demultiplexer. A striking detail is that if the
width is increased, even with the same relative amount as the number of channels (i.e. ratio N/
W MMI constant), the bandwidth decreases. Figure 6.7 shows the response of the MMI-MZI
demultiplexer over a longer wavelength range, calculated with MDS. From this figure the 1-dB
bandwidth appears to be approximately 23 nm.
Transmission [dB]
0
-1
-2
-3
2
1
3
4 2 1
3
-4
1500 1510 1520
Wavelength [nm]
1530 1540
Figure 6.7 Wavelength response of the 4 × 4 MMI-MZI demultiplexer.
Width tolerance
With respect to equation 6.9, an equivalent expression is given for the width tolerance of a
single MMI coupler:
from which it follows that the tolerance remains constant as long as the ratio N/WMMI is kept
constant. The 1-dB width tolerance calculated using this equation equals 0.13 μm and for the
MMI-MZI demultiplexer 0.09 μm. Figure 6.8 shows the transmission of the MMI-MZI
demultiplexer (calculated with MDS) versus the deviation ΔW of the width with respect to the
designed value. The 1-dB width tolerance measures approximately 0.10 μm. The figure also
demonstrates that the lateral dimensional control of ±
0.2 μm, which is a realistic value for a
standard lithographic process, is not sufficient for low-loss operation.
The effect of a width deviation might, however, not be as dramatic as figure 6.8 suggests. If we
again consider equation 6.8, we see that a deviation in the width can be compensated by a
deviation in the wavelength. This means that if the width used deviates from the designed
width, the wavelength response will shift with respect to the designed central wavelength. This
is depicted in figure 6.9. In this graph the contour lines denote an equal insertion loss for the
central channel. It shows that a negative width deviation ΔW results in a wavelength shift
towards a lower wavelength region. It also shows that the bandwidth increases linearly with the
wavelength (width of the equal-loss region increasing linearly), which follows directly from
equation 6.9.
4
δW Z( α)
Nπd 2
0
≤ --------------------
(6.10)
16W MMI
2
1

6.2 MMI-MZI demultiplexer 107
Transmission [dB]
0
-5
-10
-15
-20
-25
-30
-0.4 -0.2 0.0 0.2 0.4
ΔW [μm]
Figure 6.8 Transmission characteristic of the 4 × 4 MMI-MZI demultiplexer
versus width deviation.
Wavelength [nm]
1600
1550
1500
1450
1400
-11
-9
-8
-8
-7
-6
-4
-2
-3
-6
-5
-7
-9
-11
-11
-2
-4
-12
-10
-8
-10
-6
-6 -6
-0.4 -0.2 0.0 0.2 0.4
ΔW [μm]
Figure 6.9 Wavelength change versus width variation.
-5
-7
-3
-7
-1
-7
-1
-6
-6
-2
The wavelength shift due to a width deviation can be estimated using equation 6.8. If we use
ΔW = -0.2 μm as an example, the wavelength shift of the envelope will be approximately
43 nm. The response has been calculated for this width deviation and the result is depicted in
figure 6.10. In figure 6.10a the response is shown for the design wavelength region. The cross
talk and the insertion loss have increased. Figure 6.10b shows the response in the shifted
wavelength region, from which it follows that the wavelength shift is approximately 45 nm. If
this figure is compared with figure 6.6, it becomes apparent that the bandwidth has decreased
(from 20 to 19 nm, which is verified with equation 6.9).
-5
-4
-3
-9
-6
-5
-6
-7
-8 -9
-2
-4
-5
-8
-6
-5
-7
-3
-9
-5
-1
-7
-8
-1
1
2
3
4
-3 -2
-5 -4
-5
-6
-6
-4
-8

108 6. MMI-based components
Transmission [dB]
0
-5
-10
-15
-20
-25
4 2 1 3 4 2 1 3 4 2 1
-30
1510 1515 1520
Wavelength [nm]
1525 1530
-30
1470 1475 1480
Wavelength [nm]
1485 1490
(a) (b)
Layer thickness tolerance
A change in the transverse effective index also affects the length of the MMI coupler, as
follows from equation 6.8. The effective index is dependent on the polarisation and the
temperature, both of which can be controlled accurately. The index, however, also depends on
the layer thickness, especially the guiding layer thickness, as most of the power is present in
that layer. Figure 6.11 shows the response versus layer thickness variations.
Transmission [dB]
0
-5
-10
-15
-20
-25
Figure 6.10 Response for ΔW = -0.2 μm for the wavelength region according to
the design (a) and for the shifted wavelength region (b).
2
-30
500 550 600 650 700
Q(1.3) layer thickness [nm]
4
3
The graph of figure 6.11a shows interesting results. As the transverse effective index is mainly
determined by the guiding layer thickness, a variation of this layer has a large impact on the
response: a change in the layer thickness shifts the wavelength response. From this graph it can
also be seen that an increasing layer thickness results in a relaxed tolerance with respect to loss
and cross talk. This is explained by the fact that the relative change ∂n
⁄ n is small.
Transmission [dB]
A variation in the cladding layer, on the other hand, which only guides a small part of the
power, leads to a small relative index change and therefore the response is hardly influenced.
As can be seen from figure 6.11b, the cladding layer thickness has to be controlled within
Transmission [dB]
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
0
-5
-10
-15
-20
-25
1,2,3
-10
-15
-20
-25
-3.0
-30
200 250 300 350 400
InP layer thickness [nm]
(a) (b)
Figure 6.11 Response for guiding layer variation (a) and for cladding layer
variation (b).
4
0
-5
Transmission [dB]

6.2 MMI-MZI demultiplexer 109
± 15 nm in order to maintain a cross talk level of less than -30 dB, whereas the guiding layer
thickness has to be controlled within 5 nm for the same cross talk level.
Waveguide loss tolerance
In addition to these production deviations, waveguide losses may also have an impact on the
performance due to the different lengths of the array arms. The losses will vary from one array
guide to another, leading to a non-uniform intensity distribution at the input of the second MMI
coupler. This will especially be the case if the required path length differences are obtained by
different numbers of curved waveguide sections in the array guides, as in the structure of figure
6.5b. The imaging in the second MMI coupler is not performed properly and therefore power is
not only coupled to the desired output, but also to undesired outputs, leading to unwanted high
cross talk values.
To analyse this effect, the phase transfer in the second MMI-coupler will be considered, from
which it is found that for one particular output all contributions add up coherently, leading to a
proper image. For all other outputs each phase transfer term appears to have one counterphase
term, leading to extinction of the fields. If these terms have different amplitudes due to
attenuation in the demultiplexer, the extinction factor is reduced, i.e. the cross talk increases.
From this analysis the sensitivity to loss variations in the different array guides, which leads to
power imbalance at the input of the second MMI-coupler, can be calculated as follows and
considering the configuration of figure 6.2. It should be noted that the splitting ratio of the
MMI couplers is assumed to be uniform; the MMI couplers do not necessarily need to be
without loss. The field at output i' of the second MMI-coupler is defined as:
A i'
If we use input i = 1 as an example (calculations for other values of i are analogous) and
evaluate this formula for odd i', we arrive at:
Ai', odd
=
+
j' = odd
This can be simplified to:
Ai', odd
N
∑
N
∑
j' = even
+
=
N
∑
N
∑
N
∑
– i', j'
A j'e ϕi' j'
A j'e jϕ – = =
+
i', j' (6.11)
j' = 1
1
------- A1e N
1
------- A1e N
N
∑
j' = odd
j' = even
, A j' e jϕ
j' = odd
π
j ϕ0 + π + ------- ( j' – 1)
( 2N – j' + 1)
4N
π
j ϕ0 + ------- j'( 2N – j')
4N
1
------- A1e N
1
------- A1e N
e
e
N
∑
j' = even
π
– j ϕ0 + π + ------- ( i' – j')
( 2N – i' + j')
4N
π
– j ϕ0 + ------- ( i' + j' – 1)
( 2N – i' – j' + 1)
4N
j π
– ------- [ – ( j' – 1)
( 2N – j' + 1)
+ ( i' – j')
( 2N – i' + j')
]
4N
j π
– ------- [ – j'( 2N – j')
+ ( i' + j' – 1)
( 2N – i' – j' + 1)
]
4N
(6.12)
(6.13)

110 6. MMI-based components
In a similar manner we can find for even i':
Ai', even
=
N
∑
j' = odd
+
j' = even
1
------- A1e N
1
------- A1e N
In order to evaluate the interference of the fields from input j' to an arbitrary output i', we can
prove that for any odd (even) number j' there can always an even (odd) number j'' be found in
such a way that the contribution from input j' cancels out the one from input j''. In other words,
the phase transfer from input j' to output i' equals the phase transfer from input j'' to output i',
modulo an odd multiple k of π radians:
which holds for k = ± 1,
± 3,
…, N ⁄ 2.
Generally stated, this means that every phase transfer term has one which is in counterphase.
We look at equation 6.13, and only take into account the phases:
After some manipulations we find for j'':
N
∑
j π
– ------- [ – ( j' – 1)
( 2N – j' + 1)
+ ( i' + j' – 1)
( 2N – i' – j' + 1)
– 4N ]
4N
j π
– ------- [ – j'( 2N – j')
+ ( i' – j')
( 2N – i' + j')
+ 4N ]
4N
ϕ j' = ϕ j'' + k ⋅ 4N
– ( j' – 1)
( 2N – j' + 1)
+ ( i' – j')
( 2N – i' + j')
= – j''(
2N – j'')
+ ( i' + j'' – 1)
( 2N – i' – j'' + 1)
+ k ⋅ 4N
j''
(6.14)
(6.15)
(6.16)
⎧
⎪ 2N ( k + j' – 1)
⎪
--------------------------------- + ( 1 – j')
i',j' odd
=
i' – 1
⎨
(6.17)
⎪ 2N ( k + j' – 2)
⎪
--------------------------------- + ( 1 – j')
i',j' even
i'
⎩
Similar equations can be found if other inputs of the first MMI coupler are used. With
equations 6.13 and 6.14 the phase contributions at the second MMI coupler have been
calculated from input j' to output i' and are drawn in phase diagrams, as shown in figure 6.12.
j' = 4
j' = 3
i' = 2
j' = 2
j' = 1
j' = 1
j' = 3
i' = 3
j' = 2
j' = 4
j' = 3
j' = 2
i' = 4
Figure 6.12 Phase contributions from input j' to output i' at the second MMI
coupler with N = 4.
j' = 4
j' = 1

6.2 MMI-MZI demultiplexer 111
In this figure it can be seen that every contribution has one in counterphase. This means that at
these outputs the sum field equals zero. For output i' = 1 all contributions add up coherently (all
phase contributions equal zero). This figure makes it also clear, that a disturbance on the
uniformity of the input powers will have a drastic impact on the cancellation of the fields and
the result will be an increased cross talk level. The cross talk level can be estimated by taking
into account the U-bend losses. If we use ε for a single U-bend loss, then the amplitude of the
field at input j of the second MMI coupler can be denoted as:
whereby nj is the number of U-bend sections for guide j (nj = [2,3,1,0] for j = [1,2,3,4]), as can
be seen in figure 6.5. With the above formula we can calculate the field at output i' using
equation 6.13 and 6.14. By approximating equation 6.18 with 1 – n jε , which holds for small
values of ε, the result can be simplified to (for simplicity we have omitted the term A1 /2):
With the above equations the cross talk values have been calculated with N = 4 and are shown
in figure 6.13. As can be seen in this figure, the U-bend loss should be kept below 0.4 dB in
order to keep the cross talk below -30 dB. It is stressed again that the MMI couplers are not
assumed to be without loss, which means that the insertion loss of the MMI couplers should be
added to the insertion loss values found in 6.13, in order to obtain the insertion loss of the
demultiplexer.
Crosstalk Cross talk level level [dB]
6.2.3 Experimental results
0
-10
-20
a j ( 1 – ε)
n j
= (6.18)
A1' = 4 – 6ε
A2' = – 4εcos( π ⁄ 4)
A3' = – 4εj sin(
π ⁄ 4)
A 4' = 2ε
-30
output 1
output 2 & 3
output 4
-3
-40
-4
0.0 0.5 1.0
U-bend loss [dB]
1.5 2.0
Figure 6.13 Cross talk level versus U-bend loss with N = 4.
(6.19)
A number of experiments have been performed using different demultiplexers geometries,
which will be described below.
0
-1
-2
Insertion loss [dB]

112 6. MMI-based components
First experiment: conventional MMI-MZI demultiplexer
For the first experiment the conventional MMI-MZI demultiplexer geometry, as depicted in
figure 6.1, has been used. The device has been produced in an undeeply etched waveguide
structure consisting of a 0.66 μm thick InGaAsP guiding layer on an InP substrate covered
with a 0.32 μm thick InP layer. The designed etch depth was 80 nm into the guiding layer,
which results in a calculated TE-TM shift of 4.0 nm. The 4-channel device was designed to
operate at a central wavelength of 1536 nm with 1 nm channel spacing, thus aiming at
polarisation independent operation by means of the so-called “order trick”.
Both 1 × 4 and 4 × 4 MMI-couplers are 22 μm wide, the first being 284.5 μm long, the latter
1133.5 μm. The width was chosen in such a way that large gaps were obtained in order to
minimise coupling effects between adjacent array waveguides, which are 2.0 μm wide (both at
input and output). The device uses bends with a radius of 650 μm, having negligible radiation
loss. The overall size is mm2 , mm2 3.0 × 2.7 1.8 × 1.3 of which is occupied by the device
itself. The rest is occupied by curved waveguides placed in such a way that the output
waveguides lie in line with the input waveguides in order to simplify the measurement process.
The measured response for TE polarisation is shown in figure 6.14a, which can be compared
with the calculated response shown in 6.4. The measured response for TM polarisation is
shown in figure 6.14b. No anti-reflection (AR) coating has been applied to the cleaved end
facets. The propagation losses of a straight waveguide were measured to be 1.1 dB/cm for TE
and 2.8 dB/cm for TM polarisation. The excess loss of the device is measured relative to a
waveguide of the same length as the device. For TE polarisation it was found to be 1.2 dB for
the best channel, which is only 0.7 dB more than calculated. The response for TM polarisation
shows a higher excess loss in the order of 4 dB, approximately 2 dB of which is due to the
propagation loss difference. The cross talk is better than -15 dB and -10 dB for TE and TM
polarisation respectively. Additionally, a residual TE-TM shift of 0.5 nm was measured, which
can be accounted for by the deviation of the used etch depth (110 nm instead of 80 nm).
Excess loss [dB]
0
-5
-10
-15
-20
-25
-30
1
2
3
4
1530 1532 1534 1536 1538 1540
Wavelength [nm]
(a) (b)
1530 1532 1534 1536 1538 1540
Wavelength [nm]
Figure 6.14 Measured response of the first MMI-MZI demultiplexer for TE (a)
and TM polarisation (b).
Second experiment: MMI-MZI demultiplexer with U-bends
For the second experiment a MMI-MZI demultiplexer with U-bends, as depicted in figure 6.5b,
has been produced in a deeply etched waveguide structure in order to facilitate the usage of
extremely small bending radii, which are necessary for small device dimensions. The device
Excess loss [dB]
0
-5
-10
-15
-20
-25
-30
1
2
3
4

6.2 MMI-MZI demultiplexer 113
was designed to operate at a central wavelength of 1520 nm with 4 nm channel spacing. The
MMI-couplers are 21 μm wide and 664 μm long, with 3 μm wide input waveguides in
order to relax production tolerances [134]. The U-bends have a radius of 80 μm and a width of
1.4 μm, ensuring monomode operation. The total device size is μm2 (< 0.3 mm2 4 × 4
2800 × 106
!),
which is the smallest demultiplexer reported so far.
The measured response for TE polarisation is shown in figure 6.15a. Due to an increased width
of ± 0.2 μm, the wavelength response is shifted towards a higher centre wavelength. The losses
of the device are considerable (9-11 dB), partly due to problems in the mask, which resulted in
rough waveguide edges. The losses of straight waveguides are 2.3-2.6 dB/cm for 3.0 μm wide
waveguides, up to 4.1-4.9 dB/cm for the 1.4 μm narrow waveguides.
Measurements of the U-bends yielded 0.6 dB loss per single U-bend, which, according to
figure 6.13, cannot be the only reason for the poor cross talk performance (8-10 dB).
Therefore, the amount of TM-polarised light at the output has also been measured, while
exciting TE-polarised light at the input. The measurement results are shown in figure 6.15b. It
can be clearly seen that the power of the TM-polarised output signals is in the same order of
the TE-polarised output, which indicates that polarisation conversion up to 50% occurs in the
U-bends.
Excess loss [dB]
Transmission [dB]
0
-5
-10
-15
-20
-25
-30
1530 1535 1540 1545 1550 1555 1560
Wavelength [nm]
0
-5
-10
-15
-20
-25
3
4
2 1 3 4
2
1
-30
1530 1535 1540 1545 1550 1555 1560
Wavelength [nm]
(a) (b)
1 3 4 2
-30
1510 1515 1520
Wavelength [nm]
1525 1530
(c)
Excess loss [dB]
Excess loss [dB]
0
-5
-10
-15
-20
-25
0
-5
-10
-15
-20
-25
3
-30
1535 1540 1545
Wavelength [nm]
1550 1555
(d)
1
2
3
4
4 2 1 3
Figure 6.15 Measured response of the second MMI-MZI demultiplexer for TE
(a) and TM polarisation (b), when exciting TE polarisation at the input and
simulated response for TE polarisation: without (c) and with (d) polarisation
conversion and U-bend loss taken into account.

114 6. MMI-based components
Polarisation conversion in U-bends was unknown at the time of designing the demultiplexer. It
has been measured using a number of test waveguides, which contain an increasing number of
U-bends. The results are shown in figure 6.16. It can be seen that the amount of polarisation
conversion exceeds 50%, which is, if we only consider one polarisation, identical to an excess
waveguide loss of 3 dB. Taking into account the polarisation conversion as shown in figure
6.16, and a U-bend loss of 0.6 dB per U-bend, the response has been simulated and is shown in
figure 6.15d. The predicted excess loss is 5.5 dB and the cross talk decreases to approximately
-10 dB. This corresponds well with the measured response of figure 6.15a.
Polarisation conversion [%]
80
60
40
20
0
0 1 2 3 4 5 6
Number of U-bends
Figure 6.16 Measured polarisation conversion in the U-bends.
Third experiment: MMI-MZI demultiplxer with adapted U-bends
For a third experiment we use the same configuration as for the previous experiment (see figure
6.5b). However, the 1.4 μm narrow bends are replaced by bends with a width in the whispering
gallery (WG) regime. In this way, polarisation conversion is avoided as discussed in section
3.9. As deeply etched waveguides are used, the width and radius are chosen at 3 μm and 50 μm
respectively, which will give negligibly low polarisation conversion.
At the input and output of the MMI-couplers 3 μm wide waveguides are used in order to relax
production tolerances. In the array they are tapered down over a length of 50 μm to a width of
1.4 μm in order to ensure monomode operation. Application of such narrow waveguides leads
to increased coupling losses at junctions to the broad curved waveguides. Additonally, the
losses at a junction between two oppositely curved waveguides increase as well, due to the
highly asymmetric modal field distribution in the broad waveguide bend. Tapers cannot be
used here, as then the U-bends cannot be placed close to one other anymore, whereby avoiding
the usage of this geometry.
Figure 6.17a shows the calculated transmission at a junction from a 1.4 μm wide straight to a
curved waveguide, for two widths of the bend. In figure 6.17b the calculated transmission
between two oppositely curved waveguide is shown, from a 1.4 μm wide bend to both a
1.4 μm and a 3.0 μm wide bend respectively. As the array arm with three U-bends (the largest
number for a 4 ×
4 demultiplexer, see figure 6.5b) contains two straight-curved junctions and
six curved-curved junctions, the importance of a low junction loss becomes evident. When
using narrow bends (1.4 μm), the total junction loss amounts to 0.4 dB, which is sufficiently

6.2 MMI-MZI demultiplexer 115
low. In the case of broad bends (3.0 μm), the total of junction losses is approximately 3.2 dB
and the loss per U-bend is therefore in the order of 1.1 dB excluding radiation losses. Referring
to figure 6.13, the cross talk level is then expected to be -20 and -23 dB respectively, and the
insertion loss will increase by 1.8 dB.
Transmission [dB]
0.0
-0.5
-1.0
-1.5
1.4-1.4 μm 1.4-3.0 μm
-2.0
-0.5 0.0 0.5 1.0
Offset [μm]
(a) (b)
-2.0
-0.5 0.0 0.5 1.0 1.5 2.0
Offset [μm]
The performance has been calculated for this MMI-MZI demultiplexer and is shown in figure
6.18a. The insertion loss of the demultiplexer is approximately 1.8 dB, which is an increase of
1.5 dB with respect to the ideal case, i.e. the U-bends are considered to be without loss (see
figure 6.6). The calculated cross talk level lies between -20 and -25 dB, which corresponds
well with the predicted values of -20 and -23 dB (figure 6.13).
Transmission [dB]
The losses at a junction between two oppositely curved waveguides should be minimised, as
they mainly determine the total junction losses for the longest array arm. This can be done by
inserting a short bi-modal waveguide section, as shown schematically in figure 6.19. The
principle is explained as follows. The high junction loss is mainly due to the asymmetry of the
waveguide mode in the bend, which is inherent to WG modes. At the transition from the WG
Transmission [dB]
0.0
-0.5
-1.0
-1.5
1.4-1.4 μm 1.4-3.0 μm
Figure 6.17 Calculated transmission between a straight to a curved (a), and
between two oppositely curved waveguides (b), for two narrow waveguides (solid
lines), and for a 1.4 μm and a 3.0 μm wide waveguide (dashed lines).
0
-5
-10
-15
-20
-25
1
3 1
4
2
2 4
-30
1520 1525 1530 1535 1540 1545 1550
Wavelength [nm]
-30
1520 1525 1530 1535 1540 1545 1550
Wavelength [nm]
(a) (b)
Transmission [dB]
0
-5
-10
-15
-20
-25
1
4 3
2 1 2 4
Figure 6.18 Calculated response of the third MMI-MZI demultiplexer without
(a) and with (b) U-bends with bimodal sections for TE polarisation.
3

116 6. MMI-based components
bend to a straight waveguide not only the fundamental mode is excited, but also the first-order
mode. If the length of the straight waveguide is chosen in such a way that at the end the modes
are shifted π radians in phase with respect to each other, a mirrored replica of the input field is
obtained, which will couple with low loss to the field in the oppositely curved waveguide. In
this way, the total U-bend loss can be decreased to a value in the order of 0.4 dB (instead of the
expected 0.8 dB for two junctions, see figure 6.17b), if the transition section has a length of
approximately 11 μm. Additionally, due to the short length of the inserted waveguide, the
dimensions of the U-bend are hardly influenced.
Figure 6.19 Schematic diagram of the bi-modal transition waveguide for the
junction loss reduction between two oppositely curved waveguides.
In figure 6.18b the calculated response for a device with bi-modal sections in the U-bends is
shown. The U-bend loss is approximately 0.4 dB, leading to a predicted increase of the
insertion loss of 0.6 dB (see figure 6.13). The calculated response shows an insertion loss of
1.1 dB, which is 0.8 dB higher than for the ideal case, whereas an increase of 0.6 dB was
predicted. The cross talk is expected to be better than -30 dB, which can be verified from the
figure.
A MMI-MZI demultiplexer with optimised U-bends has been produced. The measured
response of a device without AR-coating is shown in figure 6.20a and b, for TE and TM
polarisation respectively. Using a polarisation filter, it was verified that no polarisation
conversion occurred in the array arms. The on-chip losses are 3.5-5.5 dB for TE polarisation
and 2.5-4.5 dB for TM polarisation, which include almost 1.0 dB propagation loss. The cross
talk was measured to be better than -7.5 dB (-11 dB best case) for TE polarisation and better
than -9 dB (-14 dB best case) for TM polarisation. This may be due to width deviations leading
to errors in the phase transfer. A TE-TM shift of 1.9 nm was observed.
=
=
+
+

6.3 Spatial mode filter 117
On-chip loss [dB]
0
-5
-10
-15
-20
-25
3
1 2 4 3 1
-30
1525 1530 1535 1540 1545 1550 1555
Wavelength [nm]
6.2.4 Conclusion
In this section a novel type of phased-array demultiplexer has been presented and a detailed
operation and tolerance analysis has been given. It can be concluded that, although MMI
couplers are commonly considered to be tolerant devices, the MMI-based demultiplexer is not.
It is sensitive to width variations of the MMI coupler, which makes it difficult to match the
wavelength response of a device to fixed system wavelengths. Additionally, the application of
U-bends gives rise to power imbalance in the array arms, which results in increased cross talk
levels. Therefore, an improved design may be found in the layout as depicted in figure 6.5c
[55,76]. This design has the advantage of all array arms having the same number of junctions
and bends, but, on the other hand, the device size being of larger dimension.
In contrast with conventional phased-array demultiplexers, the (narrow) bandwidth of the low
cross talk window cannot be enlarged without changing the channel spacing, which makes the
device less attractive for use in WDM systems. However, this narrow bandwidth is no problem
for a multi-wavelength laser as suggested by Herben et al. [55].
Summarising, we can conclude, that for the MMI-MZI demultiplexers to become a success,
the production process has to be accurately controlled, as they are very sensitive to width
deviations (which increase with increasing MMI-width) and to array guide loss imbalance.
Their application may therefore be restricted to low numbers of channels (up to 4).
6.3 Spatial mode filter
2
-30
1525 1530 1535 1540 1545 1550 1555
Wavelength [nm]
(a) (b)
Devices are mainly designed to operate optimally for the fundamental waveguide mode. Firstorder
waveguide modes will disturb the device operation (they cause, for instance, the “ghost”
images in a phased-array demultiplexer as discussed in section 4.4) and therefore excitation of
these modes should be avoided. Especially for the fibre-chip coupling it is difficult to maintain
low first-order excitation over a long period of time. Therefore, a - preferably compact - spatial
mode filter is desired. Mode filtering can be done by an adiabatic asymmetric Y-junction [16],
which is, however, difficult to produce due to the stringent demands on the lithographic
resolution necessary to obtain a sharp intersection angle. Additionally, this device is relatively
On-chip loss [dB]
0
-5
-10
-15
-20
-25
3
1
2 4 3 1 2
Figure 6.20 Measured response of the third MMI-MZI demultiplexer for TE (a)
and TM polarisation (b).

118 6. MMI-based components
long. A compact solution to this problem is the application of a single MMI coupler, as
developed simultaneously both at TU Delft and ETH Zurich independently of each other.
Leuthold et al. [74] published the first device, which was produced in a low-contrast
waveguide structure. The device measured 340 μm by 12 μm, had a first-order mode rejection 1
of 18 dB and an excess loss of 0.2 dB. Shortly thereafter it was followed by the device
described in this thesis [36], which is more compact and has a higher first-order mode
rejection, due to the fact that it was produced in a high-contrast waveguide structure.
6.3.1 Operation principle
The principle of such a MMI-based spatial mode filter lies in the fact that symmetric and
asymmetric modes applied at the input, are mapped differently onto output waveguides as
shown schematically in figure 6.21. The operation principle can be explained as follows.
According to theory [13,14,121], using a centre-fed MMI coupler N1-fold images of the input
field are obtained at LMMI,1 = 3Lπ ⁄ 4N 1 . This length equals the length of a N 2 × N 2 power
splitter-combiner LMMI,2 = 3Lπ ⁄ N 2 with N1 = 1 and N2 = 4. The result is that, if a zero-order
mode is applied at the input waveguide, it will be imaged at the centre output waveguide.
For first-order mode excitation, we consider the input waveguide as a combination of two
waveguides that touch each other, but neither of them lies at the centre of the MMI coupler.
The first-order field is then considered as the sum of two separate zero-order fields, which are
in counter phase, i.e. one of which has an additional phase term . From table 6.1 (columns
with i = 2 and i = 3, inputs i = 1 and i = 4 are not used) it can be directly seen that constructive
interference will occur into the outer output waveguides 1 and 4, and destructive interference
into the centre output waveguides 2 and 3. Due to the balanced power distribution over both
input fields, which is inherent to first-order fields, there is no residual power coupled into the
centre output waveguides, as long as the length and width are made as designed. Simulation
results obtained with a standard 2D Beam Propagation Method (BPM) analysis show the
operation of the spatial mode filter and are depicted in figure 6.22.
W/2
L MMI
e jπ –
j = 1
j = 2
j = 3
j = 4
Figure 6.21 Schematic diagram of a MMI-based spatial mode filter, including
mapping characteristics for zero-order mode (filled) and first-order mode (open).
1. The first-order mode rejection is defined as the amount of power emerging at the centre output
waveguide when a first-order mode is applied at the input waveguide.
W

6.3 Spatial mode filter 119
6.3.2 Tolerance analysis
(a) (b)
Figure 6.22 Simulated filter operation obtained with BPM analysis: zero-order
mode excitation (a) and first-order mode excitation (b).
As the mode filters are specially designed for usage in the raised-strip waveguide based
phased-array demultiplexer, the waveguide structure as depicted in figure 4.3 is used for the
tolerance analysis. The guiding strip is 2.2 μm thick and 3.0 μm wide in order to obtain zero
birefringence. The width of the outer waveguides is chosen at 2.0 μm for optimum coupling
efficiency. In order to obtain the smallest possible MMI coupler, the gaps between the
waveguides were chosen to be equal to the lithographic resolution of 0.6 μm. In order to obtain
low insertion loss, the width of the MMI section was chosen at 8 μm, resulting in a small offset
of the two outer output waveguides. By calculating the propagation constants of the
fundamental and first-order mode in the MMI section, the length of the section is then 134 μm.
Bandwidth of first-order mode rejection and insertion loss
As the mode filter consists of a single MMI coupler, the bandwidth equals the range 2 δλ centred
around the design wavelength λc (see equation 6.9). The waveguide structure is extremely
good guiding and the effective mode width equals approximately the waveguide width. Equation
6.9 can then be rewritten as:
2 δλ Z( α)
Nπd 2
0
≅ Z( α)
2w2
≈ (6.20)
-----------------λ
2 c
4W MMI
--------------λ
2 c
W MMI
whereby N = 4 has been used (as it operates as a 4 ×
4 coupler) and w is the waveguide width
of the narrow waveguides. Filling in the values, the 1-dB bandwidth follows as λc /10, which
demonstrates the potentially wide application range of the device.
Figure 6.23 shows the response of the mode filter versus the wavelength deviation Δλ from the
design wavelength of 1535 nm. The symbols 0_0 and 0_1 (or 1_0 and 1_1) denote the
transmission to the centre output and to one of the outer waveguides respectively, when the
fundamental (or first-order) mode is applied at the input. It can be seen that a first-order mode

120 6. MMI-based components
rejection (denoted by 1_0) better than -30 dB is obtained over a wide wavelength range. It is
noted that due to the fact that the power of a first-order mode applied at the input is equally
divided over the two outer waveguides at the output, the -3 dB level denotes zero excess loss.
Transmission [dB]
0
-1
-2
-3
-4
-5
-125
-50 -40 -30 -20 -10 0 10 20 30 40 50
Δλ [nm]
Width tolerance of first-order mode rejection and insertion loss
Analogous to the wavelength tolerance, the expression for the width is rewritten as follows:
The 1-dB width tolerance calculated using this equation equals 0.45 μm, so for this device a
lateral dimensional control of ± 0.2 μm, which is a realistic value for a standard lithographic
process, is sufficient for low-loss operation. In addition, if the width is controlled within
± 0.2 μm of the design value, the first-order mode rejection remains below -30 dB. Figure 6.24
shows the response versus the deviation ΔW of the width with respect to the designed value.
0_0
1_1
0_1
1_0
0
-25
-50
-75
-100
Figure 6.23 Response of the mode filter versus wavelength variation.
Transmission [dB]
0
-2
-4
-6
-8
2
de Suppression Rejection ratio [dB]
δW ≤ Z( α)
-----------------
(6.21)
2W MMI
-25
-50 [dB]
0_0
1_1
0_1 -75
1_0 Rejection
-100
-10
-125
-1.0 -0.5 0.0
ΔW [μm]
0.5 1.0
Figure 6.24 Response of the mode filter versus width variation.
0
Suppression ratio [dB]

6.3 Spatial mode filter 121
Layer thickness tolerance of first-order mode rejection and insertion loss
The device is very tolerant to a variation of the guiding layer thickness. When the layer
thickness is varied within ± 0.2 μm, the transverse index varies within ± 0.1 %. This can be
converted to a deviation of the length using equation 6.8, which leads to a value in the order of
± 0.1 μm.
6.3.3 Experimental results
The spatial mode filter as described in the previous section has been produced in cooperation
with Philips Optoelectronics Centre. The centre input and output waveguide is 3.0 μm wide
and the outer output waveguides are 2.0 μm wide. The MMI coupler with dimensions of
134 × 8
μm 2 , is the smallest reported so far [36]. The measured response is shown in figure
6.25. In order to be able to excite the zero-order mode as well as the first-order mode in a
controllable manner, a lateral offset was applied in the input waveguide. This offset introduces
an additional excess loss, which is depicted as the dashed line in the graph. The excess loss of
the filter was measured to be 0.5 ± 0.2 dB, which is slightly higher than expected. The firstorder
mode rejection is better than -30 dB, which corresponds well with predictions.
Rejection ratio [dB]
-20
-25
-30
-35
6.3.4 Conclusion
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Offset [μm]
Figure 6.25 Measured filter response: first-order rejection ratio (triangles) and
excess loss (squares) as a function of the offset applied at the input waveguide.
The lines denote the simulated rejection ratio (solid) and excess loss (dashed).
An analysis has been presented of a mode filter based on a single MMI coupler, which is easy
to produce as only one tolerant etching step is required. Calculations clearly show the
advantages of the device: compact size, low-loss operation, high first-order mode rejection,
large optical bandwidth and tolerance to width variations. The device can therefore be used in
a wide variety of applications. Experiments demonstrate the low loss operation (0.5 dB) and
the high first-order mode rejection (better than -30 dB).
0
-1
-2
-3
-4
-5
Excess loss [dB]

122 6. MMI-based components
6.4 Optical imaging of MMI patterns
Accurate methods for measuring two-dimensional intensity patterns in integrated optical
devices are not available at present. Techniques which image the light scattered at
inhomogeneities in the waveguide layer, suffer from the large local inhomogeneity of the
scattering sources. Another method is positioning identical devices at different distances
relative to a cleaved end-face, as shown schematically in figure 6.26. This method only
provides us with one-dimensional intensity scans at different positions in the devices, provided
that the excitation conditions can be reproduced. In this section we present a method of
imaging the field patterns in integrated optical devices using two-step cooperative
upconversion in erbium ions incorporated in the waveguides.
Cooperative upconversion is a process whereby two excited Er 3+ ions exchange energy,
promoting one of them to a higher energy level [22]. Two sequential upconversion processes
lead to emission of green light (519 and 545 nm). As the process depends on the concentration
of excited Er 3+ ions, which in turn depends on the intensity of the field distribution, the
emission of green light is a (roughly fourth-power) replica of the intensity distribution in the
waveguide. This work has been carried out in cooperation with the FOM-Institute for Atomic
and Molecular Physics, and has been presented earlier [30,59].
Figure 6.26 Schematic diagram of positioning identical devices at different
distances relative to a cleaved end face.
6.4.1 Upconversion mechanism
Figure 6.27 shows the energy level diagram of Er 3+ and a schematic graph of how cooperative
upconversion proceeds. The various energy levels of the Er 3+ ion are numbered 0 to 6. Figure
6.27a illustrates the first-order process between two Er 3+ ions in the first excited state, whereby
one of them transfers its energy to the other, promoting the latter to the third excited state. This
process depends quadratically on the concentration of Er 3+ in the first excited state, as two ions
are involved. The ions in the third excited state decay rapidly and non-radiatively to the second
excited state. As the lifetime of level 2 is relatively long (0.25 ms) a significant population in
the second excited state is built up.
Subsequently, a second upconversion process can take place (figure 6.27b), whereby two ions
in the second excited state interact in a similar fashion, thereby populating the sixth excited
state. Radiative decay from this state to the ground state causes emission at 519 nm. In
addition, non-radiative decay can occur to the fifth excited state; radiative decay of this state to
the ground state causes emission at 545 nm. As two subsequent upconversion steps are

6.4 Optical imaging of MMI patterns 123
involved, the emission of this visible green light is roughly proportional to the fourth power of
the concentration of Er 3+ in the first excited state, which, in turn, linearly depends on the
intensity of the infrared light. It thus becomes possible to image the intensity distribution of
1.48 μm pump light directly by monitoring the green emission. The measurement resolution is
then limited by the diffraction limit for 519 and 545 nm light. Therefore, field intensities can
be determined with a measuring resolution of approximately 3 times (!) better than if the pump
light, propagating in the waveguide, were imaged directly.
Energy [eV]
2.4
2.3
1.9
1.6
1.3
0.8
520
545
660
798
979
1530
Wavelength [nm]
⇒
0 0
6.4.2 Measurement principle
Figure 6.28 shows the measurement set-up, where a simple microscope objective placed above
the waveguide is used for imaging the green light intensity distribution as the 1485 nm light is
guided through the waveguide.
⇒
(a) (b)
Figure 6.27 Energy level diagram of Er 3+ showing cooperative upconversion.
SiO 2
Al 2 O 3
SiO 2 substrate
Figure 6.28 Principle of the measurement setup.
microscope objective
0.3 μm
0.6 μm
6
5
4
3
2
1

124 6. MMI-based components
Accurate measurements can be made by digitizing the output on a CCD camera. The fourth
power dependence between the green and the infrared light is favourable for attaining high
measurement accuracy. The short wavelength of the upconverted light makes it possible to
measure with a resolution considerably below the diffraction limit for the infrared light, which
allows for high accuracy imaging with medium quality objectives.
6.4.3 MMI-coupler simulation
Self-imaging is a property of multimode waveguides, which means that an input field is
reproduced in single or multiple images at periodic intervals in the MMI-section as shown in
figure 6.29. As discussed earlier, at distances L = LMMI ⁄ N an N-fold image of the input field
is obtained if the length of the MMI-coupler is chosen according to LMMI = 3Lπ ⁄ 4 .
LMMI ------------
5
LMMI ------------
3
LMMI
------------
2
L MMI
Figure 6.29 Schematic diagram of the self-imaging principle of a MMI-coupler.
Figure 6.30a shows the result of a simulation performed with the Beam Propagation Method
(BPM), using a 21 μm wide MMI-section centre-fed by a 2 μm wide input waveguide. The
light coming out of the input waveguide is seen to be diverging in the MMI-section and being
reflected by the side walls. The reflections cause the interference patterns which produce at
certain distances the single and multiple images typical for MMI devices.
(a)
(b)
Figure 6.30 Multimode interference: calculated patterns using BPM (a), and a
microscope image, visible as green light (b).

6.5 Discussion 125
6.4.4 Experiment
A MMI-coupler was produced in an aluminium oxide ridge waveguide structure [117],
implanted with erbium [57] to a peak concentration of 1.3 at.%. The device consists of a 2 μm
wide input waveguide, centre-fed to a 21 μm broad MMI-section. Light from a 1485 nm high
power laser was coupled into the input waveguide using a fibre taper. The power in the
waveguide was approximately 4 mW, calculated by substracting the estimated fibre-chip
coupling loss from the source power. Figure 6.30b shows the microscope image of the
multimode interference pattern, directly after the transition from the input waveguide to the
MMI-section. This image appears as green light due to a two-step cooperative upconversion
process as explained earlier. As can be seen, the measured intensity profile corresponds very
well with the calculated profile in figure 6.30a.
6.4.5 Conclusion
For the first time the optical interference pattern in multimode interference couplers operating
at 1485 nm has been made visible using an optical microscope. This is done by imaging the
green light (519 and 545 nm), which is generated by upconversion at high pumping power
levels in waveguides with a high erbium concentration. As the intensity of the green light is
roughly proportional to the fourth power of the pump signal intensity, it becomes possible to
image the 1485 nm intensity distribution with a resolution limited by the diffraction limit of
green light. For the 545 nm green light used here, this means that the measuring resolution is
approximately 3 times (!) better than if the pump light propagating in the waveguide was
imaged directly. This method is demonstrated with a MMI-coupler produced in an aluminium
oxide ridge waveguide structure implanted with erbium. The calculated intensity profiles
correspond very well with the measured data. This method offers an unique opportunity for
accurate measurements of lateral field patterns.
6.5 Discussion
This Chapter was dedicated to novel applications of MMI couplers. First a phased-array
demultiplexer based on MMI couplers has been presented and a detailed operation together
with a tolerance analysis has been given. Although MMI couplers are commonly considered to
be tolerant devices the MMI-based demultiplexers with U-bends have very stringent demands
on the production process. An improved design may be found in a less compact design with
identically shaped array arms (as depicted in figure 6.5c). In this way production tolerances are
relaxed, but even then variations in array arm losses have a rather large impact on the cross talk
performance. As the requirements on the width become more stringent with increasing width,
the width should be kept as narrow as possible, limiting the number of channels. Successful
application of MMI-based demultiplexers is therefore only expected for small numbers of
channels (up to 4).
Secondly, a mode filter based on a single MMI coupler has been discussed. The device is easy
to produce, as only one tolerant etching step is required. Because of its small size, it combines
a high first-order mode rejection with a large optical bandwidth and is tolerant to width
variations. It can therefore be used in a wide variety of applications.
Finally, the optical interference pattern in MMI couplers operating at 1485 nm is made visible
for the first time using an optical microscope. This is done by imaging the green light, which is
generated by upconversion at high pumping power levels in aluminium oxide ridge waveguides

126 6. MMI-based components
with a high erbium concentration. The calculated interference correspond very well with the
measured patterns and this method offers therefore an unique opportunity for accurate
measurements of lateral field patterns.

Chapter 7
Discussion and conclusions
In this thesis the design and production of polarisation independent PHASAR demultiplexers
has been described. The operation principle of PHASAR demultiplexers has been analysed and
elaborate attention has been paid to a number of different design requirements, such as
polarisation independence, flattened wavelength response, low-loss operation, etc. As a matter
of fact, in this way a sort of “PHASAR demultiplexer design manual” has been obtained.
Furthermore, an overview of the most important applications has been given.
Polarisation handling is an important issue for wavelength demultiplexers and therefore this
subject has been dealt with in a comprehensive way. A novel type of polarisation converter,
based on waveguide bends with ultra-small radii fabricated in a deeply etched waveguide structure,
has been discussed. Simulations and experiments show that high polarisation conversion
can be obtained. On the other hand, the device is sensitive to variations of the width and side
wall angle of the waveguide. Another important result of the analysis of deeply-etched
waveguide bends is, that by employing broad waveguide bends, polarisation conversion can be
minimised. As the side wall angle of the waveguide can be reproduced by using specific
settings of the etching process, a more detailed analysis of the effect of the side wall on
polarisation conversion may therefore be a suggestion for future work. Another suggestion
could be the insertion of a polarisation converter based on ultra-short bends in the middle of a
PHASAR demultiplexer.
Several methods to make demultiplexers polarisation independent are discussed in this thesis.
An extensive analysis of the polarisation independent raised-strip waveguide has been
presented. Important advantages of this type of waveguide are: low fibre-chip coupling losses,
compact device dimensions and broadband polarisation independence. A method for reducing
the insertion loss has been introduced and demonstrated, and the occurence of so-called
“ghost” images has been investigated. Finally, a packaged device integrated with
photodetectors has been described. This is the first compact PHASAR receiver in an industrystandard
Butterfly package.
Other methods for obtaining polarisation independence have also been described. The
compensation of the polarisation dispersion of the array waveguides, for instance, is discussed
extensively, including a tolerance analysis. This method has been applied to our waveguide
structure and experimental results are presented. The production is relatively simple, as a
selective wet-chemical etchant can be used for the polarisation dispersion compensating

128 7. Discussion and conclusions
section in the PHASAR. Another suggestion for future work is the analysis of the polarisation
dependent insertion loss of the device, which was obtained using this method.
Additionally, two methods which use polarisation conversion and splitting respectively, are
introduced and discussed with emphasis on cross talk tolerance, as no experimental results are
available. Obviously, future work is suggested on the application of these methods.
Novel components based on Multimode Interference (MMI) are also presented. The design of
a MMI-based demultiplexer is being discussed, together with a tolerance analysis with
experimental results being presented. It is found that the usage of this type of demultiplexers is
restricted to a low number of channels (up to 4). In addition, the bandwidth of the low cross
talk window is rather small, which, however, is not a problem for a multi-wavelength laser.
Furthermore, a novel type of spatial mode filter based on a single MMI coupler is discussed.
The discussion and tolerance analysis show the advantages of this device: compact size, large
optical bandwidth and tolerance to width variations. Experiments demonstrate the low-loss
operation combined with a high first-order mode rejection.
Finally, the interference patterns of the infrared pump light in a MMI coupler with a high
erbium concentration are made visible by imaging the green light, generated by upconversion
at high pumping power levels. In this way, the field intensity of the infrared light can be imaged
with a resolution below the theoretical diffraction limit (almost three times!). This is demonstrated
with a MMI-coupler produced in an aluminum oxide ridge waveguide structure
implanted with erbium.

Appendix A
Overview of phased-array
demultiplexers produced
In this appendix an overview is given of phased-array demultiplexers produced and some key
parameters. For the laboratories (third column) the following abbreviations are used:
Akzo Akzo Nobel Central Research, Arnhem, The Netherlands
Alcatel Alcatel Alstholm Recherche, Marcoussis, France
Lucent Lucent Technologies (f.k.a. AT&T Bell Laboratories), Holmdel, USA
Bellcore Bellcore, Red Bank, USA
BNR BNR Europe Limited, Harlow, United Kingdom
CNET France Telecom CNET, Bagneux, France
DUT Delft University of Technology, Delft, The Netherlands
Maryland University of Maryland, Baltimore, USA
NTT Nippon Telegraph and Telephone Corporation Optoelectronics
Laboratories, Ibaraki, Japan
OKI OKI Electric Industry Corporation, Tokyo, Japan
POC Philips Optoelectronics Centre, Eindhoven, The Netherlands
Siemens Siemens A.G. Research Laboratories, Munich, Germany
Furthermore, the following symbols are used:
N Number of channels
Δf Channel spacing
CT Cross talk
Δλpol TE-TM shift
The loss is defined as the total loss of the device including the chip coupling losses. However,
these losses are not always mentioned in the publications and therefore the superscript
notations (*) and (**) are used to denote the on-chip loss and the excess loss measured relative
to a straight waveguide respectively. In order to obtain a polarisation independent device
(Δλ pol = 0), a number of methods can be used (see section 2.2.4). These methods are denoted
by the following superscript numbers: (1) order trick, (2) λ/2 plate, (3) polarisation dispersion
compensation and (4) polarisation independent waveguides.

130 Appendix A. Overview of phased-array demultiplexers produced
Table A.1 Overview of PHASARs produced and some key parameters.
Ref. Year Laboratory Material N
Δf
[GHz]
Loss
[dB]
CT
[dB]
size
[mm 2 ]
162 89 DUT Al 2 O 3 4 213 0.6-3.2**

Table A.1 Overview of PHASARs produced and some key parameters.
Ref. Year Laboratory Material N
19 95 Alcatel InP 4 250 5-6*

132 Appendix A. Overview of phased-array demultiplexers produced

Appendix B
Dispersion of the phased array
The phased array is designed at a particular (freely chosen) central wavelength λ c in vacuo in
such a way that the optical path length difference ΔL between adjacent array waveguides is
equal to an integer number of wavelengths measured inside the array waveguide:
ΔL m λc = ⋅ --------
whereby N eff is the effective index of the waveguide mode. From figure 2.1b it can be seen that
the tilt angle dΘ results from a phase shift dΦ between adjacent waveguides and can be
described as:
β FPR,λc
dΘ
=
whereby is the propagation constant in the Free Propagation Regio (FPR) at the central
wavelength:
N FPR,λc
with being the effective index in the FPR calculated at the central wavelength.
The dispersion of the array is described as the displacement ds of the focal spot in the image
plane (see figure 2.1b) per unit frequency change:
N eff
dΦ ⁄ β dΦ ⁄ β FPR,λc
FPR,λc
asin⎛
---------------------------- ⎞ ≈ ----------------------------
⎝ ⎠
β FPR,λc
d a
=
N FPR,λc
R a
2π
⋅ ----λc
d a
(B.1)
(B.2)
(B.3)
ds dΘ
----- R
d f a ⋅ ------- --------------------d
f daβ FPR,λc
dΦ
= = ⋅ -------
(B.4)
d f

134 Appendix B. Dispersion of the phased array
with:
dΦ
-----d
f
whereby N g is the group index of the waveguide.
Combining these two equations leads to:
whereby Δα = da ⁄ Ra is the divergence angle between the array waveguides in the fan-in and
fan-out sections.
Finally, we find for the dispersion:
If we rearrange this equation we find:
with m' being defined as:
d----d
f
2πf ⎛-------- ⋅ N
c eff ⋅ ΔL⎞
2π
----- N
⎝ ⎠ c eff f dN ⎛ eff
+ ------------ ⎞ 2π
= = ⋅ ⋅ ΔL = ----- ⋅ N
⎝ d f ⎠ c g ⋅ ΔL (B.5)
dy
---d
f
λ c
------------------------ Ra ----- 2π
⋅ ⋅ ----- ⋅ N
c g ⋅ ΔL ----------------- ΔL 1
= = ⋅ ------- ⋅ ---- (B.6)
Δα
2πN FPR,λc
Δy
Δy
In this equation m' is the order of the demultiplexer, for which the material and waveguide
dispersion have been taken into account in contrast with the fixed (integer) order m of the
array. It is also noted that the term N eff ⁄ N in equation B.8 accounts for the transition
FPR,λc
from the array waveguides to the FPR.
From equation B.5 it an be seen that the response of the phased array is periodical. After each
phase change of 2π, the field will be imaged at the same position Δy. This period in the
frequency domain is called the Free Spectral Range (FSR) and is shown in figure 2.2. It is
found as the frequency shift for which the phase shift ΔΦ equals 2π, from which we find:
By substituting B.1 equation, we end up with:
d a
N g
----------------- ΔL
-------
Δα
Δf
= ⋅ ⋅ -----
N eff
N FPR,λc
N FPR,λc
f c
f c
N g
N FPR,λc
λ c
1
----------------- -------
Δα
Δf
= ⋅ ⋅ ----- ⋅ m' ⋅ --------
f
m' m 1 -------- dN eff
= ⋅ ⎛ + ⋅ ------------ ⎞
⎝ d f ⎠
N eff
2π
----- ⋅ Δ f
c FSR ⋅ N g ⋅ ΔL = 2π
Δ f FSR
=
f c
---m'
N eff
f c
(B.7)
(B.8)
(B.9)
(B.10)
(B.11)

Appendix C
Waveguide mode effective width
The diffraction properties of the phased array are conveniently expressed in terms of the
effective mode width w e , defined as the width of a uniform intensity distribution with the same
maximum intensity and power content as the modal field:
w e
∫
+∞
E( y)
2 dy
-∞
= -----------------------------
2
Emax (C.1)
Substitution of the expression for the (TE-polarised) modal field [160] yields the following
expression for w e :
w e
=
wwg -------- ⎛ 2
1 + --⎞
1
⋅ ≈ w ⎛
2 ⎝ v⎠
wg 0.5 + ---------------- ⎞
⎝ V – 0.6⎠
(C.2)
whereby wwg is the waveguide width and V and v are the normalised V-parameter and the
normalised transverse attenuation constant respectively. The far right expression, which is
found empirically by curve fitting in the range 1 < V < 10 , gives us a simple expression for
estimating the effective width.
Substitution of the Gaussian distribution E( y)
Eo y into equation A.1 yields
the following relation between we and wo :
2 2
= exp(
– ⁄ wo) wo = we ⋅ 2 ⁄ π
(C.3)
Using equations A.2 and A.3 the modal field is easily “translated” into an equivalent Gaussian
field.

136 Appendix C. Waveguide mode effective width

Appendix D
Cross talk penalty of the tunable laser
D.1 Measurement with a tunable laser
For the measurement of the wavelength response of the demultiplexers, the set-up as depicted
in figure D.1 is used. The HP 8168A tunable laser source is connected to a polarisation
controller, which in turn is connected to a lensed fibre, used for focusing the light onto the
cleaved facet of the chip. The light is coupled into the waveguide and after propagating through
the device, it reaches the other end of the chip. There, the light is being picked up by a microscope
objective, which has its focal plane aligned with the facet and is focused onto a pinhole
with an aditional lens. In this way, the pinhole acts as a spatial filter, so only the output of a single
waveguide is detected by the germanium photo diode.
HP 8168A
polarisation
controller
lensed
fibre
microscope
objective
Ge-diode
If we now take a look at the response of the tunable laser when operating at a wavelength of
1540 nm (see figure D.2), we can see that the side mode suppression ratio is below -40 dB (the
output power of the laser is 300 μW, or -5.2 dBm), but the laser also has a broad spontaneous
emission spectrum. When measuring the response of devices with a periodic wavelength
response, such as the phased-array demultiplexer, then not only the power of the peak
wavelength is detected by the (wavelength inselective) Ge-diode, but also periodic parts of the
spectrum. This is due to the fact that light of other diffraction orders also couple into the
receiver waveguide of the device. As a consequence, especially the measurement of the cross
talk is being influenced, as at a wavelength outside the pass-band of the device the signal is
suppressed to a level of the same order of magnitude as the level of the spontaneous emission.
chip
Figure D.1 Schematic diagram of the measurement setup.
lens
pinhole

138 Appendix D. Cross talk penalty of the tunable laser
At the transmission peak wavelength the signal level is hardly influenced, because it is a few
orders of magnitude higher than the spontaneous emission.
Response [dBm]
0
-20
-40
-60
-80
1400 1450 1500
Wavelength [nm]
1550 1600
Figure D.2 Measured response of the HP 8168A tunable laser, operating at a
wavelength of 1540 nm.
The amount of spontaneous emission detected by the Ge-diode depends on the FSR of the
measured demultiplexer and can be calculated by overlapping the response of the tunable laser
with the periodic response of the demultiplexer and integrating over the complete wavelength
range. It is obvious that a large FSR leads to a low cross talk penalty, as then only a small part
of the spontaneous emission spectrum is detected by the Ge-diode.
D.2 Measurement with an EDFA as source
For the measurement we now use the set-up as depicted in figure D.3. Instead of the tunable
laser, the Amplified Spontaneous Emission (ASE) of an Erbium Doped Fibre Amplifier
(EDFA) is used as source. As the light from the EDFA is circularly polarised, we now need a
polarisation filter. The measured ASE spectrum is shown in figure D.4a. The microscope
objective and the Ge-diode are replaced by a lensed fibre and a HP 71451A optical spectrum
analyser respectively.
EDFA
cleaved
fibre
microscope
objective
polarisation
filter
microscope
objective
chip
lensed spectrum
fibre analyser
Figure D.3 Schematic diagram of the measurement setup with EDFA and
spectrum analyser.

D.3 Conclusions 139
As an example we use the polarisation independent raised-strip-waveguide-based PHASAR as
presented in section 4.2.3, the measurement curve (using the tunable laser) of which is shown
in figure D.4b (dotted line, compare with figure 4.10). This device has a FSR of approximately
32 nm and a cross talk better than -25 dB. The response measured using the EDFA is
callibrated with respect to the ASE spectrum and is shown in figure D.4b (solid line). Both
curves are normalised to a peak maximum of 0 dB for good comparison. The improvement of
the cross talk level (from -25 dB to -32 dB) can be observed clearly.
ASE [dBm]
0
-20
-40
-60
1500 1520 1540 1560 1580 1600
Wavelength [nm]
D.3 Conclusions
-60
1540 1545 1550
Wavelength [nm]
1555 1560
(a) (b)
From the results presented here, it can be concluded that the best way to measure the response
of periodic devices is to use an EDFA and a spectrum analyser. In this way the spontaneous
emission of the tunable laser is filtered out completely and better cross talk figures are
obtained. Additionally, this method has the advantage that the measurement takes less time
(only a few seconds), during which the fibre-chip coupling efficiency will hardly vary.
Furthermore, the chips do not need to be anti-reflection coated, because of the limited slit
width (0.1 nm) of the spectrum analyser.
Transmission [dB]
0
-20
-40
5 dB
Figure D.4 ASE of an EDFA (a) and the response of the PHASARs (b).
32 dB

140 Appendix D. Cross talk penalty of the tunable laser

Appendix E
Excitation coefficient of the first-order mode
With reference to figure 4.14, an estimation is made of the excitation coefficient of the firstorder
mode at the junction between the free propagation region and the array waveguides. A
Gaussian approximation for the waveguide field is used and it is assumed that the gap between
the array waveguides equals zero. In figure E.1 both the far field of a transmitter waveguide
(dashed line) and the array waveguide fields (solid line) at the junction between the free
propagation region and the array waveguides are depicted.
intensity
array aperture
Figure E.1 Fields at the junction between the FPR and the array waveguides: far
field of a transmitter waveguide (dashed) and array waveguide fields (solid).
The maximum slope of a Gaussian field is 1/e 2 . If the number of array waveguides is chosen in
such a way that almost all power of the transmitter far-field is captured (see figure 2.3b), the
maximum slope of the far-field equals 1/(Nae 2 ) along a single array waveguide, with Na being
the number of array waveguides. (It should be noted that for larger gaps the slope is even less
steep.) We consider a single array waveguide field as denoted by the circle in the figure. We
can consider the far-field being built up locally of a uniform part and a linearly decreasing part.
The uniform part contributes to excitation of the fundamental mode in the array waveguide.
The linearly decreasing part, on the other hand, causes excitation of the first-order mode.
The excitation coefficient of the first-order mode can be calculated using the overlap integral of
the field distribution of the first-order mode and a saw tooth with slope 1/(Nae 2 ). The result of
this calculation is shown in figure E.2 as a function of Na . From this figure it can be seen that
for realistic values of Na ( N a >
10 ) the first-order excitation is well below -50 dB and may
therefore be neglected.

142 Appendix E. Excitation coefficient of the first-order mode
Excitation coefficient [dB]
-20
-40
-60
-80
0 20 40 60 80 100
Na Figure E.2 First-order mode excitation coefficient versus the number of array
guides N a .

Appendix F
Phase correction in MMI-MZI demultiplexers
As discussed in Chapter 6, a correction on the lengths of the array guides of a MMI-MZI
demultiplexer has to be made in order to obtain the proper phase distribution at the input of the
second MMI-coupler for the central wavelength. In this appendix it will be proven that this
correction is neglegibly small and will not influence the dispersion of the array.
The maximum length correction δL max will not exceed a half (central) wavelength in the
waveguide:
δL max
whereby N eff is the mode index of the waveguide. This will cause a maximum phase error:
whereby Δf ch is the channel spacing. If we neglect material and waveguide dispersion, we can
write for the far right term in the above equation:
By substituting equation F.3 and F.1 into F.2, we find for the maximum phase error:
λ c
1
c
≤ -- ⋅ -------- = ------------------
2 N eff 2 f cN eff
dβ
δϕmax = δLmax ⋅ Δβ ≈ δLmax ⋅ Δ f ch ⋅ ----d
f
dβ
----- = β
d f
1 1
---- -------- dN eff
⋅ ⎛ + ⋅ ------------ ⎞
⎝ d f ⎠
f c
N eff
δϕmax π Δ f ch
≤ ⋅ -----------
β
≈ ---f
c
As Δ f ch ⁄ f c « 1,
the maximum phase error δϕmax «
1 and therefore the influence on the
dispersion of the array is negligibly small.
f c
(F.1)
(F.2)
(F.3)
(F.4)

144 Appendix F. Phase correction in MMI-MZI demultiplexers

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April 29-May 2, 1996.

List of symbols
List of symbols and acronyms
αi starting angle of array waveguide i
αϕ angular propagation loss
β propagation constant in waveguide
βFPR propagation constant in FPR
βϕ angular propagation constant
βt transformed angular propagation constant
β0 propagation constant of fundamental mode
β1 propagation constant of first-order mode
C coupling coefficient
c speed of light
D dispersion
da pitch of the array waveguides in the array aperture
dr pitch of the receiver waveguides in the image plane
d0 waist of Gaussian field
Δα divergence angle of the array waveguides in the array aperture
Δβ propagation constant difference
Δfch channel spacing
ΔfFSR free spectral range
Δfpol TE-TM shift
ΔfL L-dB bandwidth
ΔΦ phase shift between adjacent array waveguides
Δϕj,i phase difference between port j+1 and port j when exciting port i
ΔL path length difference between adjacent array waveguides
Δλ01 modal dispersion shift
ΔNpol polarisation dispersion
Δn index contrast
Δspol polarisation shift along the image plane
Er radial component of the electrical field
Ex transverse component of the electrical field
Eϕ angular component of the electrical field
ε small loss term
η coupling efficiency

158 List of symbols and acronyms
fc central (design) frequency
ϕj,i phase transfer from port i to port j
ϕpol polarisation angle
Hi height of array waveguide i
i integer number
j integer number
j imaginary unit –
1
k integer number
k0 wave number in vacuo
kx wave number in the transverse direction
ky wave number in the lateral direction
L distance between the focal points
LMMI length of MMI coupler
La section length
Lc coupling length
Lo central channel insertion loss
Lp propagation loss in the array
Lu non-uniformity
Lπ beat length
li path length of array waveguide i
λc central (design) wavelength
m order of the array
m' order of the beam
N number of channels
Na number of array waveguides
Neff effective index in waveguide
Neff,t transformed effective index
NFPR effective index in FPR
Ng group index
Nridge effective index in the ridge region
Nstraight effective index in a straight waveguide
NTE effective index for TE polarisation
NTM effective index for TM polarisation
Nx transverse effective index in the ridge
N1 transverse effective index in the ridge
N2 transverse effective index in the region next to the ridge
n index distribution
nInP refractive index of InP substrate
nsub substrate index
nt transformed index distribution
nQ refractive index of the quaternary layer
P power
PTE power in TE field
PTM power in TM field
R radius of curvature
Ra length of FPR
Rco cut-off radius
Ri radius of curvature of array waveguide i

List of symbols and acronyms 159
Rt transformed radius of curvature
r radial coordinate
Si s
straigth section length (including Ra ) of array waveguide i
position along image plane
T transmission matrix
Tc transmission matrix of a curved waveguide
Tcc transmission matrix of a junction between two curved waveguides
Ts transmission matrix of a straight waveguide
Tsc transmission matrix of a junction between a straight and a curved waveguide
Tu transmission matrix of a U-bend
θ dispersion angle
θa angular width of the array aperture
θο angular width of the far field
U field distribution
u transformed coordinate
V lateral V-parameter (normalised film parameter)
w waveguide width
we effective width
wwg waveguide width
W waveguide width
WMMI width of MMI coupler
Wm cut-off width of the lateral mode m
ΔW waveguide width deviation
List of acronyms
ACTS Advanced Communications Technologies and Services
ADM Add-Drop Multiplexer
AR Anti-Reflection
ASE Amplified Spontaneous Emission
AW Array Waveguides
BPM Beam Propagation Method
CAD Computer-Aided Design
CATV Cable Television
CCD Charge-Coupled Device
CT Cross Talk
DBR Distributed Bragg Reflector
DEMUX Demultiplexer
DFB Distributed Feedback
DH Double Hetero
EIM Effective Index Method
EDFA Erbium-Doped Fibre Amplifier
FEM Finite Element Method
FPR Free Propagation Region
FSR Free Spectral Range
MAGIC Multistripe Array Grating Integrated Cavity
MDS Microwave Design System

160 List of symbols and acronyms
MMI Multimode Interference
MOCVD Methal-Organic Chemical Vapour Deposition
MOL Method Of Lines
MQW Multiple Quantum Wells
MSI Medium-Scale Integration
MUX Multiplexer
MW Multi-wavelength
MZI Mach-Zehnder Interferometer
NA Numerical Aperture
OCC Optical Cross Connect
OMVPE Organo-Metallic Vapour-Phase Epitaxy
PECVD Plasma-Enhanced Chemical Vapour Deposition
PHASAR Phased Array
POC Philips Optoelectronics Centre
Pt Platinum
Q Quaternary material (= InGaAsP)
RACE Research and technology development in Advanced Communications
technologies in Europe
RIE Reactive Ion Etching
RX Receiver
SEM Scanning Electron Microscope
SOA Semiconductor Optical Amplifier
SSI Small-Scale Integration
TE Transverse Electric
TM Transverse Magnetic
TOBASCO Towards Broadband Access Systems for CATV Optical Networks
TR Transition Region
TX Transmitter
WDM Wavelength Division Multiplexing
WG Whispering Gallery
X Switch

Summary
Wavelength (de)multiplexers are key components in optical networks. Research on integrated
optic (de)multiplexers has been focused on phased-array (PHASAR) based devices, which
appear to be robust and production tolerant because they can be produced in conventional
waveguide technology and require a relatively simple manufacturing process. In this thesis, a
comprehensive analysis of the operation and design of PHASAR demultiplexers is presented,
in which special attention has been paid to specific design requirements such as polarisation
independence and low-loss operation. PHASAR demultiplexers presented in this thesis are
produced on an InP substrate, as this material allows for small device dimensions and for
monolithic integration with active components such as for instance detectors and optical
amplifiers.
The major part of this thesis is focused on methods for making PHASARs polarisation
independent. As the state of polarisation of the transmitted light is unknown after propagating
through fibre and as it varies in time, it is important that the transfer of PHASAR
demultiplexers are insensitive to such variations. One way of making a PHASAR polarisation
independent is by inserting polarisation converters in the middle of the array. It was found that
waveguide bends with a very small radius, produced in a deeply etched waveguide structure,
have polarisation-converting properties, an extensive analysis of which is given in this thesis.
This work resulted in a novel type of polarisation converter with high conversion, low loss, and
of compact size.
Another way to make demultiplexers polarisation independent is by using polarisation
independent waveguides. Experiments, performed in cooperation with Philips Optoelectronics
Centre (POC), demonstrate that with this type of waveguide, compact devices can be made
with low on-chip loss and good cross talk values. Additionally such a device has been
integrated with photodetectors and packaged, which led to the first optical receiver mounted in
a compact, industry-standard butterfly package.
A third method for making PHASARs polarisation independent is by compensating the
polarisation dispersion of the array waveguides by inserting a waveguide section with a
different polarisation dispersion. Although this method is sensitive to width and layer
variations of the waveguide structure, it is relatively easy from a production point of view.
Experiments show that application of this method leads to polarisation independence at the
cost of a small increase of the device length (less than 1 mm).
Furthermore two other methods to obtain polarisation independence are discussed. The first
makes use of a compact polarisation converter (as discussed earlier) inserted in the middle of
the PHASAR demultiplexer. The second method uses a polarisation splitter at the input of the

162 Summary
PHASAR demultiplexer. Both methods are described in this thesis.
If the free propagation regions of the PHASAR demultiplexer are replaced with multimode
interference (MMI) couplers, a special type of phased-array demultiplexer is obtained. In this
way, the number of array waveguides can be reduced to a number equal to the number of wavelength
channels. Additionally, due to the uniform splitting ratio and low insertion loss of the
MMI couplers, low insertion loss of the device is expected. A number of experiments have
been performed, one of which uses a deeply etched waveguide structure. This allows for the
use of very small waveguide bends (radius 50 μm) and leads to the smallest demultiplexer ever
reported.
A single MMI coupler can also be used as a mode splitter. Such a device can be applied for
filtering higher order modes. The advantage of such a MMI-based mode splitter is the ease of
manufacture and its small size. Analysis and experiments presented in this thesis show that a
MMI-based mode splitter is very tolerant with respect to variations in wavelength, width, and
layer thickness.
Finally, the field distribution of the infrared light propagating in a waveguide has been made
visible for the first time, with a resolution below the theoretical diffraction limit. This was
possible using a two-step upconversion mechanism of erbium atoms incorporated in an
aluminum oxide waveguide structure. If two sequential upconversion processes take place,
visible green light is emitted. As the process depends on the concentration of excited erbium
ions (which in turn depends on the intensity of the field distribution) the emission of green
light is a replica of the intensity distribution in the waveguide. The field distribution of the
infrared light in a MMI coupler has been measured. It has been demonstrated that the measured
data match very well with calculated intensity profiles.

Samenvatting
Golflengte (de)multiplexers spelen een sleutelrol in optische netwerken. Onderzoek op het
gebied van golflengte (de)multiplexers heeft zich met name gericht op componenten gebaseerd
op een phased-array (PHASAR). Deze lijkt robuust en fabricage-tolerant te zijn omdat die in
een conventionele golfgeleidertechnologie gemaakt kan worden met behulp van een relatief
eenvoudig fabricageproces. In dit proefschrift wordt een uitvoerige analyse van de werking en
het ontwerp van PHASAR demultiplexers beschreven, waarbij speciale aandacht besteed
wordt aan specifieke ontwerp-eisen zoals polarisatie-onafhankelijkheid en lage verliezen. Alle
PHASAR demultiplexers in dit proefschrift zijn vervaardigd op InP substraat, hetgeen de
mogelijkheid biedt tot de realisatie van kleine component-afmetingen, en tot monolithische
integratie met actieve componenten, zoals detectoren en optische versterkers.
Het leeuwendeel van dit proefschrift is gericht op methoden om PHASAR’s polarisatieonafhankelijk
te maken. Aangezien de polarisatietoestand van het verzonden licht na
propagatie door de glasvezel onbekend is, en tevens varieert in de tijd, is het belangrijk dat de
response van PHASAR demultiplexers daarvoor niet gevoelig is. Een methode om PHASAR’s
polarisatie-onafhankelijk te maken is door polarisatie-omzetters in het midden van de reeks
golfgeleiders te plaatsen. Het blijkt dat golfgeleiderbochten met een kleine bochtstraal in een
diepgeëtste golfgeleiderstructuur, polarisatiedraaiende eigenschappen hebben, die uitgebreid
in dit proefschrift worden beschreven. Dit werk leidde tot de realisatie van een nieuw type
polarisatie-omzetter met een hoge omzetting, laag verlies en compacte afmetingen.
Een andere methode om PHASAR’s polarisatie-onafhankelijk te maken is door gebruik te
maken van polarisatie-onafhankelijke golfgeleiders. Experimenten, in samenwerking met
Philips Optoelectronics Centre (POC) uitgevoerd, laten zien dat op deze manier compacte
componenten gemaakt kunnen worden, die lage verliezen en weinig kanaaloverspraak hebben.
Daarnaast is een demultiplexer geintegreerd met detectoren en in een behuizing gemonteerd,
hetgeen leidde tot de eerste optische ontvanger die gemonteerd is in een compacte, industriestandaard
butterfly behuizing.
Een derde methode voor het verkrijgen van polarisatie-onafhankelijke PHASAR’s is door het
compenseren van de polarisatiedispersie van de reeks golfgeleiders door middel van het
plaatsen van een sectie met een andere polarisatiedispersie. Alhoewel deze methode gevoelig is
voor breedte- en diktevariaties in de golfgeleider, kan het op een vanuit het oogpunt van
fabricage eenvoudige wijze toegepast worden. Experimenten laten zien dat polarisatieonafhankelijkheid
gerealiseerd kan worden ten koste van slechts een kleine toename van de
componentlengte (minder dan 1 mm).
Verder worden twee additionele methoden voor polarisatie-onafhankelijkheid besproken. De

164 Samenvatting
eerste maakt gebruik van een compacte polarisatie-omzetter (zoals eerder beschreven), die in
het midden van de PHASAR demultiplexer geplaatst wordt. Bij de tweede methode worden de
polarisaties gescheiden aan de ingang van de PHASAR demultiplexer met behulp van een
polarisatiescheider. Beide methoden worden in dit proefschrift beschreven.
Indien de vrije-propagatie regio’s van de PHASAR demultiplexer vervangen worden door multimode
interferentie (MMI) koppelaars, wordt een speciale variant van de phased-array demultiplexer
verkregen. Op deze manier kan het aantal array-golfgeleiders gereduceerd worden tot
het aantal golflengtekanalen. Verder wordt laag verlies van het gehele component verwacht,
gezien de uniforme vermogensdeling en de lage verliezen van de MMI koppelaars. Een aantal
experimenten zijn uitgevoerd, waarvan één in een diep geëtste golfgeleider- structuur. Hierdoor
kunnen zeer kleine bochten gebruikt worden (bochtstraal 50 μm), hetgeen er toe leidde dat de
kleinste demultiplexer ooit gerapporteerd kon worden gerealiseerd.
Een MMI koppelaar kan ook gebruikt worden voor het scheiden van modes. Hiermee kunnen
dan hogere orde modes weggefilterd worden. Het voordeel van dergelijke scheiders is dat ze
eenvoudig vervaardigd kunnen worden met compacte afmetingen. Analyse en experimenten in
dit proefschrift tonen aan dat modescheiders gebaseerd op een MMI koppelaar ongevoelig zijn
voor variaties in de golflengte, breedte en dikte.
Tenslotte is voor de eerste keer de infrarode lichtverdeling in een golfgeleider zichtbaar
gemaakt met een resolutie die onder de theoretische diffractielimiet ligt. Dit bleek mogelijk
door een twee-staps opconversie mechanisme te gebruiken van erbium-atomen, die in een
aluminiumoxide golfgeleiderstructuur ingebracht zijn. Indien er twee van zulke conversies
achtereenvolgend plaatsvinden, wordt er zichtbaar groen licht uitgezonden. Aangezien het
proces afhankelijk is van de concentratie aangeslagen erbium-atomen, dat op zijn beurt weer
afhankelijk is van de veldverdeling in de golfgeleider, is de hoeveelheid uitgezonden groen
licht een replica van de veldverdeling. De veldverdeling van het infrarode licht in een MMI
koppelaar is gemeten, en er is aangetoond dat de meetresultaten goed overeenstemmen met
berekende veldverdelingen.

Dankwoord
Waarschijnlijk is het dankwoord één van de meest moeilijke hoofdstukken om te schrijven,
omdat je het risico loopt dat je iemand, die bijgedragen heeft aan het tot stand komen van dit
proefschrift, vergeet te bedanken. Omdat zoveel mensen een bijdrage geleverd hebben, zal het
moeilijk zijn om dit te voorkomen en daarom wil ik bij deze een ieder bedanken voor de
samenwerking. Een aantal mensen wil ik echter in het bijzonder noemen.
De meeste dank ben ik verschuldigd aan Meint Smit, die met zijn creativiteit en opbouwende
kritiek een grote bijdrage heeft geleverd aan het tot stand komen van dit proefschrift. Bart
Verbeek wil ik bedanken voor het opstarten van het onderzoek. Hans Blok, mijn promotor,
zorgde met zijn invalshoek voor een verhelderende kijk op zaken, hetgeen ook de leesbaarheid
van dit proefschrift verhoogde. Siang Oei, met wie ik gedurende een jaar op plezierige wijze de
kamer gedeeld heb, was onmisbaar om mij van alles over de InGaAsP technologie te leren.
Alle devices die in dit proefschrift zijn besproken, konden alleen maar gerealiseerd worden
dankzij een bijdrage van de technici en daarom wil ik ze speciaal bedanken. Tom Scholtes en
Liang Shi deponeerden siliciumnitridelagen, waarop Aad de Vreede en Koos van Uffelen de
lithografie verzorgden, hetgeen niet altijd even eenvoudig was vanwege mijn eisen ten opzichte
van de maatvoering. Samen met Ed Metaal (KPN Research) was Frans van Ham een goede
afmaker met zijn onnavolgbaar etswerk, alhoewel je het klieven van de samples maar beter niet
door hem kunt laten verzorgen voordat hij een kop koffie op heeft. Natuurlijk was dit alles
onmogelijk zonder de kwaliteitsmaskers gemaakt door Otto Meijer (Philips Research Masker
Centrum) en later door Fokke Groen. Ab Kuntze en Adrie Looyen zorgden voor de “finishing
touch” met hun anti-reflectie coatings. Laatstgenoemde wil ik nog speciaal bedanken samen
met Aad van der Lingen voor het masker schrijven en goud sputteren voor de traliedemultiplexer.
Lucas Soldano heeft mij de principes van de MMI koppelaar bijgebracht. Martin Amersfoort
leerde mij alles over fotodiodes, en samen hebben wij de eerste polarisatie-onafhankelijke
PHASAR ontworpen gebaseerd op de strip golfgeleiderstruktuur. Kees Steenbergen, Leo
Spiekman en Kees Vreeburg, met wie ik veel waardevolle discussies heb gevoerd, waren fijne
collega’s om mee samen te werken, ondanks het feit dat de eerste twee stiekem getrouwd zijn.
Wellicht zal laatstgenoemde het ook doen? Leo de Vreede heeft me vanaf het begin, al toen ik
nog aan het afstuderen was, geholpen met MDS, en later werd hij verlost van die taak door
Xaveer Leijtens. Met hem als kamergenoot was het prettig werken, niet in de laatste plaats
door het verminderen van het aantal keren koffie halen. Patrice Le Lourec leverde een
waardevolle bijdrage door het PHASAR simulatie programma verder te ontwikkelen en in
MDS te implementeren. Verder was het een genoegen om Chretien Herben, die mij van

166 Dankwoord
experimentele data voorzag, Peter Harmsma en Annett Siefke als collega te hebben.
Mijn speciale dank gaat uit naar Toine Staring, Hans Binsma en Edwin Jansen van het Philips
Optoelectronics Centre voor de vruchtbare samenwerking die leidde tot de succesvolle
realisatie van de op stripgolfgeleiders gebaseerde polarisatie-onafhankelijke phased-array
demultiplexers. Jos van der Tol en Jørgen Pedersen van KPN Research worden hartelijk
bedankt voor de discussies en suggesties. Tenslotte dank ik Gerlas van den Hoven, Albert
Polman en Pieter Kik van Amolf voor de samenwerking die heel wat publikaties opgeleverd
heeft, en - ook niet onbelangrijk - veel mooie foto’s van naar zichtbaar licht geconverteerde
veldverdelingen van infrarood licht in golfgeleiders (zie onder andere de omslag).
Een flink aantal studenten hebben mij geholpen, van wie ik er twee in het bijzonder wil
noemen. Loek van der Helm was de eerste die ik mocht begeleiden. Samen hebben we de
eerste (en, helaas, ook de laatste) tralie-demultiplexer van het lab ontworpen. Michiel ten Kate
heeft een goede bijdrage geleverd door zijn grondige aanpak van de metingen aan de MMI-
MZI demultiplexers, waardoor hij mij behoorlijk wat werk uit handen genomen heeft. Verder
waren daar nog Marco Boeren, Bart van Geest, Marco Kroonwijk, Robert Chandler, Marcel
Schaar, Martin Bouda en Richard Verhaar, die ik heb mogen begeleiden en mij veel werk uit
handen hebben genomen.
Mia van der Voort en Wendy van Schagen wil ik bedanken voor hun efficiente “office
management”, en, natuurlijk, de gezelligheid die hun aanwezigheid met zich meebracht. Ook
hebben ze altijd de uitstapjes van de vakgroep tot in de puntjes georganiseerd.
In het bijzonder wil ik Renée bedanken, omdat zij er altijd voor mij is. Zij zorgde voor een
rustige thuishaven en bracht vele avonden in eenzaamheid door, waardoor ze het op die manier
mogelijk maakte dat ik dit proefschrift kon voltooien. In de nabije toekomst zal ik haar, en
Marloes en Menno, de vrije tijd goedmaken die ik niet met hen heb kunnen doorbrengen.
Annemieke (“Micky”) bedank ik omdat ze dit proefschrift volledig heeft doorgeworsteld op
zoek naar eventuele fouten en mogelijke verbeteringen ter verhoging van de leesbaarheid. Ook
ben ik mijn ouders dankbaar voor het feit dat zij mij gestimuleerd hebben te leren en mijn
horizon te verbreden. Tenslotte dank ik al mijn vrienden: ook al hebben ze niets bijgedragen
aan dit proefschrift, ze zorgden in ieder geval voor de nodige ontspanning.

Biography
Cor van Dam was born in The Hague, the Netherlands, on 10th May 1967. After completing
his secondary education at “Maerlant Lyceum” in 1985, he started studying electrical
engineering at the Delft University of Technology, receiving his master’s degree in December
1990. His thesis research was carried out in the Integrated Optics group of the Laboratory of
Telecommunication and Remote Sensing Technology and concerned the development of an
CAD-tool for the design and analysis of photonic integrated circuits, using a microwave design
system (Hewlett-Packard’s MDS). In January 1991 he was appointed to the scientific staff of
the laboratory where he started his PhD research, the result of which lies in front of you. Since
March 1997, he has been working as a postdoctoral research scientist in the area of mobile and
satellite communications at the Physics and Electronics Laboratory of TNO (TNO-FEL) in
The Hague.