Presentation - Computational Optics Group

Dr Jasmin Smajic
Simulation based design of plasmonic waveguides,
waveguide bends, and surface-wave splitters
1 , Prof. Christian Hafner2 , 06.07.2009
1 ABB Switzerland Ltd.
Corporate Research Dättwil
Segelhofstrasse 1K, CH-5405 Baden-Dättwil, Switzerland
jasmin.smajic@ch.abb.com
© ABB Group
July 8, 2009 | Slide 1
2 Swiss Federal Institute of Technology (ETH)
Laboratory for EM Fields and Microwave Electronics
Gloriastrasse 35, CH-8092 Zürich, Switzerland
Christian.hafner@ifh.ee.ethz.ch

Outline
© ABB Group
July 8, 2009 | Slide 2
Introduction
Plasmon resonance
Surface plasmon polaritons
Numerical methods for analysis of the plasmonic
structures
Waveguide structures
Plasmonic slotline waveguide (PSWG)
Metalic heterowaveguide (MHWG)
2D eigenvalue analysis
3D analysis of the waveguide
Waveguide bend
3D analysis of the 90º waveguide bend
Plasmonic surface wave splitter
2D analysis of the surface wave splitter
Outlook

Introduction
Plasmon Resonance
Plasmon effect: the effect of collective vibrations of electrons in metal at
infrared and optical frequencies
Surface plasmon: the fluctuations of electron density at the metal-insulator
interface
Surface plasmon polariton: a surface plasmon coupled with photon
The excited polariton propagates over the metal’s outer surface until it is
either converted back into a photon or absorbed by the crystal lattice as a
phonon
Surface plasmon resonance (SPR): the excitation of the surface plasmons by
external EM radiation
Localized surface plasmon resonance (LSPR): metalic structure smaller than
the wavelength
Metal at optical and infrared frequencies: described as a homogenous
domain with complex dielectric permittivity
© ABB Group
July 8, 2009 | Slide 3

Introduction
Surface Plasmon Polaritons
© ABB Group
July 8, 2009 | Slide 4
omega (1/s)
x 1015
12
10
8
6
4
2
air
silica
surface plasmon
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
x 10 7
0
beta (1/m)

Introduction
Surface Plasmon Polaritons
© ABB Group
July 8, 2009 | Slide 5
Propagation length (um)
1000
900
800
700
600
500
400
300
200
100
0
0 500 1000 1500 2000 2500
wavelength (nm)

Introduction
Surface Plasmon Polaritons
Propagation length (um)
1000
900
800
700
600
500
400
300
200
100
© ABB Group
July 8, 2009 | Slide 6
|Ey | 0.2 m
2 |Ey | 2
350nm
0
0 500 1000 1500 2000 2500
wavelength (nm)
|E y | 2
370nm
Propagation length (um)
360nm
20
15
10
5
0
0.2 m
200 250 300 350 400 450 500
wavelength (nm)
0.2 m

Introduction
Numerical Methods
© ABB Group
July 8, 2009 | Slide 7
Domain Methods Boundary Methods
Finite Element Method (FEM)
Finite Difference
Time Domain (FDTD)
Multiple Multipole
Program (MMP)
Method of Auxiliary
Sources (MAS)
Meshless Boundary Integral
Equation (BIE) Approach
J. Smajic et al., “Comparison of Numerical Methods for the Analysis of
Plasmonic Structures”, Journal of Computational and Theoretical
Nanoscience, Vol. 6, No. 3, pp. 763-774, 2009.

Waveguide Structures
Plasmonic slotline waveguide (PSWG)
Description
Geometry
and materials
© ABB Group
July 8, 2009 | Slide 8
A plasmonic slotline is an air slot in a thin silver film deposited on a
silica substrate.
The dimensions of the slot are much smaller than the wavelength.
The goal is to find a bound optical mode supported by the slotline.
50nm
Silver
50nm
Silica
Silver
G. Veronis et al., “Guided subwavelength plasmonic mode supported by a
slot in a thin metal film”, Optics Letters, Vol. 30, pp. 3359-3361, 2005.

Plasmonic Slotline
2D Eigenvalue Analysis
Analysis
Modeling
© ABB Group
July 8, 2009 | Slide 9
Assumption: The bound mode is a hybrid mode.
Analysis: 2D vector elements are required.
Open boundary: PML absorbing boundary conditions are needed.
PML

Plasmonic Slotline
2D Eigenvalue Analysis
Analysis
Modeling
© ABB Group
July 8, 2009 | Slide 10
Bound mode: E x and Hy dominant (quasy-TEM, easy to excite by
linearly polarized light).
Significant propagation losses in silver
The z-component of time-average
Poynting vector is shown at 750nm.

Plasmonic Slotline
2D Eigenvalue Analysis
Results
© ABB Group
July 8, 2009 | Slide 11
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
bound mode
light line (air)
light line (silica)
0.03
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Dispersion relation of the fundamental mode
of the slotline (red) is shown.

Plasmonic Slotline
2D Eigenvalue Analysis
Results
© ABB Group
July 8, 2009 | Slide 12
Lpr (um)
14
12
10
8
6
4
2
0
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
wavelength (um)
Propagation length of the fundamental
mode of the slotline is shown.

Plasmonic Slotline
2D Eigenvalue Analysis
Results
© ABB Group
July 8, 2009 | Slide 13
0.12
0.1
0.08
0.06
0.04
0.02
w=50nm
w=25nm
0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Dispersion relation of the fundamental mode
of the slotline (dark blue) is shown.

Plasmonic Slotline
2D Eigenvalue Analysis
Results
© ABB Group
July 8, 2009 | Slide 14
Lpr (um)
14
12
10
8
6
4
2
w=50nm
w=25nm
0
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
wavelength (um)
Propagation length of the fundamental
mode of the slotline is shown.

Waveguide Structures
Metalic Heterowaveguide (MHWG)
Description
Geometry
and materials
© ABB Group
July 8, 2009 | Slide 15
The dimensions of the structure are smaller than the wavelength.
The goal is to find a bound optical mode supported by the MHWG.
L. Chen et al., “High efficiency 90ºbending metal heterowaveguides for
nanophotonic integration”, Applied Physics Letters, Vol. 89, pp. 243120, 2006.

Waveguide Structures
Metalic Heterowaveguide (MHWG)
Analysis
Modeling
© ABB Group
July 8, 2009 | Slide 16
Bound mode: E x and Hy dominant (quasy-TEM, easy to excite by
linearly polarized light).
Significant propagation losses in metals
The z-component of time-average
Poynting vector is shown at 750nm.

Waveguide Structures
Metalic Heterowaveguide (MHWG)
Results
© ABB Group
July 8, 2009 | Slide 17
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
bound mode MHWG
bound mode PSWG
light line (air)
light line (silica)
0.03
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Dispersion relation of the fundamental mode
of the MHWG and PSWG is shown.

Waveguide Structures
Metalic Heterowaveguide (MHWG)
Results
© ABB Group
July 8, 2009 | Slide 18
Lpr (um)
15
10
5
bound mode MHWG
bound mode PSWG
0
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
wavelength (um)
Propagation length of the fundamental
mode of the MHWG and PSWG is shown.

Waveguide Structures
3D Waveguide
© ABB Group
July 8, 2009 | Slide 19
Silver is modeled as a
homogenous material with
complex permittivity
50nm
50nm
Silica substrate, n=1.44

Waveguide Structures
3D Waveguide
© ABB Group
July 8, 2009 | Slide 20
Losses in silver (3D) = 34.43%
Losses in silver (2D) = 32.77%
100%
61.3%
Time-average Poynting vector
of the fundamental mode of the slotline is shown.

Waveguide Structures
3D Waveguide
© ABB Group
July 8, 2009 | Slide 21
The electric field confinement of the fundamental
mode of the slotline is presented.

Waveguide Bend
3D analysis of the 90ºwaveguide bend
© ABB Group
July 8, 2009 | Slide 22

Waveguide Bend
3D analysis of the 90ºwaveguide bend
© ABB Group
July 8, 2009 | Slide 23
Losses in silver (3D) = 42.98%
Losses in silver (2D) = 42.30%
100%
23.9%
Time-average Poynting vector
of the fundamental mode of the slotline is shown.

Plasmonic Surface Wave Splitter
2D Analysis of the Surface Wave Splitter
Geometry
Modeling
© ABB Group
July 8, 2009 | Slide 24

Plasmonic Surface Wave Splitter
2D Analysis of the Surface Wave Splitter
© ABB Group
July 8, 2009 | Slide 25

Outlook
© ABB Group
July 8, 2009 | Slide 26
Modern 3D simulation models are very close to reality
and therefore make virtual prototyping and design
optimization possible
High level of spatial discretization required for
accurate analysis of the plasmonic structures can be
achieved today even in the case of complicated 3D
structures
Presented waveguide solutions (PSWG) are within the
current fabrication abilities
Problem of losses in metal is an important drawback

© ABB Group
July 8, 2009 | Slide 27