InP-based polarisation independent wavelength demultiplexers

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.