InP-based polarisation independent wavelength demultiplexers

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)