## 2 Design of the 1 \(\times\) 4 Channel Wavelength Demultiplexer
### MZI Based 1 \(\times\) 4 Channel Wavelength Demultiplexer
It will be shown in Section 3 that the thermal heaters designed in this work, can compensate up to 0.5\(\uppi\) of phase shift error at the expense of 150 mW (25 V, 6 mA) electrical power consumption. We have also investigated the effect of waveguide width variation on the phase shift between the two long delay arms (25.13 mm) of each MZI filter. As an example, we include a 2 nm width variation on the two delay arms (_i.e._, 2.8 \(\upmu\)m and 2.802 \(\upmu\)m wide) of each of the three MZI filters in the demultiplexer. From a similar mode simulation method described in Section 2.1, we find that for a 2.802 \(\upmu\)m waveguide width, the group index increases by \(\Delta n_{g}=1.55\times 10^{-5}\) at 1550 nm wavelength. The change in group index induces \(\pi\)/2 phase mismatch between the two 25.13 mm long delay waveguides which can be compensated by the thermal heaters. However, if the waveguide width variation is more than 2 nm over 25.13 mm long waveguide, the thermal heaters designed in this work cannot compensate for the phase error. However, the MZI delay waveguides are placed in proximity, and it is unlikely that two waveguides maintain such width difference over the 25.13 mm length. In fact, two delay waveguides in proximity are more likely to have  
Figure 4: Schematic of the 1 \(\times\) 4 channel wavelength demultiplexer architecture with the integrated Cr heater on the delay arms of the Mach-Zehnder interferometer (MZI) (not to scale). \(V_{1}\) to \(V_{6}\): electrical pad to apply the DC voltages for thermal tuning, _G:_ ground pad, \(L_{1}\) to \(L\)_s:_ delay waveguide lengths (in green color). the same width offset, which would induce near zero phase shift in the demultiplexer compensable by the thermal heaters  
Thermal heaters were integrated on top of the MZI delay waveguides for tuning the phase of the optical signal upto \(\pi\)/2. As mentioned in the paragraph above, we have added an extra delay length of \(L_{\pi 2}\) = 0.257 \(\upmu\)m to passively achieve the \(\pi\)/2 phase shift. Despite this delay, thermal heaters make the design of the demultiplexer more robust against fabrication variations. The electrical contact pads on the heaters were 2 mm \(\times\) 0.5 mm in dimension with pitch = 1 mm (Figure 6a). The large separation between the contact pads will simplify and lower the cost of wire bonding to the chip. However, in this work we have applied electrical voltage to the heaters using external DC probes. We have used proprietary data from LioniX BV to keep the separation between the thermal heaters from 8 mm to 16 mm, to avoid thermal crosstalk (Figure 6b). Figure 5: Simulation result of the (**a**) overlapped transmission responses of the four optical output channels and (**b**) overlapped transmission responses of the four optical output channels in the presence of a delay length mismatch error 100 nm. Figure 6: (**a**) Dimension and vertical separation between the electrical contact pads, (**b**) Layout of the thermal heaters, minimum distance is kept to 8 mm to avoid thermal crosstalk.