\(\) MZI
According to Eq.(\ref{eqn:x}), in order to create a set of MZIs that are evenly spaced in FSR, the interferometer arm length difference should be calculated as \(\Delta L=\frac{\lambda^2}{\text{FSR}\cdot n_g}\). In this design, the range of FSR is chosen as [0.25,0.5,1,2,3,4] nm. The corresponding \(\Delta L\) is \([2290,1145,573,286,191,143]\ \mu\text{m}\).
A parameter sweep of arm length differece is performed in Lumerical INTERCONNECT and the transmission gain results are exported to MATLAB for analysis. The FSR is calculated as the average interval between all peaks within 1540~1560 nm wavelength range. The simulated FSR results are displayed in Fig. 5. The simulation result of FSRs matches the theoretical predictions well, especially for narrow FSR cases, where the result is averaged across a larger number of peaks.