After the effective index information was obtained using simulation, the next step is to get a model based on a second order polynomial fit. As it was mentioned in the course, we can use MATLAB or Lumerical scripting tool to obtain the fit parameters. For the quasi-TE mode the effective index approximates to:

\(n_{eff} = 2.44763 - 1.12907(\lambda - 1.55) - 0.0354547(\lambda - 1.55)^2\)

And for the quasi-TM mode an approximation of the effective index is:

\(n_{eff} = 1.77031 - 1.24432(\lambda - 1.55) + 1.92466(\lambda - 1.55)^2\)

In the following sections, the responses of some MZI designs will be obtained.