In simulations, S-Parameters from PDK has been used. S-Parameters mostly defined by 3D FDTD simulations and measured data from already produced components. Values in S-Parameter matrix are wavelength dependent and define insertion loss due to transmitted light, return loss due to reflected light and couplings in between.
Interferometer needs a kind of phase difference between transmitted and reflected lights, and in order to have this effect, there are 2 options according to theoretical calculations. \(\alpha\) is imaginary side of complex refractive index, which is used to calculate losses due to scattering from sidewall imperfections created during E-Beam lithography process. Because of it's dependency on fabrication process, only some estimated values can be used. (Typically 3dB/cm for \(\lambda\)=1500nm, straight waveguide in TE mode) \(\beta\) is propagation constant of waveguide, and depends on wavelength and effective index.    
\(\beta_1 =\frac{2 \pi n_1}{\lambda}\)\(\beta_2 =\frac{2 \pi n_2}{\lambda}\)
\(E_{output}=\frac{E_i}{2}\left(e^{-i\beta_1L_1-\alpha_1/2L_1}\right)+\left(e^{-i\beta_2L_2-\alpha_2/2L_2}\right)\)
\(I_{output}= \frac{I_{input}}{4}\mid\left(e^{-i\beta_1L_1-\alpha_1/2L_1}\right)+\left(e^{-i\beta_2L_2-\alpha_2/2L_2}\right)\mid^2\)
As can be seen from equations, output intensity can be adjusted by changing propagation constants of each branches, or creating a path length difference between them. 
If propagation loss is ignored, equation can be simplifed as :
\(I_{output}=\frac{I_{input}}{2}[1+cos(\beta_1L_1-\beta_2L_2)]\)