Polarisation dependent loss calculation in echelle gratings using finite element method and Rayleigh expansion

We describe a numerical method to compute the reflectivity of a metallised integrated echelle grating. The modelling is based on a combination of a finite element method in the region inside the grating teeth and the Rayleigh field expansion outside. Results show a net dependence of the efficiency on the polarisation state (directly related to PDL), as a function of the wavelength, due to two factors: a lower reflectivity for the TM light in the operating order and a shift in the maximum of the response curve.