Design of optical lattice filters using the Schur algorithm in the z-transform domain

Abstract

We propose a design method for optical lattice filters using the Schur algorithm in the z-transform domain. The algorithm of Schur (on a power series bounded in the unit circle) is used for the one-dimensional inverse scattering problem to determine the reflection coefficients of multilayer medium modeled by the lattice filter. The proposed algorithm can also be used to determine reflection coefficients in Fabry-Perot etalons and multilayer thin film modeled by the lattice filter structure. We use the FFT method to find the transmission transfer function from transmission magnitude only. To verify the method, we give three simple examples.