Resonant mode coupling approximation for calculation of optical spectra of photonic crystal slabs

This article represents the development of the resonant mode coupling approximation method for determining optical spectra of a stack of two photonic crystal slabs. This method is based on the derivation of the input and output resonant vectors in each slab in terms of the Fourier modal method in the scattering matrix form. We show that using the resonant mode approximation of the scattering matrices of the upper and lower slabs one can construct the total scattering matrix of the stack. We demonstrate that the developed procedure dramatically decreases the computation time without sufficient loss of accuracy. We believe that the proposed technique can be a powerful tool for the fast solving of inverse scattering problems using stochastic optimization methods such as genetic algorithms or machine learning.