Vectorial diffraction analysis of periodic dielectric gratings using a transmission matrix

A numerical method has been developed for the solution of the vectorial diffraction problem of an homogeneous plane wave of arbitrary incidence by an infinite dielectric grating. The method is based on the Coupled Wave Theory. After discretization of the grating by division into planar layers, the transmission matrix of each layer is calculated with a Pade approximation. The overall transmission behaviour is given by a product series of all the single-layer transmission matrices. It is shown that a special arrangement of the state variables leads to the same structure of the system matrix as the one obtained in the case of scalar diffraction problems. Therefore, the same numerical algorithms for computing the matrix exponential may be used