Coupled { Wave Analysis of Planar { Grating

A numerical method using a Pad e Approximation has been developed for the solution of the vectorial diiraction problem of a homogeneous plane wave with arbitrary angle of incidence by an innnite dielectric grating. The method is based on the Coupled Wave Theory. After discretization of the grating by a division into planar layers, the transmission matrix of each layer is calculated with a Pad e Approximation. The overall transmission behaviour is given by the product series of all single{layer transmission matrices. As the structure of the eld describing diierential equation, obtained by Maxwell's equations, is very easy, the algorithm has been optimized with respect to the calculation time and the required memory. The structure of the system matrix, mentioned above, is obtained by a special arrangement of the state variables within the state vector. This leads to the same structure of the system matrix as the one obtained in the case of scalar diiraction problems. Therefore, the same numerical algorithms for computing the matrix exponential may be used.