Computational Efficient Solution of Maxwell's Equations for Lamellar Gratings

In this work, a new implementation of the analytic modal method (AMM) based on an improved and computationally e±cient approach to calculate the eigenvalues and corre- sponding eigenfunctions of the Helmholtz equation is presented. In case of TE polarization the computational time is remarkably reduced by adopting the perturbation approach. The portion of the computation time required to calculate eigenfunctions in case of TE polarization become almost negligible when a large number of eigenfunctions in the expansion is used. In case of TM polarization we use the pseudospectral method to calculate an initial guess solution for eigenval- ues which are subsequently re¯ned by Newton's method. The proposed improved AMM allows to calculate the electromagnetic ¯eld in arbitrary stack of lamellar gratings.