A new modeling system to determine the optical response function of a multilayer structure with imposed periodicity in the plane of the layers, a multilayer diffraction grating, is described. This new model has two essential ingredients. This model is based on the well-established coordinate transformation procedure developed by Chandezon et al. [ J. Opt. Soc. Am. 72, 839– 846 ( 1982)] in which a periodically modulated surface is transformed into a frame in which it is flat, permitting simpler use of Maxwell’s boundary conditions. Then, instead of using the conventional transfer-matrix method, we developed a scattering-matrix technique that permits the modeling of very thick (of the order of 1 μm or greater) multilayer systems with many field components without numerical instability. Model programs have been developed based on this new scattering-matrix approach and tested by comparison with other models and experimental data.
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