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Numerical performance of finite-difference modal methods for the electromagnetic analysis of one-dimensional lamellar gratings

Philippe Lalanne 1 Jean-Paul Hugonin 1
1 Laboratoire Charles Fabry de l'Institut d'Optique / Naphel
LCFIO - Laboratoire Charles Fabry de l'Institut d'Optique
Abstract : The numerical performance of a finite-difference modal method for the analysis of one-dimensional lamellar gratings in a classical mounting is studied. The method is simple and relies on first-order finite difference in the grating to solve the Maxwell differential equations. The finite-difference scheme incorporates three features that accelerate the convergence performance of the method: (1) The discrete permittivity is interpolated at the lamellar boundaries, (2) mesh points are located on the permittivity discontinuities, and (3) a nonuniform sampling with increased resolution is performed near the discontinuities. Although the performance achieved with the present method remains inferior to that achieved with up-to-date grating theories such as rigorous coupled-wave analysis with adaptive spatial resolution, it is found that the present method offers rather good performance for metallic gratings operating in the visible and near-infrared regions of the spectrum, especially for TM polarization.
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Philippe Lalanne, Jean-Paul Hugonin. Numerical performance of finite-difference modal methods for the electromagnetic analysis of one-dimensional lamellar gratings. Journal of the Optical Society of America. A Optics, Image Science, and Vision, Optical Society of America, 2000, 17 (6), pp.1033-1042. ⟨hal-00867708⟩

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