Abstract
Several improvements have been introduced for the Fourier modal method in the last fifteen years. Among those, the formulation of the correct factorization rules and adaptive spatial resolution have been crucial steps towards a fast converging scheme, but an application to arbitrary two-dimensional shapes is quite complicated.We present a generalization of the scheme for non-trivial planar geometries using a covariant formulation of Maxwell's equations and a matched coordinate system aligned along the interfaces of the structure that can be easily combined with adaptive spatial resolution. In addition, a symmetric application of Fourier factorization is discussed.
Highlights
14th Physics Institute, University of Stuttgart, Stuttgart, Germany; 2LASMEA, Université Blaise Pascal, Aubière Cedex, France; 3General Physics Institute, Russian Academy of Sciences, Moscow, Russia; The Fourier modal method is a common rigorous Maxwell solver for calculating the optical properties of periodic nano-structured materials. It has been improved by a number of numerical methods such as adaptive spatial resolution [1] and factorization rules [2]
For more general applications, such as arbitrarily shaped two-dimensional and three-dimensional metallic photonic crystals and metamaterials, we develop coordinate transformations with the mesh locally aligned along the surface of the metallic structure, which enables us to use adaptive spatial resolution and factorization rules in the same way as for the simpler structures [3]
We are going to present the scheme of calculation in matched coordinates and apply it on several numerical examples such as a periodic arrangement of cylinders
Summary
14th Physics Institute, University of Stuttgart, Stuttgart, Germany; 2LASMEA, Université Blaise Pascal, Aubière Cedex, France; 3General Physics Institute, Russian Academy of Sciences, Moscow, Russia; The Fourier modal method is a common rigorous Maxwell solver for calculating the optical properties of periodic nano-structured materials.
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