Our approach consists in finding the eigenmodes and the complex eigenfrequencies of structures using
a finite element method (FEM), that allows us to study mono- or bi-periodic gratings with a maximum
versatility : complex shaped patterns, with anisotropic and graded index material, under oblique incidence
and arbitrary polarization. In order to validate our method, we illustrate an example of a four layer
dielectric slab, and compare the results with a specific method that we have called tetrachotomy, which
gives us numerically the poles of the reflection coefficient (which corresponds to the eigenfrequencies of
the structure). To illustrate our method, we show the eigenvalues of one- and two-dimensional gratings.
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