Analysis of diffraction gratings via their resonances

We analyze diffraction gratings via their resonances by a direct determination of the eigenmodes and the complex eigenfrequencies using a finite element method (FEM), that allows 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).