Phenomenological theory of filtering by resonant dielectric gratings

Using a phenomenological theory of diffraction gratings made by perturbing a planar waveguide allows us to deduce important properties of the sharp filtering phenomena generated by this kind of structure when the incident light excites a guided wave. It is shown that the resonance phenomenon occurring in these conditions acts on one of the two eigenvalues of the Hermitian reflection matrix only. As a consequence, we deduce a mathematical expression of the reflectivity and demonstrate that high-efficiency filtering of unpolarized light requires the simultaneous excitation of two uncoupled guided waves. Numerical examples are given.