Proceedings PaperAnalytical approach of rugate filter properties using Mathieu functions
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Rugate filters have raised interest for a decade as examples of simple periodic continuous structures. As continuous, they are supposed to offer a much wider set of spectral responses than discrete structures. As periodic they typically exhibit a spectrum with high reflectivity bands in much the same way their discrete counterparts do. These properties are of a great interest, for it allows the possibility of making high reflectivity mirrors with very narrow bandwidth. The purpose of this paper is an attempt to study such filters in the particular case of sinusoidal index profiles, by solving rigorously the wave equation. This approach is compared with more conventional approximation methods such as the coupled mode theory or numerical methods.