Electromagnetic study of photonic band gaps

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Abstract
Using a rigorous integral theory of diffraction gratings, we investigate the properties of two-dimensional photonic crystals made with lossless dielectric materials using a model where the crystal is represented by a finite stack of dielectric grids of infinite extension. After studying the influence of the thickness of the crystal, we analyse the variations of the properties of the gap with the filling ratio, the index of dielectric, the geometry of the crystal, the shape of the rods, the polarization and finally with a contrast inversion. The validity of this multi-grid model is checked by varying the angle of incidence, which appears to have a significant influence. Some surprising properties emerge from these results, in particular the fact that contrast inversion has opposite effects according to whether the incident wave is s or p polarized. Finally, we give a very simple empirical rule that enables one to predict with a good precision the location of the centres of the gaps.