Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals

We present a numerical study of bidimensional photonic crystals with an emphasis on the behavior of the gaps versus the polarization and the conicity of the incident plane wave. We use a rigorous modal theory of diffraction at oblique incidence by a set of arbitrarily shaped parallel fibers. This theory allows the study of the refractive properties of bidimensional photonic crystals. We develop a heuristic method of homogenization that allows us to predict the position of the gaps and their behavior with respect to the polarization and the conicity angle. With this homogenization scheme, we also present some important elements for obtaining full gaps.