Contribution à la résolution numérique des équations de Maxwell dans le domaine temporel-application à la propagation des ondes électromagnétiques dans les fibres à cristaux photoniques.

Abstract

Photonic crystals are structures in which the refractive index of the dielectric material varies periodically along one or more directions in space. This periodic variation along the three directions produces a photonic band (BIP) on the light propagating in photonic crystals, corresponding to an energy interval where the propagation of light is forbidden in certain directions of this crystal. This effect is analogue to the effect of periodic potential on electrons in a crystal. Maxwell's equations are proposed to describe the propagation of an electromagnetic wave in a photonic crystal with a two-dimensional hexagonal structure, and this description is calculated by finite-difference time-domain methods (FDTD). A numerical simulation using this method allowed us to study the influence of the variation of some properties and characteristics of photonic crystals on the propagation of an electromagnetic wave in a photonic crystal fiber.