Modélisation et Simulation des Effets Non linéaires dans les Cristaux Photoniques.

Abstract

Photonic crystals are structures made up of a periodic arrangement of dielectric materials, these crystals have a spatial periodicity in their dielectric constant varies periodically at the wavelength scale on one, two or three directions in space. However, an analogy with solid-state physics allows us to develop the fundamental concepts and to understand the behaviour of these objects. In this work, we will focus on the advantages of photonic crystals for the enhancement of second order (GSH) and third order (Kerr effect) non-linear effects, since the parameters of these structures are correctly chosen. For the analysis of such structures, dispersive properties and prohibited band diagrams are determined using the plane wave method. As the analytical resolution of these equations is not evident, the use of numerical methods such as FDTD is essential to obtain the time and space solutions of the evolution of electromagnetic fields in such structures. We have found that the coupling between non-linear effects and photonic crystals is now essential for the explanation of several phenomena from different fields of technological applications.