Cristaux photoniques et métamatériaux etude et simulation de la bande interdite photonique

Abstract

This thesis falls within the field of periodic artificial materials and focuses on the study and simulation of the photonic bandgap in and two-dimensional (2D) photonic crystals with square and triangular lattices, in connected and disconnected configurations. Three dielectric materials of major interest for optical and telecommunications applications have been selected: silicon (Si), gallium arsenide (GaAs), and lithium niobate (LiNbO₃). Considered as artificial materials with a periodic refractive index structure, they enable control over the of electromagnetic waves. The fundamental property of these materials lies in the emergence of a photonic bandgap (Photonic Band Gap – PBG), which prevents light propagation in certain frequency ranges, regardless of the angle of incidence or polarization state, making them effective components for photonic control. The study concentrates on the modeling and analysis of two-dimensional (2D) photonic crystals with square and triangular geometric lattices, in connected and disconnected configurations. These materials, of scientific and technological interest, were selected due to their remarkable photonic and optical properties. Numerical simulations were conducted using the Rsoft software, relying on the plane wave method (Plane Wave Expansion Method), to determine the optimal geometric parameters of the lattices that maximize the width of the photonic bandgap. The results indicate that the connected triangular structure, for silicon and gallium arsenide, exhibits the widest photonic bandgap for both transverse electric (TE) and transverse magnetic (TM) polarizations. It has also been observed that the emergence of a common photonic bandgap, which simultaneously blocks both polarizations, is limited to connected structures. In contrast, disconnected structures prove more effective for achieving wide photonic bandgaps specific to the TE mode. Furthermore, a notable convergence in photonic performance between silicon and gallium arsenide has been highlighted regarding the properties of the photonic bandgaps.This study represents an essential contribution to determining the optimal dimensions of photonic lattices, enabling the integration of new optical functions such as resonant cavities, superprisms, and add-drop filters. These devices are indispensable for the development of advanced photonic systems intended for applications in telecommunications, optical fibers, and microwave systems.