Solução numérica das equações de Maxwell para cavidades dielétricas bidimensionais

Abstract

The objective of this work is to find numerical solutions for Maxwell's equations in two-dimensional dielectric cavities. Such structures can trap light by means of total internal reflections and can be used for constructing lasers in the micron scale, known as microlasers. The shape of the cavity affects the dynamics of rays inside it, so that it can be regular or chaotic, and completely determines the emission pattern of the radiation. During the development of our computational algorithms, we have considered the problem of the circle, whose dynamics is integrable, and the stadium, which has chaotic dynamics. We partially reproduced results in the literature. In addition, we also considered a new geometry, which probably can provide unidirectional emission, a goal that is being sought by the scientific community.