Ergodicity and chaos in the multiple light reflection

Abstract

ABSTRACT The main goal of this work is the implementation of some mathematical notions like attractors, orbits, sensitivedependence and chaos in the study of the multiple reflection of a light beam. We shall analyse some concrete situations ofreflection on a circle, on a rectangle and the general case of a conic, all this cases with direct application to the optical resonant cavities oflasers. Using some general results concerning the dynamical systems, we shall point out the conditionsthat the multiple reflection must satisfy in order to obtain a periodic reflection or chaotic behaviour. 1. INTRODUCTION Despite the fact that only the wave theory offers a good explanation of the nature of the light and can be applied without any limitations, the geometrical approximation of the light rays travelling in straight lines turns out to be equally useful inthe study of optical instruments. This is the case for example with the resonant cavities of the lasers, where a whole set of theoretical problems can be successfully studied in the context of the geometrical optics.One of this problems concerns the stability and the periodicity of a light ray during the multiple reflection in a resonator.The apparent simple problem of the multiple reflection of a light beam could appear like an interesting example of a discrete