Investigation of the onset of chaos in an ergodic cavity

Abstract

The behavior of light is well understood and well documented in many different scenarios. Nonetheless the situations can get more complicated. We can easily calculate the electromagnetic field confined to a cubic volume by solving the wave equations. However, this is not so easy for arbitrary geometries of the boundary. The wave equation most likely does not have well defined Eigenmodes for arbitrary shape of the boundary and conditions on this boundary. This complex situation can give a chaotic field. In this bachelor thesis we are going to investigate this situation for a 2-dimensional cavity in the shape of a quarter stadium, in which light can move freely and is reflected on the boundaries. The shape of our cavity is expected to result in a really chaotic field, whose properties will be studied in detail below. We will introduce ergodicity and compare the behaviors of a chaotic and non-chaotic cavity using ergodic properties and looking at the divergence of two neighboring trajectories. Furthermore we will look at the onset of chaos in the wave field inside the cavity and suggest a test to determine if a field is completely chaotic.