Particlelike states in D-shaped fibers

Abstract

In this thesis we investigate the classical (particle) and wave dynamics in a three-dimensional fiber with a D-shaped cross section. Dependent on the placement of the cut the system shows regular, completely chaotic or mixed classical dynamics. Here, we are mainly interested in the latter two cases in which chaos can counteract the formation of so-called particlelike states, which are highly collimated beams. Regarding the classical dynamics we use Monte-Carlo methods to generate trajectory bundles that mimic initial wavefronts in order to achieve the best agreement with our wave simulations. In the framework of the Helmholtz equation, our search for particlelike wave states is focused on finding a new operator constructed from the transmission matrix which contains states with the desired beam-like behavior among its eigenstates. These states remain highly collimated rather than showing a fan-like spreading along their propagation through the system. The behavior of these wave states will be investigated in the spatial domain as well as in classical phase space by means of Husimi distributions, where we will also make a comparison with the results obtained by classical trajectory-bundle simulations.