Wave coupling within systems with irregular boundaries is a common phenomenon in many branches of science such as acoustics, vibrations, electromagnetics, and others. If the wavelength of the incident wave is small compared with the structure size, and the dynamics of the ray trajectories within the scattering region are chaotic, the scattering properties of the cavity will be extremely sensitive to small perturbations. These structures are then termed wave chaotic. Exact solutions of such systems are not feasible and various alternative methods are sought.

In the first part of this dissertation, such alternative methods are used to calculate the power delivered to a port in a two-dimensional wave chaotic enclosure. These methods are the ray tracing (RT), the Dynamical Energy Analysis (DEA) and the Power Balance methods (PWB). Particularly, the RT and DEA are used to calculate power received at an aperture and are compared with the established PWB. These results indicate that the RT and DEA are equivalent methods. Additionally, RT is compared with direct numerical simulations of the wave fields and found to be accurate if the wavelength is sufficiently small.

The Random Coupling Model (RCM) gives a statistical description of coupling of radiation in and out of large enclosures through localized and/or distributed ports. The RCM, in contrast to DEA, PWB, and standard RT, includes both amplitude and phase information. It combines both deterministic and statistical information and makes use of wave chaos theory to extend the classical modal description of the cavity fields in the presence of boundaries that lead to chaotic ray trajectories. In the second part of this dissertation, a correction to the RCM termed the Short Orbit Formulation (SOF) is used to calculate successfully the impedance of a two-port wave chaotic enclosure in two dimensions using RT. Also, a directed beam approach was used to launch energy in a wave chaotic enclosure to break the so called 'random plane wave hypothesis', a fundamental basis of the RCM formulations. Results show that launching of such directed beams lead to enhanced short orbit effects which make the RCM inapplicable.