Coherent scattering enhancement in systems bounded by rough surfaces

When an electromagnetic wave is incident on a bounded random system that supports two or more discrete eigenmodes at the frequency of the incident wave, the angular distribution of the intensity of the fields scattered incoherently from, and transmitted incoherently through, the system can display peaks at special scattering angles and angles of transmission, determined by degenerate time-reversal symmetry, in addition to the well-known enhanced backscattering and enhanced transmission peaks. These additional peaks are multiple-scattering phenomena caused by the coherent interference between each multiply-scattered wave and a degenerate time-reversed partner. We illustrate both analytically and numerically the occurrence of satellite peaks in scattering and transmission in the case that the scattering system is a thin, supported, dielectric film, and in the case that it is a free-standing metal film, into which the randomness is introduced by making the illuminated surface of each film a one-dimensional, random surface. The origins of the satellite peaks, and their positions are explained on the basis of a simple argument based on the phase coherence of multiply-scattered trajectories mediated by the degenerate surface or guided waves supported by each of these structures. Perturbative and computational approaches to the calculation of the scattering and transmission spectra are described, and experimental conditions most favorable for the observation of the predicted features are presented. The coherent interference of multiply-scattered fields affects drastically the time evolution of a wave packet (electron or electromagnetic pulse) injected into a closed disordered cavity. We show that in this case conventional perturbative methods are inapplicable for the calculation of the statistical moments of the wave field, and introduce the random matrix theory (RMT) approach for the description of disordered closed systems. The statistics of the eigenlevels and eigenfunctions of such systems is studied employing the RMT method for different types of symmetry. The existence of coherent enhancement (a peak in the stationary distribution of the intensity of a pulse) in cavities with random boundaries is demonstrated analytically, and confirmed by numerical experiments in an acoustic resonator with random boundaries.