Spectral Coherence of Wave Fields in Random Media

Abstract

An original approach to the analysis of classical wave localization and diffusion in random media is developed. This approach is based on a cumulant path integral technique and, being universal with respect to the dimensionality of the system, accounts explicitly for the correlation properties of the disorder. The general theory is applied to the evaluation of a two-frequency mutual coherence function, which is an important quantity in itself, and also determines the evolution of transient signals in the time domain. Our results describe a ballistic to diffusive transition in the wave transport, and, for not too large distances, are consistent, in general, with a classical diffusion paradigm. In particular, the coherence function is shown to possess a well-pronounced two-scale structure, especially, when the absorption is taken into account. However, the final results are related to a power spectrum of the disorder, rather than to a phenomenological diffusion constant. Also, the propagation in random media is described explicitly as a process of wave scattering by resonant Bragg lattices hidden in a disordered structure, and an additional dwell time due to local resonances is taken into account. Since the coherence function is expressed via an arbitrary form power spectrum, the results obtained in the work open a new avenue in studying wave transport in anisotropic and/or fractally correlated systems.