Resonances and localization of classical waves in random systems with correlated disorder

An original approach to the description of classical wave localization in weakly scattering random media is developed. The approach accounts explicitly for the correlation properties of the disorder, and is based on the idea of spectral filtering. According to this idea, the Fourier space (power spectrum) of the scattering potential is divided into two different domains. The first one is related to the global (Bragg) resonances and consists of spectral components lying within a limiting sphere of the Ewald construction. These resonances, arising in the momentum space as a result of a self-averaging, determine the dynamic behavior of the wave in a typical realization. The second domain, consisting of the components lying outside the limiting sphere, is responsible for the effect of local (stochastic) resonances observed in the configuration space. Combining a perturbative path-integral technique with the idea of spectral filtering allows one to eliminate the contribution of local resonances, and to distinguish between possible stochastic and dynamical localization of waves in a given system with arbitrary correlated disorder. In the one-dimensional (1D) case, the result, obtained for the localization length by using such an indirect procedure, coincides exactly with that predicted by a rigorous theory. In higher dimensions, the results, being in agreement with general conclusions of the scaling theory of localization, add important details to the common picture. In particular, the effect of the high-frequency localization length saturation is predicted for 2D systems. Some possible links with the problem of wave transport in periodic or near-periodic systems (photonic crystals) are also discussed.