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

An original approach to the description of classical wave localization in w eakly scattering random media is developed. The approach accounts explicitl y for the correlation properties of the disorder, and is based on the idea of spectral filtering. According to this idea, the Fourier space (power spe ctrum) of the scattering potential is divided into two different domains. T he first one is related to the global (Bragg) resonances and consists of sp ectral components lying within a limiting sphere of the Ewald construction. These resonances, arising in the momentum space as a result of a self-aver aging, 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 obs erved in the configuration space. Combining a perturbative path-integral te chnique with the idea of spectral filtering allows one to eliminate the con tribution of local resonances, and to distinguish between possible stochast ic and dynamical localization of waves in a given system with arbitrary cor related disorder. In the one-dimensional (1D) case, the result, obtained fo r the localization length by using such an indirect procedure, coincides ex actly with that predicted by a rigorous theory. In higher dimensions, the r esults, being in agreement with general conclusions of the scaling theory o f localization, add important details to the common picture. In particular, the effect of the high-frequency localization length saturation is predict ed for 2D systems. Some possible links with the problem of wave transport i n periodic or near-periodic systems (photonic crystals) are also discussed. [S1063-651X(99)08010-1].