Spectral coherence and time-domain transport of waves in random media

An original approach is developed for the description of spectral coherence and time-domain transport of wave fields scattered in random media. This approach accounts explicitly for the correlation properties of the disorder and is universal with respect to the dimensionality of the system. Specifically, a two-frequency mutual coherence function is evaluated by using a procedure of embedding the initial Helmholtz equation into an auxiliary problem of a directed wave propagating in a higher-dimensional space. The resulting Schrödinger-like equation is solved perturbatively by means of a cumulant path integral technique. Mean intensity profiles and temporal moments of a narrowband wave packet scattered in a random medium are calculated by using the Fourier transformation of the coherence function. The theory describes the ballistic to diffusive transition in wave transport, and is consistent with experimental results. Since the coherence function is expressed via an arbitrary form power spectrum, the results obtained open a new avenue for studying wave transport in anisotropic and/or fractally correlated systems.