Coherence properties of retroreflected radiation in a power-law random medium

The presence of random refractive-index fluctuations in location and remote-sensing experiments and double passage of the scattered radiation through the same random inhomogeneities as the incident radiation results in new statistical effects not observed along one-directional paths. To account for the correlation of the forward-backward propagating events, there is a need for a measure in which the random information along the propagation path is preserved. For generation of the even statistical moments, the relevant measure defined in the recently formulated stochastic geometrical theory of diffraction is the two-point random function. We present approximate analytical solutions for the high-frequency propagators based on the multiscale expansion asymptotic procedure applied to the stochastic partial differential equation governing the propagation of the two-point random fluctuation. Analysis of the correlation properties of the retroreflected plane wave is presented for a random medium characterized by a Kolmogorovian refractive-index fluctuation spectrum.