Maarten V. De Hoop, Josselin Garnier, Sean F. Holman, Knut Solna
We analyze the �field-field� cross correlation associated with partly coherent scattered waves generated by a wave packet. The configuration consists of a slab in which random medium fluctuations occur; the bottom of the slab is bounded by a deterministic discontinuity (a smooth reflector). Following the dyadic parabolic scaling of wave packets, and scaling the random fluctuations appropriately, we arrive at a description in terms of a system of linear Itô--Schrödinger diffusion models. Studying the Wigner distributions of the fields generated by these models leads to a �blurring� transformation, providing a complete characterization of the cross correlation. We obtain a description of the cross correlation in terms of this transformation applied to the effective transmission operator that arises as a solution of the Itô--Schrödinger model. Most of the analysis is focussed on the interaction of the deterministic reflector with the random fluctuations through the waves in the regime of fine scales
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