The Mean Green's Function: A Nonlinear Approximation
Shalom Rosenbaum · Radio Science · 1971
In this paper, we examine the behavior of the coherent Green's function in a randomly fluctuating, unbounded, and statistically homogeneous medium. The starting point of the analysis is a ‘nonlinear’ approximation of the Dyson equation which has been pointed out by several investigators. Although exact solutions seem out of reach, owing to the inherent complexity of the problem, approximate solutions that are applicable in the limits of small and large‐scale fluctuations can be obtained. The large‐scale fluctuations are emphasized in this paper. Both one‐ and three‐dimensional fluctuations are considered, and explicit calculations are made for the case in which an exponential correlation governs the refractive‐index fluctuations. The solutions obtained are investigated in various limiting cases for which closed‐form results are derived.