Forward and Markov approximation: the strong-intensity-fluctuations regime revisited

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Abstract
The forward and Markov approximation for high-frequency waves propagating in weakly fluctuating random media is the solution of a stochastic Schrödinger equation. In this context, the strong-intensity-fluctuations regime corresponds to long propagation distances. This regime has been studied by several different methods, such as expansion of the moment equations and path-integral representations. It is an accepted fact that, in this regime, the field becomes Gaussian and completely decorrelated which implies, in particular, that the intensity has an exponential probability distribution. The aim of this paper is to give additional evidence for this by analysing the stationary moment equations. Under the natural hypothesis of asymptotic spatial decorrelation of the field, we construct boundary conditions for these stationary equations which can then be solved explicitly. We note that the limiting probability distribution does not depend on the spectral contents in the regime of saturation of the intensity fluctuations. Our analysis deals with the of the randomness, which plays an essential role at finite propagation distance long-distance, equilibrium behaviour of the statistics of the intensity without having to deal with the approach to equilibrium.

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