Probability density function and moments of the field in a slab of one-dimensional random medium

Abstract

The problem of a plane wave normally incident on a slab of one‐dimensional random medium is studied. The refractive index variations of the random medium are taken to be a stationary Gaussian‐Markov process. By employing an invariant imbedding technique and by using the Markov property of the refractive index variations, two cascaded diffusion equations are obtained for the probability density function of the reflection coefficient and the field in the slab. These equations are then solved approximately for small refractive index fluctuations and an expression is obtained for mean intensity in the slab interior.