Optical Wave Propagation in Random Media: Statistical Approach

The problem of optical wave propagation through an irregular atmosphere, consisting a lot of inhomogeneous structures (see Chapter 1) could be understood by using the statistical description of the wave field (vector and/or scalar) and quantum theory [17—37]. Because the problems of random equations are not tractable with standard mathematical tool, we should use here some special methods such as Feynman’s diagram method [17—20], the method of renormalization [21,23,33,34,38], and so forth.

Main Wave Equations and Random Characteristics

A random medium is a medium whose parameters, such as pressure, density, temperature, etc. are random functions of position and time (all definitions, for example, can be found in References 31, 32, 39—41). This means that we are not describing the exact values of these parameters, but only the probability to find them between a given range of values at given intervals in the space and time domains. A random medium can also be thought of as a collection of inhomogeneous media, each of which may be either continuous (turbulent medium [32,33,35—37,41]) or discrete (medium with random inclusions [34,40,42,43]). In the following, we introduce the main equations that describe stochastic processes in a random medium.

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