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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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Optical Waves Propagation: Deterministic Approach
Main Equations The theoretical analysis of optical wave propagation, as a part of the whole electromagnetic spectrum [1—6] (see also Figure 1.1 in Chapter 1), is based on Maxwell’s equations [10—16]. In vector notation, their representations in the uniform macroscopic form are [1—6]: Here...
(Optical Waves and Laser Beams in the Irregular Atmosphere)
Basic Aspects of Optical Wave Propagation
Identity of Optical and Radio Waves Electromagnetics plays a key role in modern radio and optical communication systems, including optical telecommunication systems and LIDAR [1—16]. Therefore, optical communication emphasizes the electromagnetic phenomena described mathematically by Maxwell’s...
(Optical Waves and Laser Beams in the Irregular Atmosphere)
Wave Propagation in Fluid Media
A typical ultrasonic nondestructive evaluation setup always concerns fluid and solid media with fluid-solid interfaces. Here predominantly the incompressible fluids are considered. When ultrasonic energy is excited using a transducer in water or in any incompressible fluid media, the energy propagates...
(Computational Nondestructive Evaluation Handbook: Ultrasound Modeling Techniques)
Propagation of Optical Waves through the Boundary of Two Media
Boundary Conditions The simplest case of wave propagation over the intersection between two media is that where the intersection surface can be assumed as flat, and the second medium perfectly conductive. If so, for a perfectly conductive flat surface, the total electric field vector is equal...
(Optical Waves and Laser Beams in the Irregular Atmosphere)
Wave equation with random non-uniform refractive index
1.20.1 General theory Here e(cc,r) is the random frequency dependent permittivity of the medium while the permeability // is a constant. The Maxwell curl equations are curlE(a>, r) = —ju>pH(a>,r), curlH(cc, r) = jcde(cd, r)E(uj, r) To this we append the other two...
(Waves and Optics)
One-Dimensional Wave Equation
Let us consider the 1D wave equation (Kreysig 2010) with the boundary conditions as where c2 = T/p. Here, T and p are the tension and mass of the deflected string. Boundary Conditions Here, u(x, t) is the deflection of the string, and it is fixed at the ends x = 0 and x =...
(Neutron diffusion : concepts and uncertainty analysis for engineers and scientists)
Wave Equations
The propagation phenomena of optical waves in random medium are described by a linear differential equation with random coefficients, instead of deterministic one (see Equation 2.17), used for description of deterministic models. Thus, a scalar wave Equation 2.17 can be presented in the following form:...
(Optical Waves and Laser Beams in the Irregular Atmosphere)