Random Media and Boundaries: Unified Theory, Two-Scale Method, and Applications

by Koichi Furutsu

Overview

For a system consisting of a random medium with rough boundaries, the governing (Bethe-Salpeter) equation for boundary-value transport problems can be written in a form such that the medium and the boundaries are treatedon an equal footing. This enables several expressions for the solution to be obtained by interchanging the roles of the medium and the boundaries, thus allowing the most convenient one to be selected according to the specific situation and the information required. This book presents a unified theory based on the Bethe-Salpeter equation with particular attention being paid to: boundary-value problems of transport, layer problems, a fixed scatterer imbedded in a bounded random medium, construction of an optical scattering matrix for a complete system, and optical wave propagation in a turbulent medium. The last topic is treated in terms of first moment equations combined with the cluster expansion and, second, the two-scale method based on the Lagrange variational principle.

Product Details

ISBN-13:	9783642848094
Publisher:	Springer Berlin Heidelberg
Publication date:	12/30/2011
Series:	Springer Series on Wave Phenomena , #14
Edition description:	Softcover reprint of the original 1st ed. 1993
Pages:	270
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1 Operator Representation of a Random Medium.- 1.1 Single Random Quantity.- 1.2 N Discrete Random Quantities.- 1.3 Random Function in Space.- 1.4 Multi-Component Random Medium.- 2 Waves in a Homogeneously Random Medium.- 2.1 Operator Representation of Statistical Green’s Functions in a Medium of Independent Particles.- 2.2 Green’s Functions of First and Second Orders.- 2.3 Bethe-Salpeter Equation in a General Random Medium.- 2.4 Random Layer with Free Boundaries.- 2.5 Eigenfunction Expansions and Diffusion Approximation.- 3 Random Rough Boundaries.- 3.1 Rough Surface (One-Sided Boundary).- 3.2 Statistical Green’s Functions of First and Second Orders.- 3.3 Transmissible (Two-Sided) Rough Boundary.- 4 System of Random Media and Rough Boundaries.- 4.1 Bethe-Salpeter Equation for the Entire System and Scattering Matrices.- 4.2 Effective Boundary Scattering Matrices in a Random Medium and Construction of Solutions.- 5 Optical Cross Sections of a Random Layer.- 5.1 Construction of the Cross Sections.- 5.2 Application of the Diffusion Approximation.- 6 Fixed Scatterer.- 6.1 Basic Equations.- 6.2 Power Equations and Optical Relations.- 6.3 Optical Cross Section and Shadowing Effect.- 6.4 Observation of a Fixed Scatterer Embedded in a Semi-Infinite Random Layer.- 7 Forward Scattering Approximation.- 7.1 Moment Equations of a Light Wave in a Turbulent Medium 185 7.1.1 Turbulent Medium of Kolmogorov Spectrum.- 7.2 Solutions of the Moment Equations.- 7.3 High Order Intensity Moments and the Cluster Approximation.- 7.4 Probability Distribution Function of Intensity.- 7.5 Two-Scale Method.- References.

Editorial Reviews

Translated from the Japanese Statistical Waves in Random Media, 1982. The author presents a theory of transport based on the Bethe-Salpeter equation. When written in a unified form this allows the media and the boundaries to be treated on an equal footing. Topics include boundary-value problems of transport, layer problems, a fixed scatterer imbedded in a bounded random medium, construction of an optical scattering matrix for a complete system, and optical wave propagation in a turbulent medium. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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