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For a system consisting of a random medium with roughboundaries, the governing (Bethe-Salpeter) equation forboundary-value transport problems can be written in a formsuch that the medium and the boundaries are treatedon anequal footing. This enables several expressions for thesolution to be obtained by interchanging the roles of themedium and the boundaries, thus allowing the most convenientone to be selected according to the specific situation andthe information required. This book presents a unifiedtheory based on the Bethe-Salpeter equation with particularattention being paid to: boundary-value problems oftransport, layer problems, a fixed scatterer imbedded in abounded random medium, construction of an optical scatteringmatrix for a complete system, and optical wave propagationin a turbulent medium. The last topic is treated in terms offirst moment equations combined with the cluster expansionand, second, the two-scale method based on the Lagrangevariational principle.
List 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.
