Random Media and Boundaries

Random Media and Boundaries presents a theory of boundary-value transport problems based on the Bethe-Salpeter equation. The topics discussed include: layer problems, a fixed scatterer imbedded in a bounded medium, construction of an optical scattering matrix for a complete system, and optical wave propagation in a turbulent medium. This book will be of interest to graduate students and researchers.

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.