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.
Inhaltsverzeichnis
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.
