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Full-wave approach to the scattered radiation fields by rough surfaces: Numerical and iterative solutions
Abstract
A full-wave approach has been developed to study the problem of electromagnetic wave propagation in stratified media with nonuniform boundaries and varying electromagnetic parameters (Bahar, 1972a, b). By expanding the electromagnetic field vectors E and H using the generalized Fourier Transforms and imposing the exact boundary conditions at the irregular boundary, Maxwell's equations are converted into the generalized telegraphist's equations for the forward and backward traveling wave amplitudes. The generalized telegraphist's equations have been solved for the radiation fields scattered from rough surfaces using iterative approaches for the single scatter and the double-scatter. A numerical method is developed in this dissertation to solve the generalized telegraphist's equations for the diffuse scattered radiation fields from one-dimensional rough surfaces. The full-wave numerical solution includes both single scatter and all the higher-order multiple scatters. Using this approach, the coupled generalized telegraphist's equations are first combined into a single integro-differential equation for the forward and backward wave amplitudes on applying the analytical properties of the basis functions and the scattering coefficients. Then, the primary (unperturbed) field components are subtracted from the total fields. The rapidly varying phase components of the wave amplitudes are factored out. The singularities in the scattering coefficients are removed through integration by parts. Thus, the integro-differential equation is converted into an integral equation for the diffuse scattered wave magnitudes which depend on the wave vector variable only. Finally, the continuous wave vector variables are discretized and the integral equation is converted into a matrix equation (moment method). The wave magnitudes are determined by solving the matrix equation. The far field vectors at a remote observation point are obtained from the field transformation using the steepest descent approach. The full-wave numerical solution for the diffuse scattered radiation fields is applied to both deterministic rough surfaces with known profile and random rough surfaces with known statistics. The Monte-Carlo technique is used to simulate random rough surfaces. The numerical results indicate that the diffuse scattered radiation fields can be approximated using the single scatter iterative solutions when the maximum rough surface slope is less than 35 degrees.
Subject Area
Electrical engineering
Recommended Citation
Shi, Xiaochuan, "Full-wave approach to the scattered radiation fields by rough surfaces: Numerical and iterative solutions" (1995). ETD collection for University of Nebraska-Lincoln. AAI9611068.
https://digitalcommons.unl.edu/dissertations/AAI9611068