Ezekiel Bahar

Full-wave solutions for the depolarization of the scattered radiation fields by rough surfaces of arbitrary slope

Employing a variable coordinate system associated with the local features of two-dimensionally rough surfaces with arbitrary slope, full-wave solutions are derived for the depolarization of the scattered radiation fields. An outline of the analytical procedures used in the derivations of the solutions are presented. Furthermore, the engineer who is not familiar with them can also use the final result which is expressed as a definite integral whose integrand is given explicitly and in closed form. These full-wave solutions are compared with the quasi-optics solution and the iterative or perturbational solutions for slightly rough surfaces, and they are shown to bridge the wide gap that exists between them. The full-wave solutions are consistent with energy conservation, duality, and reciprocity relationships in electromagnetic theory. These solutions account for upward and downward scattering of the incident waves with respect to the horizontal reference plane, thus shadowing and multiple scattering are considered. Applications to two-dimensionally periodic structures and random rough surfaces are also presented. The fullwave solutions are examined for Brewster, grazing, and specular angles and backscatter. Special consideration is also given to good conducting boundaries.

Depolarization and scattering of electromagnetic waves by irregular boundaries for arbitrary incident and scatter angles full-wave solutions

Explicit expressions are presented for the radiation fields scattered by rough surfaces. Both electric and magnetic dipole sources are assumed, thus excitations of both vertically and horizontally polarized waves are considered. The solutions are based on a full-wave approach which employs complete field expansions and exact boundary conditions at the irregular boundary. The scattering and depolarization coefficients axe derived for arbitrary incident and scatter angles. When the observation point is at the source these scattering coefficients are related to the backscatter cross section per unit area. Solutions based on the approximate impedance boundary condition are also given, and the suitability of these approximations are examined. The solutions are presented in a form that is suitable for use by engineers who may not be familiar with the analytical techniques and they may be readily compared with earlier solutions to the problem. The full-wave solutions are shown to satisfy the reciprocity relationships in electromagnetic theory, and they can be applied directly to problems of scattering and depolarization by periodic and random rough surfaces.

Full-wave solutions for the scattered radiation fields from rough surfaces with arbitrary slope and frequency

Full-wave solutions are derived for the scattered radiation fields from rough surfaces with arbitrary slope and electromagnetic parameters. These solutions bridge the wide gap that exists between the perturbational solutions for rough surfaces with small slopes and the quasi-optics solutions. Thus it is shown, for example, that for good conducting boundaries the backscattered fields, which are dependent on the polarization of the incident and scattered fields at low frequencies, become independent of polarization at optical frequencies. These solutions are consistent with reciprocity, energy conservation, and duality relations in electromagnetic theory. Since the full-wave solutions account for upward and downward scattering, shadowing and multiple scatter are considered. Applications to periodic structures and random rough surfaces are also presented.

Scattering cross sections for composite rough surfaces using the unified full wave approach

The full wave approach is used to derive a unified formulation for the like and cross polarized scattering cross sections of composite rough surfaces for all angles of incidence. Earlier solutions for electromagnetic scattering by composite random rough surfaces are based on two-scale models of the rough surface. Thus, on applying a hybrid approach physical optics theory is used to account for specular scattering associated with a filtered surface (consisting of the large sonic spectral components of the surface) while perturbation theory is used to account for Bragg scattering associated with the surface consisting of the small scale spectral components. Since the full wave approach accounts for both specular point scattering and Bragg scattering in a self-consistent manner, the two-scale model of the rough surface is not adopted in this work. These unified full wave solutions are compared with the earlier solutions and the simplifying assumptions that are common to all the earlier solutions are examined. It is shown that while the full wave solutions for the like polarized scattering cross sections based on the two-scale model are in reasonably good agreement with the unified full wave solutions, the two solutions for the cross polarized cross sections differ very significantly.

Depolarization of electromagnetic waves excited by distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness. Generalized field transforms

A suitable basis for the full wave expansion of electromagnetic fields in inhomogeneous multilayered structures of arbitrarily varying thickness is presented in this paper. To this end, we formulate appropriate sets of transform pairs for the transverse electric and magnetic fields. Since arbitrary distribution of electric and magnetic sources are considered, the complete expansion must be composed of both vertically and horizontally polarized waves. Each set of generalized transforms, for the vertically and horizontally polarized waves, consists of two infinite integrals (continuous spectrum) which correspond to the radiation and the lateral wave terms as well as a finite number of terms (discrete spectrum) which correspond to the surface waves. For a general three‐dimensional distribution of sources in any of the structures layers, the transverse electric and magnetic fields are in general two component vector functions. Thus, the transform pairs involve vector rather than scalar functions. Exact bound...

Full wave analysis for rough surface diffuse, incoherent radar cross sections with height-slope correlations included

The bistatic scattering cross sections are derived for rough one-dimensional perfectly conducting surfaces using the full wave approach. The surfaces are characterized by four-dimensional Gaussian joint probability density functions for heights and slopes. Thus, correlations between the rough surface heights and slopes are accounted for in the analysis. Convergence of the formal series solution is considered. Self-shadowing effects are included. The full-wave solutions are compared with the small perturbation solutions, which are polarization dependent, and the specular point (physical optics) solutions, which are independent of polarization. Both the physical optics and the small perturbation solutions can be obtained from the full-wave solution. >

Computations of scattering cross sections for composite surfaces and the specification of the wavenumber where spectral splitting occurs

The scattering cross sections for composite random rough surfaces are evaluated using the full wave approach. They are compared with earlier solutions based on a combination of perturbation theory which accounts for Bragg scattering, and physical optics which accounts for specular point theory. The full wave solutions which account for both Bragg scattering and specular point scattering in a self-consistent manner are expressed as a weighted sum of two cross sections. The first is associated with a filtered surface, consisting of the larger scale spectral components, and the second is associated with the surface consisting of the smaller scale spectral components. The specification of the surface wavenumber that separates the surface with the larger spectral components from the surface with the smaller spectral components is dealt with in detail. Since the full wave approach is not restricted by the limitations of perturbation theory, it is possible to examine the sensitivity of the computed values for the backscatter cross sections to large variations in the value of the wavenumber where spectral splitting is assumed to occur.

Depolarization of electromagnetic waves excited by distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness. Full wave solutions

Full wave solutions to the problem of depolarization of electromagnetic waves excited by general three‐dimensional distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness are derived. Generalized field transforms that provide an appropriate basis for the expansion of transverse electromagnetic fields are employed to convert Maxwells equations into a set of coupled first order ordinary differential equations for the forward and backward, vertically and horizontally polarized wave amplitudes. The continuous parts of the complete wave spectrum correspond to the radiation and lateral wave terms while the discrete part of the wave spectrum corresponds to the surface wave or trapped waveguide modes. Exact boundary conditions are imposed at all the interfaces of the structure and the solution is not restricted by the surface impedance concept. When the bounding media of the structure are characterized by perfect electric or magnetic walls, the fie...

Generalized WKB Method with Applications to Problems of Propagation in Nonhomogeneous Media

A generalized WKB method is derived for the solution of the general second‐order differential equation. The problem is reduced to the solution of two coupled first‐order differential equations. By an appropriate choice of auxiliary functions, the coupling coefficients may be made sufficiently small to facilitate the solution of the coupled equations. It is shown that these solutions can be used in a range of problems in which the regular WKB solutions fail. These generalized solutions may also be used to derive asymptotic expansions of known functions. Applications of the method to higher‐order differential equations are indicated, and solutions to the nonlinear Riccati equation are considered.

Like- and cross-polarized scattering cross sections for random rough surfaces: theory and experiment

The unified full-wave solutions for the vertically and horizontally polarized scattered radiation fields and the like- and cross-polarized scattering cross sections for random rough surfaces are presented in this paper. They are compared with the corresponding physical-optics, geometric-optics, and perturbation solutions that are obtained on adopting a two-scale model of the composite rough surface. Computations based on the unified full-wave solution (which accounts for both specular point scattering and diffuse scattering in a self-consistent manner) as well as those based on the two-scale representation of the rough surface are provided for several illustrative examples. It is shown that the two solutions for the cross-polarized backscatter cross sections differ significantly for near-normal incidence. The solution based on the unified approach is consistent with experimental data.