Mary Ann Fitzwater

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.

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.

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.

Depolarization and backscatter enhancement in light scattering from random rough surfaces: comparison of full-wave theory with experiment

The full-wave approach is used to interpret the recently observed depolarization and enhanced backscattering of light from random rough surfaces fabricated in photoresist with an aluminum overcoating [ MendezE. R.O’DonnellK. A., Opt. Commun.61, 91 ( 1987); O’DonnellK. A.MendezE. R., J. Opt. Soc. Am. A4, 1194 ( 1987)]. A second-order iterative solution based on the rigorous full-wave approach indicates that, contrary to the suggestions made by Mendez and O’Donnell (who performed the experiments and considered numerous other theories), the observed enhanced backscatter is a first-order effect that can be attributed to single scatter rather than to multiple scatter.

Full wave theory and controlled optical experiments for enhanced scattering and depolarization by random rough surfaces

Abstract Controlled laboratory experiments afford an indispensable tool in the validation of the numerous theories on electromagnetic scattering and depolarization. In a recent article in Optics Communications [61 (1987) 91], a group at Imperial College reported some very stimulating observations on enhanced backscatter from rough surfaces with large mean square slopes. A second order iterative solution based on the rigorous full wave approximation indicates that contrary to the suggestions made by the researchers at Imperial College (based on their consideration of many other theories), the observed enhanced backscatter can be attributed to single scatter rather than multiple scatter.

Full-wave copolarized nonspecular transmission and reflection scattering matrix elements for rough surfaces

A 2 × 2 scattering matrix for rough surfaces that separate two different media is derived. To this end, explicit closed-form expressions for the nonspecular transmission scattering coefficients are derived for the rough-surface elements to complement previous derivations of the nonspecular reflection scattering coefficients. Both vertically and horizontally polarized electromagnetic excitations are considered here. Thus the elements of scattering matrices represent the polarization-dependent nonspecular transmission and reflection properties of each arbitrarily oriented and elevated element of the rough surface. The total nonspecularly transmitted and reflected fields are expressed as integrals (not integral equations). The full-wave solutions derived here are compared with the corresponding high-frequency physical-optics results, and the low-frequency perturbation results are also derived. They are shown to satisfy the reciprocity and duality relationships in electromagnetic theory, and they are invariant to coordinate transformations. These results may be applied to both deterministic and random rough surfaces.

Scattering and depolarization by conducting cylinders with rough surfaces

Like- and cross-polarized scattering cross sections are determined at optical frequencies for conducting cylinders with rough surfaces. Both normal and oblique incidence with respect to the cylinder axis are considered. The full wave approach is used to account for both the specular point scattering and the diffuse scattering. For the roughness scales considered, the scattering cross sections differ significantly from those derived for smooth or slightly rough conducting cylinders. Several illustrative examples are presented and the albedos for smooth and rough cylinders are compared.

Enhancement of backscattered diffuse specific intensities from random distributions of finitely conducting particles with rough surfaces

The incoherent diffuse specific intensities (modified Stokes parameters) backscattered from a horizontal layer consisting of random distributions of finitely conducting particles with smooth surfaces and finitely conducting particles with rough surfaces are evaluated. The normally and obliquely incident excitations at infrared and optical frequencies are vertically or horizontally polarized. The particle-surface roughness, which is characterized by its joint probability-density function, is assumed to be sufficiently rough to affect the diffuse specific intensities significantly. Thus the full-wave approach is used to determine the phase matrix as well as the extinction coefficient that appears in the equation of radiative transfer. The enhanced backscattered intensities that depend on the particle-surface roughness are compared with the enhanced backscatter that is associated with Mie scatter from smooth spherical particles. The enhanced backscattered diffuse specific intensities are evaluated for different particle sizes, complex permittivities, roughness parameters, and excitations. The effects of varying the optical thickness of the layer are also considered. Since the enhanced backscatter phenomenon reported here is primarily due to the particle-surface roughness, it appears in both the first-order solution and the multiple-scatter solution of the radiative-transfer equations.

Copolarized and cross-polarized incoherent specific intensities for waves at oblique incidence upon layers of finitely conducting particles with rough surfaces

Optical and infrared electromagnetic scattering and depolarization by layers of randomly distributed particles of irregular shape and finite conductivity are determined through the use of the equation of transfer. The irregularly shaped particles are characterized by their random rough-surface height spectral density function or autocorrelation function. The extinction cross section and the elements of the scattering matrix in the equation of transfer are evaluated by using a full-wave approach, which accounts for specular point and diffuse scattering in a self-consistent manner. Both single-scatter and multiple-scatter incoherent specific intensities are evaluated for particles with smooth and rough surfaces.

Scattering and depolarization of linearly polarized waves by finitely conducting particles of irregular shape

In this work a layer consisting of a large variety of randomly distributed finitely conducting particles with irregular shapes is assumed to be excited at infrared and optical frequencies by a linearly polarized wave. The resulting incoherent specific intensities, as well as the copolarized and cross polarized intensities, are evaluated. Both single scatter and multiple scatter results are presented for particles with smooth and rough surfaces, and the effects of particle surface roughness on the degree of polarization are considered in detail.