Scattering of light beams propagating through a dielectric surface with a large-scale roughness: I. The Kirchhoff method

摘要

The Kirchhoff method and Stratton-Chu integral relations are used to develop for the first time an analytical vector theory of scattering for a normal-incidence arbitrarily polarized light beam with an arbitrary intensity distribution propagating through a dielectric surface with a large-scale Gaussian isotropic roughness (l(c) much greater than lambda, where lambda is the wavelength of incident radiation and l(c) is the correlation radius of surface roughnesses). General expressions for the distribution of the mean illumination intensity related to the directed and diffuse components of the scattered field (analogous to Beckmann formulas, describing the reflection of a plane wave from a rough surface with an ideal conductivity) are derived. These expressions take into account the effect of total internal reflection and hold true in both Fraunhofer and Fresnel zones, remaining applicable not only for low-angle, but also for steep roughnesses. Scattering theories based on the model of a phase screen are shown to provide an adequate description only for low-angle rough surfaces with sigma < sigma(0) equivalent to 1/2(n(2) - 1)(1/2). The cases of weak (h much less than lambda) and strong (h much greater than lambda) phase fluctuations (where h and sigma are the root-mean-square height and slope of the relief surface, respectively, and n is the refractive index of the dielectric medium) are studied. A special attention is focused on the analysis of the applicability range of the derived formulas. The coefficients of light transmission through a rough surface are determined. In the case of strong phase fluctuations, we will find criteria specifying the statistical parameters of the surface allowing the illumination intensity of the directed component to be neglected in the near- and far-field zones relative to the illumination intensity of the diffuse component. We will identify a class of surfaces providing a distribution of the mean illumination intensity of scattered radiation in the plane of the far-field zone perpendicular to the incident beam with no circular symmetry in the case of a linearly polarized incident beam with an arbitrary intensity distribution (including the case of a circularly symmetric incident beam). [References: 45]