Coherent scattering by one-dimensional randomly rough metallic surfaces

Abstract

A critical evaluation of various theoretical techniques for calculating the reflectivity of one-dimensional metallic randomly rough surfaces is presented. We proceed by comparing experimental and rigorous numerical results with those obtained with three perturbation theories and the Kirchhoff approximation. The samples were fabricated in photoresist, and their metallized surface profiles constitute good approximations to Gaussian-correlated, Gaussian random processes. The correlation lengths of these surfaces range from approximately one third to approximately three times the infrared wavelengths employed. The results show that the phase-perturbation theory has wider applicability than the other perturbation theories and the results based on the Kirchhoff approximation.

<title>Effective impedance boundary condition for the coherent scattering of light from a one-dimensional randomly rough surface</title>

“…The optical skin depth d(w) in this case is given by d(w) = (26.6 + iO.426) nm. For comparison, the reflectivity of the corresponding planar surface is also plotted in this figure, as is the reflectivity calculated by phase perturbation theory [19] . The latter approach to the calculation of the reflectivity of a one-dimensional random metal surface was recently shown to be more accurate than smallamplitude perturbation theory, self-energy perturbation theory, and the Kirchhoff approximation for incident light in the infrared region of the optical spectrum [19].…”

Transfer Relations for Electromagnetic Wave Scattering from Periodic Dielectric One-Dimensional Interface: TE Polarization Lines

“…The reciprocity (26) relates the operator wave transmission coefficient A to A, whereas the reciprocity (27) and (28) relates the operator wave reflection coefficient B to B andB toB , respectively.…”

“…Ordinarily this physical problem is studied either by a straightforward approach process using exact integral equations for the boundary values of the field and then obtaining approximative solutions of these equations or by applying to the given boundary problem perturbative analysis. Some of these methods are presented in monographs [15][16][17] and papers [18][19][20][21][22][23][24][25][26][27]. It is worth noting for us paper [28] where the Wood anomalies [29], discovered by light diffraction from a grating, are studied by light diffraction on a rough surface.…”

Radiative Properties of Gold Surfaces with One-Dimensional Microscale Gaussian Random Roughness

“…Rapid advances in computer modeling have resulted in new approaches, for example, finite difference methods, finite element methods, and Monte Carlo simulations, in the numerical analysis of random media scattering [5]. Numerical simulations allow us to solve the Maxwell equations exactly without the limitations of analytical approximations, for example, the Kirchhoff approximation [2] and small perturbation theory [6], whose regimes of validity are often difficult to assess [7]. On the other hand, there are also challenges to improve the numerical simulations, for example, large memory and computational time requirement in multi-dimensional and complex geometry problems.…”

“…Due to the difficulties in computing higher-order terms and in the solution convergence, perturbation series have been limited to weakly rough surfaces [6]. Geometric ray tracing is limited to roughness being larger than the incident wavelength, so the wave interference effect can be neglected [9].…”