ELECTROMAGNETIC WAVE SCATTERING FROM ROUGH LAYERED INTERFACES: ANALYSIS WITH THE SMALL PERTURBATION METHOD AND THE SMALL SLOPE APPROXIMATION

Abstract

We propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using the small perturbation method and the small slope approximation. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. They can be correlated or not. The electromagnetic fleld in each medium is represented by a Rayleigh expansion and a perturbation method is used for solving the boundary value problem and determining the flrst-order scattering amplitudes by recurrence relations. The scattering amplitude under the flrst-order small slope approximation are deduced from results derived from the flrst-order small perturbation method. Comparison between these two analytical models and a numerical method based on the combination of scattering matrices is presented. The study of electromagnetic wave scattering from rough layered interfaces has many applications in remote sensing, communication techniques, civil engineering, geophysics and optics. Several models give the average scattered fleld and the average intensity. Analytical methods are based on physical approximations and give closed-form formulae for the flrst- and second-order moments of the scattered fleld. Exact methods estimate the average scattered fleld and the average intensity from the results over many realizations of rough layered interfaces. In this paper, we propose a theoretical study on the electromagnetic wave scattering from layered structures with an arbitrary number of rough interfaces by using two analytical models: the flrst-order small perturbation method (SPM) and the flrst-order small slope approximation (SSA). Elson was one of the flrst authors to develop a vector theory of scattering from a stratifled medium. This vector theory allows the angular distribution of scattered light to be determined and can be used with correlated or uncorrelated surface roughness (1,2). The SPM has been used for the study of light scattering from multilayer optical coatings (1{5) and many authors have also implemented a perturbative theory for analyzing remote sensing problems (6{12). The small slope approximation (SSA1) has an extended domain of applicability (13{15) which includes the domain of the small-perturbation method that is only valid for surfaces with small roughness (16) and the domain of the Kirchhofi approximation that is applicable to surfaces with long correlation length (17,18). In the present paper, the structure under consideration is a stack of several rough one-dimensional interfaces. The interfaces are characterized by Gaussian height distributions with zero mean values and Gaussian correlation functions. The electromagnetic fleld in each region is represented by a continuous spectrum of plane waves, the amplitudes of which are found by matching the boundary conditions