Scattering of electromagnetic waves from 3D multilayer random rough surfaces based on the second-order small perturbation method: energy conservation, reflectivity, and emissivity

Abstract

A theoretical investigation of energy conservation, reflectivity, and emissivity in the scattering of electromagnetic waves from 3D multilayer media with random rough interfaces using the second-order small perturbation method (SPM2) is presented. The approach is based on the extinction theorem and develops integral equations for surface fields in the spectral domain. Using the SPM2, we calculate the scattered and transmitted coherent fields and incoherent fields. Reflected and transmitted powers are then found in the form of 2D integrations over wavenumber in the spectral domain. In the integrand, there is a summation over the spectral densities of each of the rough interfaces with each weighted by a corresponding kernel function. We show in this paper that there exists a "strong" condition of energy conservation in that the kernel functions multiplying the spectral density of each interface obey energy conservation exactly. This means that energy is conserved independent of the roughness spectral densities of the rough surfaces. Results of this strong condition are illustrated numerically for up to 50 rough interfaces without requiring specification of surface roughness properties. Two examples are illustrated. One is a multilayer configuration having weak contrasts between adjacent layers, random layer thicknesses, and randomly generated permittivity profiles. The second example is a photonic crystal of periodically alternating permittivities of larger dielectric contrast. The methodology is applied to study the effect of roughness on the brightness temperatures of the Antarctic ice sheet, which is characterized by layers of ice with permittivity fluctuations in addition to random rough interfaces. The results show that the influence of roughness can significantly increase horizontally polarized thermal emission while leaving vertically polarized emissions relatively unaffected.

Modelling Scattering of Electromagnetic Waves in Layered Media: An Up-to-Date Perspective

“…Second and higher-order perturbative developments have also been investigated [9,[26][27][28][29]. It is worth highlighting that pertinent analytical developments following a boundary perturbation approach can be particularly cumbersome [27]; conversely, rigorous second-order volumetric-perturbative developments demand for an appropriate mathematical playground (the distribution theory for discontinuous test functions) [9].…”

“…Notice that the first-order solution for the scattered field does not predict the cross-polarized intensity in the incidence plane. In [29] it has been demonstrated that there exists a "strong" condition of energy conservation in that the kernel functions multiplying the spectral density of each interface obey energy conservation exactly. Accordingly, the energy is conserved independent of the roughness spectral densities of the rough surfaces.…”

Electromagnetic Scattering From One Dimensional Random Rough Surfaces of Dielectric Layered Media With Waveguide Modes Using Second Order Small Perturbation Method

“…The small perturbation method has been studied for random rough surface scattering extensively [1][2][3][4][5][6][7][8][9][10][11][12]. Recently, the method has been studied for multi-layered random rough surfaces [2,5,7] as an analytical method which has advantages over numerical methods for multiple rough interfaces.…”

“…Recently, the method has been studied for multi-layered random rough surfaces [2,5,7] as an analytical method which has advantages over numerical methods for multiple rough interfaces. As the number of layers increases, numerical methods become costly in CPU and memory.…”

“…The small perturbation method must be carried out to the second order [5] for energy conservation in emissivity calculations. In carrying out the Small Perturbation Method, the higher order field is expressed in terms of a convolution of the layered medium Green's function with the lower order field, where the convolution is performed in the spectral domain.…”