Theoretical Model of Electromagnetic Scattering From 3d Multi-Layer Dielectric Media With Slightly Rough Surfaces

Abstract

Abstract-A theoretical model of scattering from three-dimensional arbitrary layered media with 3D infinite rough surfaces based on the small perturbation method (SPM) is derived in the present paper. The scattering field and bistatic scattering coefficient for linear polarized waves are derived respectively. Firstly, the electric and magnetic fields in each region of the layered structure are expanded into perturbation series in spectral domain. Secondly, the expansion coefficients of each order are obtained by applying the boundary conditions. As a result, the expressions of the zeroth-, first-and second-order solutions of the scattering problem based on the SPM are obtained, in which the second-order solution is the primary contribution of this work. The theoretical model is helpful to understand the dependence between the scattering field and physical properties of the layered structure (such as surface roughness and dielectric constants at different depths). The result can be applied to modeling of the received radar signal from nature targets such as layered soil and ice with full polarizations.

Optical Antireflection of a Medium by Nanostructural Layers

“…The problem can thus be treated in this approach only numerically, which requires a long computation time. Similar difficulties are encountered in other methods that directly solve Maxwell's equations, such as the finite element method (FEM) [22][23][24], finite-difference time-domain (FDTD) method [25,26], small perturbation method (SPM) [27]. Moreover, taking into account the interaction between a layer of nanoparticles and the substrate adds considerable complexity to the computation process or requires a number of approximations, e.g., averaging of the refractive indices of the substrate and environment [28], which can be done by different procedures, or the introduction of an imaginary nanostructured layer, a reflection of the real layer [18].…”

“…In this case, to calculate the reflection and transmission spectra of the system with these parameters, the exact electrodynamics finite element method [22][23][24][25][26][27][28][29][30][31][32][33][34] is used in order to exclude the effect of made approximation (2) and the absence of multipole terms in the nanoparticle interaction tensor (6) (which are significant for the considered case of touching spheres) on the result. According to [29], for such geometrical parameters of the nanoaggregate, the considered analytical approach can be used only for estimating investigations.…”

Fast Computation of the Forward Solution in Controlled-Source Electromagnetic Sounding Problems

“…the transverse electric plane wave reflection coefficient R TE at the air-ground interface [30][31][32]. The surface admittance Y 1 is obtained through the recurrence relation…”

Second-Order Scattering Induced Reflection Divergence and Nonlinear Depolarization on Randomly Corrugated Semiconductor Nano-Pillars

“…In most works, the surface anti-reflection property of the nano-roughened structure was typically realized as a multi-layered model with gradually changed refractive index induced by different air-Si mixture compositions [8]. In addition, the investigation of light scattering from the roughened anti-glare surface has caused great interests in scientific researches [9][10][11][12][13][14][15][16]. In 1967, the surface depolarization on the backscattered light from either the disordered metallic or inhomogeneous dielectric surfaces under a linearly polarized incidence at different angles were experimentally characterized without theoretical modeling [9].…”