Direct Electromagnetic Wave Scattering Calculation Using Methods of Moments through Layered Rough Surface
Authors: Abdullah Sajid  , M Salman Latif  
Published: May 2024

This thesis focuses on the direct calculation of electromagnetic wave scattering through layered rough surfaces using the Method of Moments. The study aims to contribute to existing knowledge by addressing the problems associated with accurately predicting scattered electromagnetic fields from rough surfaces with layered structures. By using the Method of Moments, this research seeks to provide insights into the behavior of electromagnetic waves when interacting with multi-layered rough surfaces, offering valuable implications for practical engineering applications and the development of advanced computational tools for electromagnetic wave analysis. In practical terms, the surface is typically divided into small patches, and the electromagnetic field at each patch is determined using MoM. This involves solving integral equations describing the interaction between the induced currents on the surface and the incident field. The layered structure may require additional equations to model the reflection of waves and the transmission at the boundaries between the layers.
The direct problem is also examined in a two-dimensional picture, where the rough surface profile and the medium are known parameters, and the electromagnetic waves scattered from the surface to the entire space are the unknowns. The rough surface is considered to have a finite length and can be deterministic or arise from a stationary stochastic random process, with a focus on Gaussian-type rough surfaces. The roughness is considered as two basic types: as a perfect electric conductor (PEC) in free space and as a boundary between two dielectric media. The equations of integration obtained are based on the scalar solution of Green's theory, Helmholtz equations, and using Hankel type green functions as kernels due to the one-dimensional nature. The MoM is extensively used to solve these integral equations and is compared to asymptotic approaches and analytical. Various simulations are conducted to test the feasibility of the algorithms, and the results are thoroughly discussed.
The study of electromagnetic wave scattering in one-dimensional rough surfaces involves the direct problem, where the field distribution in the whole space is determined using the equation of integration. These equations take into account the surface roughness and medium parameters they are solved using the Method of Moments (MoM) by expressing the field distribution on the surface using basis functions. The direct calculation of electromagnetic wave scattering through a layered rough surface using the Method of Moments (MoM) is a computationally intensive process and  complex and. It contains simulating the interaction of EM waves with a complex surface, which presents challenges due to the multiple layers with different properties, and a roughly surface causing and diffraction of incident waves and scattering.
When working with a layered rough surface increases the electromagnetic wave interaction complexity. Additional multiple layers introduce considerations, such as layer interfaces and accounting for different material abilities. This requires careful modeling and analysis to exactly capture the behavior of electromagnetic waves as they traverse through and interact with layers.
MoM, a commonly used numerical method for solving electromagnetic scattering problems, discreteness the surface into small segments and solves integral equations to determine the fields that is scattered. This approach allows for a maximum analysis of electromagnetic interactions at a grained level.