## Document Type

Dissertation

## Date of Award

Spring 5-31-2003

## Degree Name

Doctor of Philosophy in Electrical Engineering - (Ph.D.)

## Department

Electrical and Computer Engineering

## First Advisor

Gerald Martin Whitman

## Second Advisor

Felix K. Schwering

## Third Advisor

Gregory A. Kriegsmann

## Fourth Advisor

Haim Grebel

## Fifth Advisor

Edip Niver

## Sixth Advisor

Ali Abdi

## Abstract

A new full wave method for scattering of plane waves from a rough dielectric surface is developed. This new theory begins by postulating a zero-order field solution which does not satisfy Maxwell's source-free field equations. The zero-order field, however, is made to satisfy Maxwell's source equations. This is done by introducing a fictitious volume current distribution. Since the original problem does not possess a volume current distribution, its introduction represents a measure of the error in the postulated zero-order solution. To improve this solution, the fictitious volume current distribution is cancelled by the introduction of a second fictitious current distribution, consisting of an infinite number of fictitious sheet current densities. Each sheet current distribution meanwhile produces a mode field that does not satisfy Maxwell's source-free equations. To insure that the mode fields are electromagnetic fields, they are required to satisfy Maxwell's equations with sources; this dictates the introduction of fictitious first-order volume current distributions. The superposition of the mode fields constitutes the first-order solution. The procedure is continued so as to generate a series solution. The theory is developed for both TE- and TM- polarization.

This new full wave theory is shown to yield good agreement with Method of Moments (MoM) solutions, which are extremely accurate but computationally intensive, whereas the new full wave theory provides a formula with a single integration. The new theory is applied to both random rough surfaces and deterministic rough surfaces. The solution in first-order satisfies reciprocity and the theory intrinsically provides an error criterion to assess its accuracy. The results are also shown to yield the correct solution for plane wave scattering from perfect metal rough surfaces. This new full wave method for scattering by a dielectric rough interface provides enhanced physical insight and permits a systematic procedure for obtaining higher-order terms in the series representation of the scattered field.

## Recommended Citation

Yoon, Byung-Tae, "New full wave theory for plane wave scattering by a rough dielectric surface - the fictitious current method" (2003). *Dissertations*. 585.

https://digitalcommons.njit.edu/dissertations/585