Electromagnetic Wave Scattering from Random Rough Surfaces

Asymptotic Models

Nicolas Pinel, Christophe Boulier

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781848214712
• eBook ISBN: 9781118579466
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Electromagnetism

Electromagnetic wave scattering from random rough surfaces is an active, interdisciplinary area of research with myriad practical applications in fields such as optics, acoustics, geoscience and remote sensing.
Focusing on the case of random rough surfaces, this book presents classical asymptotic models used to describe electromagnetic wave scattering. The authors begin by outlining the basic concepts relevant to the topic before moving on to look at the derivation of the scattered field under asymptotic models, based on the Kirchhoff-tangent plane, in order to calculate both the scattered field and the statistical average intensity.
More elaborated asymptotic models are also described for dealing with specific cases, and numerical results are presented to illustrate these models. Comparisons with a reference numerical method are made to confirm and refine the theoretical validity domains.
The final chapter derives the expressions of the scattering intensities of random rough surfaces under the asymptotic models. Its expressions are given for their incoherent contributions, from statistical calculations. These results are then compared with numerical computations using a Monte-Carlo process, as well as with experimental models, for sea surface backscattering.

Contents

1. Electromagnetic Wave Scattering from Random Rough Surfaces: Basics.
2. Derivation of the Scattered Field under Asymptotic Models.
3. Derivation of the Normalized Radar Cross-Section under Asymptotic Models.
APPENDIX 1. Far-Field Scattered Fields under the Method of Stationary Phase.
APPENDIX 2. Calculation of the Scattering Coefficients under the GO for 3D Problems.

About the Authors

Nicolas Pinel worked as a Research Engineer at the IETR (Institut d'Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) before joining Alyotech Technologies in Rennes, France, in July 2013. His research interests are in the areas of radar and optical remote sensing, scattering and propagation. In particular, he works on asymptotic methods of electromagnetic wave scattering from random rough surfaces and layers.
Christophe Bourlier works at the IETR (Institut d'Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) and is also a Researcher at the French National Center for Scientific Research (CNRS) on electromagnetic wave scattering from rough surfaces and objects for remote sensing applications and radar signatures. He is the author of more than 160 journal articles and conference papers.

1

Electromagnetic Wave Scattering from Random Rough Surfaces: Basics

This chapter recalls the basic necessary concepts for dealing with electromagnetic wave scattering from random rough surfaces, by using integral equations. First, it recalls the notions of Maxwell equations, plane wave propagation, polarization, Snell–Descartes laws. Second, it gives a statistical description of the heights of random rough surfaces and defines the concept of electromagnetic roughness through the Rayleigh roughness parameter. Last, it introduces the integral equations describing the electromagnetic scattering, and the necessary Green functions, for both 2D and 3D problems, and defines the notion of a normalized radar cross section.

1.1. Introduction

In this book, the incident wave illuminating the surfaces will be considered as a plane wave. A wave can be called locally plane if it is located in the so-called Fraunhofer zone¹ of the transmitter source, or far-field zone of the source. This assumes that the source is far enough from the surface such that the incident wave may appear as a plane on a distance greater than any dimension of the surface [LYN 70a]. The media are assumed to be linear, homogeneous and isotropic (LHI), stationary and non-magnetic. The incident medium is perfectly dielectric², and can be assimilated to vacuum in general, although we will endeavor to write the equations in the general case of any lossless perfect dielectric medium.

The problem of electromagnetic (EM) wave scattering from non-flat surfaces, called rough surfaces, has been studied for decades. In particular, let us quote the works of Lord Rayleigh [RAY 45, RAY 07], who was the first to give a rigorous definition of the EM roughness of a surface (characterized by the so-called Rayleigh roughness criterion, which will be detailed further). Among rough surfaces, two main categories may be distinguished: periodic surfaces (such as square surfaces, triangular surfaces, sawtooth surfaces and sinusoidal surfaces), which are deterministic, and random surfaces for which only some statistical features are known. This latter category is discussed in this book.

This chapter aims at introducing the main necessary concepts for understanding the tools used in the following chapters. In section 1.2, first, we will recall some generalities on EM waves and their propagation in LHI media. The case of dielectric media will be discussed in general, these media being potentially lossy dielectric³. Then, the interaction of these EM waves with a flat interface will be studied by detailing the reflection and transmission of a plane wave at a flat (perfectly conducting, lossless or lossy dielectric) interface of infinite length. In section 1.3, a description of random rough surfaces, with either sp...

Table of contents

• Cover
• Content
• Title Page
• Copyright
• Preface
• Introduction
• Chapter 1. Electromagnetic Wave Scattering from Random Rough Surfaces: basics
• Chapter 2. Derivation of the Scattered Field Under Asymptotic Models
• Chapter 3. Derivation of the Normalized Radar Cross-Section Under Asymptotic Models
• Appendix 1. Far-Field Scattered Fields under the Method of Stationary Phase
• Appendix 2. Calculation of the Scattering Coefficients under the GO for 3D Problems
• Bibliography
• Index