Electromagnetic Waves

Carlo G. Someda

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781351837422
• Edition: 2
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Adapted from a successful and thoroughly field-tested Italian text, the first edition of Electromagnetic Waves was very well received. Its broad, integrated coverage of electromagnetic waves and their applications forms the cornerstone on which the author based this second edition. Working from Maxwell's equations to applications in optical communications and photonics, Electromagnetic Waves, Second Edition forges a link between basic physics and real-life problems in wave propagation and radiation.Accomplished researcher and educator Carlo G. Someda uses a modern approach to the subject. Unlike other books in the field, it surveys all major areas of electromagnetic waves in a single treatment. The book begins with a detailed treatment of the mathematics of Maxwell's equations. It follows with a discussion of polarization, delves into propagation in various media, devotes four chapters to guided propagation, links the concepts to practical applications, and concludes with radiation, diffraction, coherence, and radiation statistics. This edition features many new and reworked problems, updated references and suggestions for further reading, a completely revised appendix on Bessel functions, and new definitions such as antenna effective height.Illustrating the concepts with examples in every chapter, Electromagnetic Waves, Second Edition is an ideal introduction for those new to the field as well as a convenient reference for seasoned professionals.

CHAPTER 1

Basic equations for electromagnetic fields

1.1 Introduction: Experimental laws

Electromagnetic waves form a chapter of mathematical physics which can be organized as an axiomatic theory. Indeed, all the fundamental concepts, as well as many notions of technical interest, can be deduced from a small set of postulates. This type of approach is convenient in terms of conceptual economy and compactness. On the other hand, there is a danger in it, shared in general by all axiomatic theories: connections with physical intuition may become very weak, especially in the beginning. However, in our case, we expect this drawback to be mitigated, since we take it for granted that the reader has already been exposed to a more elementary description of electromagnetic phenomena, at least in their time-independent or slowly-varying versions. Our first concern will be to show how the postulates of the axiomatic theory can be linked to what the reader knows already about slowly-varying fields, although postulates, by definition, do not require justification.

For this purpose, let us briefly review the basic laws of slowly-varying electromagnetic fields. We will take them simply as experimental data.

1.1.1 Conservation of electric charge

The theory to be presented here deals only with phenomena on a macroscopic scale, where consequences of the discrete nature of the electric charge are irrelevant. Therefore, we shall model charge in terms of a function of spatial coordinates P and time t, which we denote as ρ(P, t) and refer to as electric charge density. Throughout this book, the phrase “charge density” will mean the so-called free charge density, i.e., the local imbalance between densities of positive and negative charges, even though, on a microscopic scale, charges of opposite signs cannot be located exactly at the same points. In order not to make the text unnecessarily cumbersome, the term “function” (of spatial coordinates and/or time) will also implicitly include the case of a generalized function. Those cases where this is not acceptable will be outlined explicitly. A typical example of generalized function, that we will use soon, is a point charge q(P₀) = qδ(P − P₀), where δ(r) stands for a three-dimensional Dirac delta function.

The infinitesimal charge contained, at the time t, in the infinitesimal volume dV_P, centered at the point P, is expressed by $\underset{\sim }{\rho }(P,t)d{V}_P$. In SI (or rational-ized MKS) units (e.g., see Weast, 1988-89), $\underset{\sim }{\rho }$ is expressed in coulombs per cubic meter (C/m³). Consequently, electric currents, as effects of moving electric charges, will be modeled in terms of a vector $\underset{\sim }{\mathbf{\text{J}}}(P,t)$ in three-dimensional (3-D) real space, which depends on the coordinates of the point P and on the time, t. We shall refer to $\underset{\sim }{\mathbf{\text{J}}}(P,t)$ as the electric current density (expressed in amperes per square meter, A/m²). It is defined so that the infinitesimal current that flows across the incremental surf...