This comprehensive and self-contained resource conveniently combines advanced topics in electromagnetic theory, a high level of mathematical detail, and the well-established ubiquitous Method of Moments applied to the solution of practical wave-scattering and antenna problems formulated with surface, volume, and hybrid integral equations. Originating from the graduate-level electrical engineering course that the author taught at the Technical University of Eindhoven (NL) from 2010 to 2017, this well-researched two-volume set is an ideal tool for self-study. The subject matter is presented with clear, engaging prose and explanatory illustrations in logical order. References to specialized texts are meticulously provided for the readers who wish to deepen and expand their mastery of a specific topic. This book will be of great interest to graduate students, doctoral candidates and post-docs in electrical engineering and physics, and to industry professionals working in areas such as design of passive microwave/ optical components or antennas, and development of electromagnetic software. Thanks to the detailed mathematical derivations of all the important theoretical results and the numerous worked examples, readers can expect to build a solid and structured knowledge of the physical, mathematical, and computational aspects of classical electromagnetism. Volume 1 covers fundamental notions and theorems, static electric fields, stationary magnetic fields, properties of electromagnetic fields, electromagnetic waves and finishes with time-varying electromagnetic fields. Volume 2 starts with integral formulas and equivalence principles, then moves on to cover spectral representations of electromagnetic fields, wave propagation in dispersive media, integral equations in electromagnetics and finishes with a comprehensive explanation of the Method of Moments.
Inspec keywords: dispersive media; electromagnetic field theory; waveguide theory; Maxwell equations; integral equations
Other keywords: antenna theory; electromagnetic fields; electromagnetic field theory; waveguide theory; wave propagation; dispersive media; computational electromagnetics; Maxwell equations; integral equations; electric field integral equations
Subjects: Electromagnetic waves: theory; Handbooks and dictionaries; Textbooks; Monographs, and collections; Function theory, analysis; Maxwell theory: general mathematical aspects; Steady-state electromagnetic fields; electromagnetic induction; Numerical approximation and analysis; Waves and wave propagation: general mathematical aspects
So far we have determined integral solutions to the time-harmonic Maxwell equations in a homogeneous unbounded isotropic medium with the aid of the retarded potentials. In theory, an integral representation of time-harmonic fields in a bounded region of space may be obtained by combining decompositions with the integral representations of the and the dual ones for the potentials due to magnetic sources. Such procedure, though feasible, is quite involved as it entails the non-trivial calculation of the derivatives of a few surface integrals. One more downside is that the resulting formula will initially involve the values of the potentials, rather than the fields, on the boundary of the region of interest, and some more algebra will be needed to arrive at representations in terms of fields only. For all these reasons in this section we tackle the problem by working directly with the Maxwell equations in the frequency domain without the intervention of the electrodynamic potentials.
In this chapter we discuss the spectral representation of the electromagnetic field in a cavity and in a cylindrical waveguide, both with metallic walls. Then, we investigate the important special case of layered structures in which the constitutive parameters depend periodically on one coordinate. Lastly, we examine the case of a continuum spectrum in, which are essentially two-dimensional problems and can be regarded as the limit of a waveguide whose cross-section grows infinitely large.
The subject of this chapter was a detailed analysis of the wave propagation in linear penetrable media, that is, materials whose constitutive parameters depend only on the properties of the underlying medium but not on the applied electromagnetic field.
In this chapter, after reviewing general concepts related to integral equations, we focused mostly on the derivation of surface and volume integral equations for equivalent sources in the time-harmonic regime.
Since the time-harmonic integral equations as well as the hybrid formulations developed in Chapter 13 can rarely be solved analytically, one resorts to numerical approaches in order to construct approximate, though accurate, solutions. Although a few strategies are available, in this and the following chapter we examine the Method of Moments in great detail. After describing the main features of the strategy in general terms we go on to specialize the MoM to surface integral equations for PEC and homogenous isotropic scatterers, where it will become clear that, as part of the solution process, one has to compute nested surface integrals. The solution of the EFIE for antenna problem is addressed separately because of the additional difficulty posed by the delta-gap model of the antenna port. Finally, we show how the solution to a given scattering or antenna problem is affected when the size of the object in question is scaled and the frequency is modified accordingly.
We continue the discussion of the Method of Moments presented in the previous chapter by describing the application to volume integral equations for inhomogeneous anisotropic objects. The solution of coupled electric-field and volume integral equations is addressed. Lastly, we apply the MoM to the combination of surface integral equation and wave equation. The latter calls for specially devised sub-domain basis functions whose properties are considered.