Pulsed Electromagnetic Waves Between Parallel Plates: The Modal-Expansion and Generalized-Ray Approaches

The electromagnetic field propagated between two perfectly electrically conducting screens is investigated in the time domain using two approaches. In addition to a solution based on the well-known eigenfunction expansion, we provide an alternative series expansion composed of generalized-ray constituents. As the constructed closed-form space-time expressions are straightforward and easy to implement in any computational tool, they may serve for educational purposes. In particular, they may be useful for those who want to get acquainted with some basic aspects of the propagation of the pulsed electromagnetic field. Key features of both time-domain approaches are discussed, and illustrative numerical examples are given.

1 Introduction

The electromagnetic wave field can be trapped and guided via reflections against electromagnetically impenetrable boundaries. One of the simplest guiding configurations treated in most books on introductory electromagnetics [1], [2] is the parallel-plate waveguide. It consists of two parallel perfectly electrically conducting (PEC) planes of infinite extent that confine the propagating wave field. The solution of such a problem is well known in the frequency domain, and its detailed description can be found in several books (e.g., [3, Section 5.5]). On this subject, the eigenfunction representation over the direction perpendicular to the boundaries of the planes, and the alternative hybrid ray-mode representation employing the Fourier representation parallel to them, were illustratively discussed by Felsen et al. [4].