Guided complex waves. Part 1: Fields at an interface

TLDR

The interface between two media supports various surface and complex waves, including guided complex waves that propagate without attenuation as inhomogeneous slow plane waves at an angle to the interface. The study aims to analyze all interface‑supported waves as pole contributions in alternative integral representations, emphasizing the steepest‑descent method. The authors investigate pole locations, field distributions, and power‑transport characteristics of all wave types via steepest‑descent and related integral representations. The analysis shows that complex waves on lossless structures occur in degenerate forward–backward pairs with distinct power‑flow, and that power transport either compensates system losses or transfers energy to radiation.

Abstract

The variety of waves which can be supported by a plane homogeneous interface includes surface waves of the forward and backward type, and several kinds of complex wave, the latter being characterized by wave numbers which are complex even though the media involved are not necessarily lossy. The present study views all these waves as contributions due to poles in several alternative integral representations of a source-excited field, and places particular stress on the steepest-descent representation. The pole locations, field distributions and power-transport properties are explored in detail for all the wave types. Distinctions are made between proper (spectral, modal) and improper waves, and between lossy and lossless structures; complex waves along lossless structures are shown to appear always in degenerate pairs consisting of a forward and a backward wave, with interesting power-flow characteristics. The different wave types are grouped into the general category of guided complex waves which propagate without attenuation as inhomogeneous slow plane waves at some angle to the interface. Power-transport considerations via the steepest-descent representation show that these waves either carry power to compensate for losses in the system or account for a transfer of energy into the radiation field.