Guided complex waves. Part 2: Relation to radiation patterns

Abstract

The presence of complex waves in the near field of a source-excited plane homogeneous interface is shown to play an important role in determining certain features of the radiation field. A Kirchhoff-Huygens integration over the near field reveals that, whenever these complex waves are strongly excited, they account for peaks in the radiation pattern. Under unidirectional excitation, each complex wave yields a single peak at some oblique angle; for bi-directional excitation, either two peaks appear symmetrically located about a normal to the interface, or a single peak is present in this normal (broadside-on) direction. It is also shown that, when the complex wave is slowly decaying at the interface, the peaks occur close to the angle of definition θ_c for that wave. These angles of maximum radiation and the associated gain functions are expressed, in all these cases, in terms of the location in the steepest-descent plane of the pole corresponding to the complex wave. These features are also shown to be consistent with the radiation mechanism discussed in the companion paper, Part I.