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 θc 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.