Nonradiating sources and the inverse source problem.

摘要

The existence of radiationless solutions to the inhomogeneous wave equation is demonstrated and important results relating to such solutions are reviewed and proven. Three open questions regarding such nonradiating sources are introduced: (1) the experimental confirmation of the existence of nonradiating sources, (2) consequences of their existence, and (3) the existence of unique solutions to the inverse source problem. Methods of experimentally producing nonradiating sources are investigated by examining nonpropagating excitations on a vibrating string. Some unusual consequences of the existence of nonradiating sources are found. Finally, it is shown that no nonradiating quasi-homogeneous sources exist—the inverse source problem for quasi-homogeneous sources is therefore uniquely solvable, and methods of performing the inversion are described.