Nonradiating surface sources

The class of three-dimensional (3D) nonradiating sources to the inhomogeneous Helmholtz equation is generalized to include nonradiating surface sources that are localized on closed or infinite surfaces sigma and that generate no radiation throughout one of the two space regions whose common boundary is sigma. The class of non-radiating surface sources is shown to be identical to the class of so-called secondary surface sources that are generated from boundary values of a field radiated by a 3D source. In particular, it is proven that any secondary surface source radiating into the interior (exterior) of sigma is a nonradiating surface source relative to the exterior (interior) of sigma, and vice versa. Examples of nonradiating surface sources are included, and a discussion is given of possible applications of such sources.