Observations on “Nonradiating Surface Sources”

The proof, established in a recent paper (A.J. Devaney, “Nonradiating surface sources”, J. Opt. Soc. Am. A, Vol. 21, 2216-2222, 2004), of existence of nonradiating surface sources formed by singlet plus doublet components whose generated fields vanish in either of the regions separated by a closed or infinite surface where the source resides is corroborated by means of an equivalent but slightly different formalism based on treatment of partial differential operators in a weak derivative or distributional sense. This approach yields a construction procedure applicable to a broad class of singular nonradiating sources. A fundamental question raised in that paper concerning the nonexistence of non-trivial nonradiating infinite planar sources that generate vanishing fields at both associated half-spaces is re-examined, with the conclusion that it is actually possible to mathematically construct such singular nonradiating sources so long as one enables higher-order singularities such as certain combinations of singlet and triplet components.