Inverse source problem and minimum-energy sources

We present a new linear inversion formalism for the scalar inverse source p roblem in three-dimensional and one-dimensional (1D) spaces, from which a n umber of previously unknown results on minimum-energy (ME) sources and thei r fields readily follow. ME sources, of specified support, are shown to obe y a homogeneous Helmholtz equation in the interior of that support. As a co nsequence of that result, the fields produced by ME sources are shown to ob ey an iterated homogeneous Helmholtz equation. By solving the latter equati on, we arrive at a new Green-function representation of the field produced by a ME source, It is also shown that any square-integrable (L-2), compactl y supported source that possesses a continuous normal derivative on the bou ndary of its support must possess a nonradiating (NR) component. A procedur e based on our results on the inverse source problem and ME sources is desc ribed to uniquely decompose an L-2 source of specified support and its fiel d into the sum of a radiating and a NR part. The general theory that is dev eloped is illustrated for the special cases of a homogeneous source in 1D s pace and a spherically symmetric source. (C) 2000 Optical Society of Americ a [S0740-3232(00)01901-3].