  Global minimality and uniqueness are established for a class of inverse
source problems in non-homogeneous, electromagnetic backgrounds with
generalized constitutive parameters satisfying the condition $\epsilon \, \mu >
0$, where $\epsilon$ is the electric permittivity and $\mu$ is the magnetic
permeability. The radiating source, i.e., current density, is reconstructed by
minimizing its $L^{2}$-norm subject to a prescribed radiated field and a
vanishing reactive power. The $L^{2}$-norm constitutes a useful and
analytically tractable measure of the physical resources of the source. The
vanishing of the reactive power corresponds to the maximization of the power
transmitted in the far-field.
