Inverse source problem in nonhomogeneous background media. part ii: Vector formulation and antenna substrate performance characterization

This paper solves analytically and illustrates numerically the full-vector, electromagnetic inverse source problem of synthesizing an unknown source embedded in a given substrate medium of volume V and radiating a prescribed exterior field. The derived formulation and results generalize previous work on the scalar version of the problem, especially the recent Part I of this paper [A. J. Devaney, E. A. Marengo, and M. Li, SIAM J. Appl. Math., 67 (2007), pp. 1353-1378]. Emphasis is put on substrates having constant constitutive properties within the source volume V, which, for formal tractability, is taken to be of spherical shape. The adopted approach is one of constrained optimization which also relies on spherical wavefunction theory. We find that the observed peaks in the spectrum of the singular values are primarily due to the phenomenon of Mie resonance. Therefore, for a given antenna radiating at a prescribed frequency, the set of solutions to the Mie resonance conditions corresponds to a set of constitutive parameters that maximize the radiated electromagnetic fields. The derived theory and associated implications for antenna substrates are illustrated numerically.