Reconstruction of electromagnetic minimum energy sources in a prolate spheroid

The inverse problem of reconstructing time-harmonic minimum energy current distributions in a spheroidal volume from given data of far-field radiation is addressed. Following the procedure outlined by Marengo and Devaney [1999], we formulate, upon deriving a spherical harmonics expansion of the electromagnetic field radiated by a current inside a prolate spheroid, the inverse problem in terms of linear operator theory. Owing to the lack of orthogonality of spheroidal vector wave functions, every eigenfunction will couple with several spherical radiation modes at a time, making the solution rather involved. Simplification is achieved in the special case of rotationally symmetric fields, for which numerical examples are given. As an application, the use of minimum energy currents for identifying distributions of nonradiating current in a spheroidal volume is pointed out.