Time-reversal operator for a small sphere in electromagnetic fields

The paper investigates the time-reversal operator (TRO) for a planar array of crossed dipole antennas illuminating a small spherical scatterer in frequency domain. A simple approach making use of the reciprocal theorem is used to construct the TRO. The eigenvalues and eigenvectors of the TRO are obtained by transforming the original system into an equivalent system where a six-by-six governing matrix is built up, each singular vector of which specifies a set of electric current dipole moments and normalized magnetic current dipole moments induced in the small sphere. The results show that the polarization of the radiation from each crossed antenna driven by the currents specified by the eigenvectors depends on the composing material of the small sphere and the configuration of the antenna array. For some composing materials of the sphere, circularly polarized radiation is possible, depending on the positions and the lengths of the antennas of the array. For a nonmagnetic dielectric or perfectly conducting sphere, however, the eigenvectors produce only linearly polarized radiation from each crossed antenna, and no elliptically polarized wave can be radiated regardless of the configuration of the antenna array. This polarization property suggests its application for target classification.