The Spatial Singularity Expansion Method for Electromagnetics

We develop a general singularity expansion method (SEM) focused on the spatial structure of electromagnetic fields and currents. In contrast to the traditional temporal SEM, where complex analytical continuation is performed on the forward Green's function of free space, we propose applying the SEM to the reverse Green's function of the electromagnetic device, the recently introduced antenna current Green's function, leading to the discovery of new current and radiation modes. The new spatial SEM turns out to depend only on single-frequency field/current measurement besides completely avoiding the problem of separating early- and late-time responses that have been hindering the traditional approach. The theory is first developed at a very general level and then applied in detail to 1-D wire antennas. We manage to express the far field in terms of the spatial-SEM modes in a closed analytical form. The theory is confirmed by directly comparing with the full-wave method of moment solutions, and excellent agreement between theory and numerical analysis was obtained for generic wire array configurations. The resulting spatial-SEM is expected to stimulate researches into a new generation of frequency-domain RCS target identification technologies and electromagnetic sensing by developing special algorithms relying mainly on the spatial structure of the fields and currents fed by measurements at single frequency instead of the time-domain data usually required in traditional SEM.