Application of the Riemann-Silberstein vectors for the analysis of electromagnetic fields in reflector antennas

Electromagnetic fields of an antenna are traditionally analyzed through the transverse electric (TE) and magnetic (TM) waves expansion. In this paper, an alternative way of electromagnetic field calculation is presented. It is based on a linear combination of the electric and magnetic field vectors, the Riemann-Silberstein vectors, and its' vector spherical expansion. The general vector spherical harmonics are introduced, which together with utilizing helical coordinates give a simple and symmetrical spherical representation of an electromagnetic field in terms of the Riemann-Silberstein vectors. We apply the new vector spherical expansion to the reflector antenna scattering problem. The amount of computational work can be reduced comparing to the TE and TM waves expansion due to the initial independence of the Riemann-Silberstein vectors.