The Riemann-Silberstein vectors theory and vector spherical expansion

Abstract

The Fourier expansion of the electromagnetic field is one of the most effective techniques for analytical and numerical solving of Maxwell's Equations. Traditionally, TE and TM waves expansion is used. However, there is an alternative form of electromagnetic field modal representation, which has certain advantages over the conventional electric and magnetic field vectors. Is based on the Riemann-Silberstein vectors, which are a linear combination of the electric and magnetic field vectors. In homogeneous space, utilizing the RS vectors Maxwell's Equations are converted into a system of two independent equations, and each vector describes the total electromagnetic field of an ideal circular polarization. The novel vector spherical expansion technique in terms of the RS vectors is described using the helical coordinate system and the generalized spherical harmonics. The new representation of the electromagnetic field vector spherical expansion is simple and symmetrical; it also has a physically apparent expression. The necessary and sufficient boundary conditions for cross-polarization free scattering when the incident wave is circularly polarized is stated. We apply the new vector spherical expansion to the reflector antenna scattering and compare the results with the simulated ones. The amount of computational work is reduced comparing to the TE and TM expansion due to the initial independence of the Riemann-Silberstein vectors.