UTILIZATION OF RIEMANN-SILBERSTEIN VECTORS IN ELECTROMAGNETICS

Electromagnetic field modal expansion is traditionally an effective technique for solving Maxwell’s Equations for numerous high-frequency engineering problems. In this paper, an alternative form of electromagnetic field representation is described. It is based on the Riemann-Silberstein vectors, which are a linear combination of the electric and magnetic field vectors. Utilizing such combination in homogeneous space, Maxwell’s Equations are converted into a system of two independent equations. Under these circumstances, each vector describes the total electromagnetic field of an ideal circular polarization. Electromagnetic fields are simply expressed in the form of the Riemann-Silberstein vectors using the helical coordinate system and special functions, which form a set of generalized spherical harmonics. The new representation of vector spherical harmonics differs in simplicity and symmetry while having a more physically apparent expression. The amount of computational work is reduced due to the initial independence of the Riemann-Silberstein vectors. The purpose of this paper is to show the efficiency of a new approach that is based on Riemann-Silberstein vector field representation and spherical wave expansion.