The Angular Spectrum of Dyadic Green’s Function in 3-D Scattering Environments

A rigorous representation of the dyadic Green's function of the 3-D vector wave equation is derived between two disjoint communication volumes with arbitrary external scattering. The resulting expression is a double-integral of two plane waves multiplied with a dyadic kernel called the double-angular spectrum of the system. The two plane waves are the wave components traveling in various directions on the transmit and receive sides, respectively, and the dyadic spectrum, which is composed of orthogonal vector spherical harmonics, describes the waves' interaction strength and polarization change. The derived DGF representation offers valuable physical insights and provides a rigorous mathematical framework that potentially can facilitate other electromagnetic propagation-related studies. As the core of this framework, the dyadic spectrum is numerically investigated in a model system with random scattering. The results bring to light many insightful characteristics on the statistical behaviors of the wave propagation between the communication volumes.