Green's Matrix and Propagator Matrix for Three-Dimensional Electromagnetic Wave Propagation and Scattering in a Time-Variant Material

Abstract

Electromagnetic wave propagation and scattering in materials with time-variant parameters are subjects of an active field of research. The theory is usually restricted to transverse-electric or transverse-magnetic modes in one-or two-dimensional settings. Here we discuss the theory of three-dimensional, multi-component electromagnetic waves in a homogeneous, time-variant material. We present 3 × 3 causal and acausal Green’s matrices, and a 6 × 6 propagator matrix. We derive several fundamental properties such as the conservation of momentum density for a piecewise continuous, time-variant material, symmetry properties of the propagator matrix, and a relation between the causal and acausal Green’s matrices. These properties are used in derivation of a general wave-field representation (the counterpart of the Kirchhoff integral for a time-invariant material) and an expression for Green’s function retrieval with space correlations (the counterpart of Green’s function retrieval with time correlations in a time-invariant material).