2026-08-06 Latest Published
By Kees Wapenaar
Evert C. Slob
Progress In Electromagnetics Research, Vol. 186, 11-23, 2026
Abstract
Electromagnetic wave propagation and scattering in materials with time-variant parameters is subject 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 a number of fundamental properties such as 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).
