Three-dimensional vector waves in time-variant materials, with applications in time-reversed focusing and Green's function retrieval

The behavior of wave propagation and scattering in time-variant materials has been studied by many authors, for electromagnetic as well as for mechanical waves. Most studies consider two-dimensional waves, governed by scalar wave equations. Here we introduce a unified wave equation for three-dimensional electromagnetic and elastodynamic vector-wave propagation and scattering in homogeneous, time-variant materials. Using the symmetry properties of this equation, we establish the conservation of net field-momentum density, and a reciprocity relation between causal and acausal Green's functions. The latter relation is exploited in the derivation of the counterparts of classical time-reversed focusing and Green's function retrieval for time-variant materials.