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

Kees Wapenaar; Dirk-Jan van Manen

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arXiv · 2609.20357

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

Kees Wapenaar·Dirk-Jan van Manen

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Abstract

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.

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Kees Wapenaar, Dirk-Jan van Manen. 2026-09-17. Three-dimensional vector waves in time-variant materials, with applications in time-reversed focusing and Green's function retrieval. https://arxiv.org/abs/2609.20357

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