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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{wapenaar2026threedimensional,
  title = {{Three-dimensional vector waves in time-variant materials, with applications in time-reversed focusing and Green's function retrieval}},
  author = {Kees Wapenaar and Dirk-Jan van Manen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20357},
  eprint = {2609.20357},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20357},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Three-dimensional vector waves in time-variant materials, with applications in time-reversed focusing and Green's function retrieval
AU  - Kees Wapenaar
AU  - Dirk-Jan van Manen
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20357
UR  - https://arxiv.org/abs/2609.20357
AB  - 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.
ER  -