Fundamental Asymmetries between Spatial and Temporal Boundaries in Electromagnetics

Wending Mai, Jingwei Xu, Douglas H. Werner

Research output: Contribution to journalArticlepeer-review


Time-varying materials bring an extra degree of design freedom compared to their conventional time-invariant counterparts. However, few discussions have focused on the underlying physical difference between spatial and temporal boundaries. In this letter, we thoroughly investigate those differences from the perspective of conservation laws. By doing so, the building blocks of optics and electromagnetics such as the reflection law, Snell’s law, and Fresnel’s equations can be analogously derived in a temporal context, but with completely different interpretations. Furthermore, we study the unique features of temporal boundaries, such as their nonconformance to energy conservation and causality.

Original languageEnglish (US)
Article number858
Issue number4
StatePublished - Apr 2023

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • General Mathematics
  • Physics and Astronomy (miscellaneous)

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