Analytical transient analysis of temporal boundary value problems using the d’Alembert formula

Wending Mai, Douglas H. Werner

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Temporal boundary value problems (TBVPs) provide the foundation for analyzing electromagnetic wave propagation in time-varying media. In this paper, we point out that TBVPs fall into the category of unbounded initial value problems, which have traveling wave solutions. By dividing the entire time frame into several subdomains and applying the d’Alembert formula, the transient expressions for waves propagating through temporal boundaries can be evaluated analytically. Moreover, unlike their spatial analogs, TBVPs are subject to causality. Therefore, the resulting analytical transient solutions resulting from the d’Alembert formula are unique to temporal systems.

Original languageEnglish (US)
Pages (from-to)5727-5730
Number of pages4
JournalOptics Letters
Volume46
Issue number22
DOIs
StatePublished - Nov 15 2021

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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