Analytical transient analysis of temporal boundary value problems using the d’Alembert formula
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Nov 15, 2021
- Source ID
- 10.1364/ol.440210
Entities
People
- Douglas H. Werner
- Wending Mai
Organizations
- Defense Advanced Research Projects Agency
- National Science Foundation
- Pennsylvania State University