Time-Varying Electromagnetic Systems - Challenges and Methodologies

Time-varying (TV) electromagnetic (EM) systems and devices introduce a fundamentally new framework in EM theory by extending classical concepts beyond traditional time-invariant formulations. In conventional EM systems, temporal invariance combined with the steady-state assumption permits the elimination of explicit time dependence. In contrast, the modeling of TV EM systems generally requires the explicit incorporation of the universal principle of causality. Indeed, in a TV system, the cause-effect relationship evolves over time, making it essential to account for when an excitation is applied and when its effects are observed. This requirement poses profound challenges, as many well-established concepts, analytical tools and modeling approaches cease to be directly applicable. At the same time, TV systems offer truly unprecedented opportunities and functionalities that are unattainable with conventional time-invariant designs. Addressing these challenges therefore necessitates the development of new theoretical foundations and engineering methodologies applicable to general TV EM systems. This paper provides the first systematic overview of TD methodologies for the modeling of TV EM systems, with an emphasis on approaches that explicitly account for and preserve causality. Several such methodologies are presented and illustrated through representative examples.