Electromagnetic Fields in a Time-Varying Medium: Exceptional Points and Operator Symmetries

• Published in: IEEE transactions on antennas and propagation 2020-09, Vol.68 (9), p.6717-6724
• Main Authors: Koutserimpas, Theodoros T., Fleury, Romain
• Format: Article
• Language: English
• Subjects: Conductivity; Electromagnetic fields; Electromagnetic propagation; Electromagnetic radiation; Electromagnetic scattering; Electromagnetism; Energy conservation; exceptional point theory; Media; Parity; parity operator symmetry; Periodic variations; Permittivity; Time-domain analysis; time-reversal; time-varying systems
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2020.2996822

In this article, we study the interactions of electromagnetic waves with a non-dispersive dynamic medium that is temporally dependent. Electromagnetic fields under material time-modulation conserve their momentum but not their energy. We assume a time-variation of permittivity, permeability, and conductivity, and derive the appropriate time-domain solutions based on the causality state at a past observation time. We formulate a time-transitioning state matrix and connect the unusual energy transitions of electromagnetic fields in time-varying media with the exceptional point theory. This state-matrix approach allows us to analyze further the electromagnetic waves in terms of parity and time-reversal symmetries and signify parity-time symmetric wave-states without the presence of a spatially symmetric distribution of gain and loss, or any inhomogeneities and material periodicity. This article provides a useful arsenal to study electromagnetic wave phenomena under time-varying media and points out novel physical insights connecting the resulting energy transitions and electromagnetic modes with exceptional point physics and operator symmetries.