Parity-Time Symmetry and Exceptional points: A Tutorial

TL;DR

This tutorial introduces non-Hermitian physics in electromagnetics, focusing on parity-time symmetry and exceptional points, highlighting their unique phenomena and potential applications in sensing, lasing, and energy transfer.

Contribution

It provides a comprehensive introduction to PT-symmetric electromagnetic systems, emphasizing the role of exceptional points and their implications for novel electromagnetic responses.

Findings

Discussion of PT symmetry in electromagnetic systems

Analysis of exceptional points and their scattering responses

Exploration of potential applications in sensing and energy transfer

Abstract

The physics of systems that cannot be described by a Hermitian Hamiltonian, has been attracting a great deal of attention in recent years, motivated by their nontrivial responses and by a plethora of applications for sensing, lasing, energy transfer/harvesting, topology and quantum networks. Electromagnetics is an inherently non-Hermitian research area because all materials are lossy, loss and gain distributions can be controlled with various mechanisms, and the underlying systems are open to radiation. Therefore, the recent developments in non-Hermitian physics offer exciting opportunities for a broad range of basic research and engineering applications relevant to the antennas and propagation community. In this work, we offer a tutorial geared at introducing the unusual electromagnetic phenomena emerging in non-Hermitian systems, with particular emphasis on a sub-class of these systems that obey parity-time (PT) symmetry. We discuss the basic concepts behind this topic and explore their implications for various phenomena. We first discuss the basic features of P, T and PT operators applied to electromagnetic and quantum mechanical phenomena. We then discuss the exotic response of PT-symmetric electromagnetic structures and their opportunities, with particular attention to singularities, known as exceptional points, emerging in these systems, and their unusual scattering response.