Simple models of three coupled $\mathcal{PT}$-symmetric wave guides allowing for third-order exceptional points

TL;DR

This paper develops theoretical models of three coupled $PT$-symmetric wave guides to identify parameter regimes where third-order exceptional points can be experimentally realized, including both realistic and idealized configurations.

Contribution

It introduces a realistic three-mode matrix model for coupled wave guides and compares it with previous models to find conditions for observing EP3s in experiments.

Findings

Parameter ranges for EP3 in semiconductor wave guides identified

Continuous distributions of exceptional points can occur in idealized models

Comparison shows how to experimentally access EP3 regimes

Abstract

We study theoretical models of three coupled wave guides with a $\mathcal{PT}$-symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3) in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.