A model of three coupled wave guides and third order exceptional points

TL;DR

This paper models three coupled wave guides with PT symmetry to explore third-order exceptional points, revealing richer structures and emphasizing the fine tuning needed for experimental observation of these singularities.

Contribution

It introduces a PT-symmetric three-wave guide model with delta potentials and analyzes the occurrence and physical effects of third-order exceptional points.

Findings

Third-order exceptional points are identified in the model.

The three-wave guide system exhibits a richer structure than two-wave systems.

Fine tuning is crucial for experimental realization of EP3.

Abstract

A ${\cal PT }$-symmetric model for three interacting wave guides is investigated. Each wave guide is represented by an attractive $\delta$-function potential being in equidistant positions. The two outer potentials are complex describing loss and gain, respectively. The real parts of the outer potentials are assumed to be equal. The major focus of the study lies on the occurrence of an exceptional point of third order and the physical effects of such singularity. While some results resemble those from similar studies with two wave guides, the three wave guides appear to have a richer structure. Emphasis is placed on the fine tuning in the approach of the EP3 as this appears to be a particular challenge for an experimental realization.