Visualization of Branch Points in PT-Symmetric Waveguides

TL;DR

This paper demonstrates how to visualize exceptional points in PT-symmetric waveguides and uses perturbation theory to analyze their spectral properties, providing methods to measure the radius of convergence in such systems.

Contribution

It introduces a visualization technique for exceptional points in PT-symmetric waveguides and links the radius of convergence to physical measurements in these systems.

Findings

Exceptional points can be visualized in PT-symmetric waveguides.

The spectrum remains real within the radius of convergence.

A method to measure the radius of convergence using PT-symmetric directional couplers.

Abstract

The visualization of an exceptional point in a PT symmetric directional coupler(DC) is demonstrated. In such a system the exceptional point can be probed by varying only a single parameter. Using the Rayleigh-Schroedinger perturbation theory we prove that the spectrum of a PT symmetric Hamiltonian is real as long as the radius of convergence has not been reached. We also show how one can use a PT symmetric DC to measure the radius of convergence for non PT symmetric structures. For such systems the physical meaning of the rather mathematical term: radius of convergence, is exemplified.