Intensity-Based Criterion for Determining Exceptional Point in Parity-Time (PT) Symmetric Coupled Array of Optical Waveguides

TL;DR

This paper introduces a simple intensity-based criterion for identifying the exceptional point in PT-symmetric optical waveguide arrays, offering an efficient alternative to eigenvalue computation applicable to various systems.

Contribution

A novel, straightforward intensity-based method for determining the PT symmetry-breaking point, reducing computational complexity and applicable across different tight-binding systems.

Findings

The criterion accurately identifies the exceptional point, matching eigenvalue-based methods.

It effectively distinguishes propagation patterns before and after PT symmetry breaking.

The method is computationally efficient and broadly applicable.

Abstract

In this study, we investigated the propagation pattern and the site-to-site correlation function in a PT-symmetric waveguide array with different input quantum states. Recognizing the stark difference in propagation pattern before and after the PT symmetry-breaking point, we have developed a novel, straightforward intensity-based criterion to determine the exceptional point (EP). This new criterion shows excellent agreement with those obtained by directly computing the Hamiltonian's eigenvalues. Given the computational complexity of Hamiltonian diagonalization, our proposed criterion provides a highly efficient and valuable alternative for identifying the PT symmetry-breaking point. Importantly, the proposed criterion is not restricted to the specific system studied here, but is generally applicable to a wide class of systems that can be described within the tight-binding framework.