Spectral singularity in composite systems and simulation of a resonant lasing cavity

TL;DR

This paper explores spectral singularities in composite non-Hermitian systems, deriving conditions for their existence and demonstrating how such systems can simulate resonant lasing cavities.

Contribution

It derives a general condition for spectral singularities in composite systems with multiple scattering centers, including non-Hermitian ones, and applies this to simulate a resonant lasing cavity.

Findings

Spectral singularities occur when reflection amplitudes satisfy a specific phase condition.

The condition extends to systems with multiple scattering centers.

A simple system can simulate a resonant lasing cavity using these principles.

Abstract

We investigate herein the existence of spectral singularities (SSs) in composite systems that consist of two separate scattering centers A and B embedded in one-dimensional free space, with at least one scattering center being non-Hermitian. We show that such composite systems have an SS at $k_{c}$ if the reflection amplitudes $r^{A}\left( k_{c}\right) $ and $r^{B}\left( k_{c}\right) $ of the two scattering centers satisfy the condition $r_{\mathrm{R}% }^{A}\left( k_{c}\right) r_{\mathrm{L}}^{B}\left( k_{c}\right) e^{i2k_{c}\left( x_{B}-x_{A}\right) }=1$. We also extend the condition to the system with multi-scattering centers. As an application, we construct a simple system to simulate a resonant lasing cavity.