A universal form of arrays with spectral singularities

TL;DR

This paper reveals a universal form for arrays with spectral singularities in non-Hermitian optical systems, enabling systematic construction of potentials with multiple or higher-order singularities, leading to enhanced lasing responses.

Contribution

It introduces a universal gain-loss distribution form for arrays with spectral singularities and demonstrates systematic methods to design potentials with multiple or higher-order singularities.

Findings

Potential with multiple spectral singularities at arbitrary wavelengths

Higher-order spectral singularities lead to high-intensity lasing modes

Universal form of gain-loss distribution for spectral singularities

Abstract

An array of non-Hermitian optical waveguides can operate as a laser or as a coherent perfect absorber, which corresponds to a spectral singularity of the underlying discrete complex potential. We show that all lattice potentials with spectral singularities are characterized by the universal form of the gain-and-loss distribution. Using this result we systematically construct potentials characterized by several spectral singularities at arbitrary wavelengths, as well as potentials with second-order spectral singularities in their spectra. Higher-order spectral singularities demonstrate a greatly enhanced response to incident beams resulting in the excitation of high-intensity lasing modes.