Spectral Singularities of a Complex Spherical Barrier Potential and Their Optical Realization

TL;DR

This paper investigates spectral singularities in complex spherical potentials, linking them to optical lasing phenomena, and determines the size constraints of gain media for their realization in spherical laser systems.

Contribution

It provides a novel analysis of spectral singularities in spherical geometries and their physical realization as spherical laser emissions.

Findings

Spectral singularities correspond to zero-width resonances in spherical potentials.

A lower size bound for gain media to support these singularities is established.

The results connect mathematical spectral properties with practical optical laser design.

Abstract

The mathematical notion of a spectral singularity admits a physical interpretation as a zero-width resonance. It finds an optical realization as a certain type of lasing effect that occurs at the threshold gain. We explore spectral singularities of a complex spherical barrier potential and study their realization as transverse spherical electromagnetic waves emitted by a gain medium with a spherical geometry. In particular, for a typical dye laser material, we obtain a lower bound on the size of the gain medium for the occurence of this kind of spectral singularities.