Spectral Singularities and Whispering Gallery Modes of a Cylindrical Gain Medium

TL;DR

This paper explores spectral singularities in cylindrical gain media, revealing a new class of whispering gallery modes with divergent quality factors that can lase at threshold without a traditional gain threshold.

Contribution

It introduces singular gallery modes (SGMs) that support spectral singularities, enabling thresholdless lasing and multi-wavelength emission in cylindrical gain systems.

Findings

SGMs have divergent quality factors and support spectral singularities.

Small gain coefficients can excite SGMs, often smaller than the actual gain.

Multiple SGMs can be excited simultaneously, leading to multi-wavelength lasing.

Abstract

Complex scattering potentials can admit scattering states that behave exactly like a zero-width resonance. Their energy is what mathematicians call a spectral singularity. This phenomenon admits optical realizations in the form of lasing at the threshold gain, and its time-reversal is responsible for antilasing. We study spectral singularities and whispering gallery modes (WGMs) of a cylindrical gain medium. In particular, we introduce a new class of WGMs that support a spectral singularity and, as a result, have a divergent quality factor. These singular gallery modes (SGMs) are excited only if the system has a positive gain coefficient, but typically the required gain is extremely small. More importantly given any amount of gain, there are SGMs requiring smaller gain than this amount. This means that, in principle, the system lacks a lasing threshold. Furthermore, the abundance of these modes allows for configurations where a particular value of the gain coefficient yields an effective excitation of two distant SGMs. This induces lasing at two different wavelengths.