Spectral Singularities in the Surface Modes of a Spherical Gain Medium

TL;DR

This paper analyzes surface modes in spherical gain media, revealing spectral singularities called singular gallery modes that can be excited with minimal gain, enabling thresholdless lasing and multi-wavelength operation.

Contribution

It provides an analytic framework for understanding spectral singularities in spherical gain media and demonstrates their excitation with arbitrarily small gain, highlighting potential for thresholdless lasing.

Findings

Spectral singularities occur in surface modes of spherical gain media.

Singular gallery modes can be excited with minimal gain, eliminating lasing threshold.

Multiple wavelengths can be simultaneously excited with the same gain.

Abstract

We study the surface modes of a homogeneous spherical gain medium and provide a comprehensive analytic treatment of a special class of these modes that support spectral singularities. Because the latter have a divergent quality factor, we call them the singular gallery modes. We show that they can be excited using arbitrarily small amounts of gain, and as a result, the system lacks a lasing threshold, effectively. This shows that we can realize spectral singularities in the surface modes of extremely small spherical samples with modest amounts of gain. We also examine the possibility of exciting singular gallery modes with different wavelengths using the same amount of gain. This corresponds to the situation where the system undergoes simultaneous lasing at different wavelengths.