Mode-dependent Emission Thresholds and Frequencies in Metal Nanoparticles within Gain-enhanced Media

TL;DR

This paper analyzes how emission thresholds and frequencies in metal nanoparticles depend on mode and size within gain media, using Mie theory to guide the design of plasmonic nanolasers.

Contribution

It introduces a rigorous mode-resolved analysis of emission thresholds in metal nanoparticles with gain, employing a hybrid numerical scheme for precise determination of lasing conditions.

Findings

Higher-order modes in larger particles have lower threshold gains.

Emission thresholds are strongly dependent on particle size and mode order.

The analysis provides insights for designing active plasmonic nanolasers.

Abstract

We present a mode-resolved analysis of emission thresholds in metal nanoparticles embedded within an infinite gain medium, using Mie scattering theory as a rigorous framework. Focusing on the first three resonant modes, we identify the onset of emission by locating the complex zeros of the electric scattering coefficient a_n(omega), which serve as indicators of lasing conditions. Our hybrid numerical scheme-combining coarse bracketing and two-dimensional Newton refinement-enables precise determination of both the threshold gain G_th,n and the corresponding emission frequency omega_th,n across varying particle radii. The results uncover strong size-dependent behavior, with higher-order modes in larger particles exhibiting significantly reduced threshold gain. These insights elucidate the modal dynamics underlying plasmonic nanolasing and provide design guidelines for active photonic systems leveraging gain-enhanced nanoparticles.