Mode-dependent Emission Thresholds and Frequencies in Metal Nanoparticles within Gain-enhanced Media
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 an(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 Gth,n and the corresponding emission frequency omegath,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.
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