# Analysis of a multi-mode plasmonic nano-laser with an inhomogeneous distribution of molecular emitters

## TL;DR

This paper extends laser theory to analyze a plasmonic nano-laser with inhomogeneous molecular distribution, revealing how molecular arrangement and driving strength influence lasing and plasmon excitation limits.

## Contribution

It introduces a model accounting for molecular inhomogeneity and mode-correlation in a plasmonic nano-laser, providing insights into lasing conditions and excitation limits.

## Key findings

- Large number of strongly driven molecules is needed for lasing.
- Molecular inhomogeneity affects plasmon mode excitation.
- Compact molecular arrangements can limit plasmon excitation.

## Abstract

We extend Lamb's reduced density matrix laser theory to analyze the inhomogeneous molecular couplings and the mode-correlation in a plasmonic nano-laser consisting of a gold sphere and many dye molecules interacting with a driving optical field and with the quantized plasmon modes. The molecular inhomogeneity is accounted for by simulating their random distribution around the sphere. Our analysis shows that in order to obtain lasing we must employ a large number of strongly driven molecules to compensate strong damping of the plasmon modes. The compact molecular arrangement, however, can lead to molecular energy-shifts and thus reduce the excitation of the plasmon modes and ultimately suggests a maximum limit for the plasmon excitation for any specific system.