Toy model for plasmonic metamaterial resonances coupled to two-level system gain

TL;DR

This paper introduces a simple analytical model for a plasmonic metamaterial with optical gain, capturing complex resonance behaviors and dynamic responses like relaxation oscillations, akin to laser rate equations.

Contribution

It presents a novel, solvable toy model linking plasmonic resonances with two-level gain systems, enabling analytical insights into absorption, gain lineshapes, and lasing dynamics.

Findings

Analytical expressions for absorption and gain lineshapes.

Steady-state inversion determined by gain pinning.

Simulation of relaxation oscillations in the model.

Abstract

We propose, solve, and discuss a simple model for a metamaterial incorporating optical gain: A single bosonic resonance is coupled to a fermionic (inverted) two-level-system resonance via local-field interactions. For given steady-state inversion, this model can be solved analytically, revealing a rich variety of (Fano) absorption/gain lineshapes. We also give an analytic expression for the fixed inversion resulting from gain pinning under steady-state conditions. Furthermore, the dynamic response of the 'lasing SPASER', i.e., its relaxation oscillations, can be obtained by simple numerical calculations within the same model. As a result, this toy model can be viewed as the near-field-optical counterpart of the usual LASER rate equations.