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

Toy model for plasmonic metamaterial resonances coupled to two-level system gain
Author: M. Wegener, J.L. Garcia-Pomar, C.M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden links:
Source: Opt. Express 16, 19785 (2008) 
Date: 14.12.2008


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.

Supporting materials

We have a version of this publication available on arxiv.org.

In order to allow for a broad overview, we provide a program free of cost that allows for playing with all parameters of the toy model in real time. Obviously, each of the two uncoupled resonances has four parameters (center frequency, damping, dipole moment, and density). In addition, the important phenomenological local-field coupling parameter L and the two-level-system occupation can be freely adjusted – altogether 10 parameters.


  • Download software: toymodel_simtool.zip (60 MB, 32bit version)
  • Unzip this file with a decoding tool like 7-ZIP.
  • If Labview 8.2 (by National Instruments) is not installed locally on your computer, please start "ToyModel/SetupToyModel/setup.exe" and follow the installation instructions.
  • Start our simulation tool by executing "ToyModel/ToyModel/Toymodel.exe".