Toy model for plasmonic metamaterial resonances coupled to two-level   system gain
  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. 
Martin Wegener, Juan Luis Garcia-Pomar, Costas M. Soukoulis, Nina   Meinzer, Matthias Ruther, and Stefan Linden