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We propose, solve, and discuss a simple model for a metamaterialincorporating optical gain: A single bosonic resonance is coupled to afermionic (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 ananalytic expression for the fixed inversion resulting from gain pinning understeady-state conditions. Furthermore, the dynamic response of the 'lasingSPASER', i.e., its relaxation oscillations, can be obtained by simple numericalcalculations within the same model. As a result, this toy model can be viewedas the near-field-optical counterpart of the usual LASER rate equations.

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