Dynamics of light amplification and gain in nano-plasmonic fishnet metamaterials

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Plasmonic metamaterials form an exciting new class of engineered media that promise a range of important applications, such as subwavelength focusing, cloaking and slowing/stopping of light. At optical frequencies, using gain to overcome potentially not insignificant losses has recently emerged as a viable solution to ultralow-loss operation that may lead to next-generation active metamaterials. Here, we employ a Maxwell-Bloch methodology for the analysis of these gain-enhanced optical nanomaterials. The method allows us to study the dynamics of the coherent plasmon-gain interaction, nonlinear saturation, field enhancement as well as radiative and non-radiative damping such as tunnelling and F¨orster coupling. Using numerical pump-probe experiments on a double-fishnet metamaterial with dye-molecule inclusions we investigate the build-up of the inversion and the formation of the plasmonic modes in the low-Q fishnet cavity. We find that loss compensation occurs in the negative-refractiveindex regime and that, due to the loss compensation and the associated sharpening of the resonance, the real part of the refractive index of the metamaterial becomes more negative compared to the passive case. Furthermore, we investigate the behaviour of the metamaterial above the lasing threshold, and we identify the occurrence of a far-field lasing burst and gain depletion when higher dye densities are used. Our results provide deep insight into the internal processes that affect the macroscopic properties of active metamaterials. This could guide the development of amplifying and lasing plasmonic nanostructures.