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With the help of a theoretical model and finite-difference-time-domainsimulations based on the hydrodynamic-Maxwell model, we examine the effect ofdifference frequency generation in an array of L-shaped metal nano-particlescharacterized by intrinsic plasmonic nonlinearity. The outcomes of thecalculations reveal the spectral interplay of the gain and loss in the vicinityof the fundamental frequency of the localized surface-plasmon resonances.Subsequently, we identify different array depths and pumping regimesfacilitating parametric amplification and parametric down-conversion. Ourresults suggest that the parametric amplification regime becomes feasible on ascale of hundreds of nanometers and parametric downconversion on the scale oftens of nanometers, opening up new exciting opportunities for developingbuilding blocks of photonic metasurfaces.

Interplay of gain and loss in arrays of nonlinear plasmonic nanoparticles: toward parametric downconversion and amplification