  With the help of a theoretical model and finite-difference-time-domain
simulations based on the hydrodynamic-Maxwell model, we examine the effect of
difference frequency generation in an array of L-shaped metal nano-particles
characterized by intrinsic plasmonic nonlinearity. The outcomes of the
calculations reveal the spectral interplay of the gain and loss in the vicinity
of the fundamental frequency of the localized surface-plasmon resonances.
Subsequently, we identify different array depths and pumping regimes
facilitating parametric amplification and parametric down-conversion. Our
results suggest that the parametric amplification regime becomes feasible on a
scale of hundreds of nanometers and parametric downconversion on the scale of
tens of nanometers, opening up new exciting opportunities for developing
building blocks of photonic metasurfaces.
