Metallic nanostructures as electronic billiards for nonlinear terahertz photonics

Optical properties of metallic nanoparticles are most often considered in terms of plasmons, the coupled states of light and quasi-free electrons. Here we predict that confinement of electrons inside the nanostructure leads to another, very different, type of resonance, which determines the optical properties in the frequency range significantly below the plasmonic resonance. We demonstrate that closely placed confinement-induces resonances typically join into a single composite "super-resonance" which produces giant nonlinearity at low frequencies. Our simulations show how such nonlinearities can be used for efficient down-conversion of optical pump to terahertz and mid-infrared frequencies in sub-micrometer devices based on nanoparticle composites. We discuss the interaction of these quantum-confinement-induced resonances with the conventional plasmonic ones, as well as the unusual quantum level statistics, adapting here the paradigms of the electronic billiard theory.