Metallic nanostructures as electronic billiards for nonlinear terahertz photonics

The optical properties of metallic nanoparticles are most often considered in terms of plasmons, the coupled states of light and quasifree electrons. Confinement of electrons inside the nanostructure leads to another, very different type of resonances. We demonstrate that these confinement-induced resonances typically join into a single composite "super-resonance," located at significantly lower frequencies than the plasmonic resonance. This super-resonance influences the optical properties in the low-frequency range, in particular, producing giant nonlinearities. We show that such nonlinearities can be used for efficient down-conversion from optical to terahertz and midinfrared frequencies on the submicrometer propagation distances in nanocomposites. We discuss the interaction of the quantum-confinement-induced super-resonance with the conventional plasmonic ones, as well as the unusual quantum level statistics, adapting here the paradigms of the quantum billiard theory and showing the possibility to control the resonance position and width using the geometry of the nanostructures.