Absorption of harmonic light in plasmonic nanostructures

Surface plasmons are known for their ability to provide large field enhancement at the interface between a metal and another medium. They can be observed in a variety of structures ranging from plain metallic films to nanoparticles and gratings. Thanks to their large electric field enhancement, surface plasmons have also been exploited for the enhancement of second and third harmonic generation. In fact, metals possess a relatively high third order susceptibility and, although dipole-allowed quadratic nonlinearities are not present in the bulk, they also display an effective second order response that arises from symmetry breaking at the surface, magnetic dipoles (Lorentz force), inner-core electrons, convective nonlinear sources, and electron gas pressure. While much attention has been devoted to achieve efficient excitation of surface plasmons to improve far-field harmonic generation, little or no attention has been paid to the dissipation of the generated harmonic light. Therefore, we undertake a discussion of both harmonic generation and absorption in simple metallic/dielectric interfaces with or without excitation of surface plasmons. We demonstrate that, despite the best efforts embarked upon to study plasmon excitation, the absorbed harmonic energy can far surpass the energy emitted in the far-field. These findings suggest that quantification of the absorbed harmonic light should be an important parameter in evaluating designs of plasmonic nanostructures for frequency mixing.