Surface second-harmonic generation from metallic-nanoparticle configurations: A transformation-optics approach

We study surface second-harmonic generation (SHG) from a singular plasmonic structure consisting of touching metallic wires. We use the technique of transformation optics and relate the structure to a rather simpler geometry, a slab waveguide. This allows us to obtain an analytical solution to the problem, revealing rich physical insights. We identify various conditions that govern the SHG efficiency. Importantly, our analysis demonstrates that apart from the mode-matching condition, the phase-matching condition is relevant even for this subwavelength structure. Furthermore, we identify a geometric factor which was not identified before. We support our analysis with numerical simulations.