# Surface second-harmonic from metallic nanoparticle configurations - a transformation optics approach

## TL;DR

This paper uses transformation optics to analytically study surface second-harmonic generation in metallic nanoparticle structures, revealing new physical insights and conditions affecting SHG efficiency.

## Contribution

It introduces an analytical approach linking complex nanoparticle geometries to simpler structures, uncovering new phase-matching and geometric factors influencing SHG.

## Key findings

- Phase-matching is relevant even at sub-wavelength scales.
- A previously unidentified geometric factor affects SHG efficiency.
- Analytical solutions are supported by numerical simulations.

## Abstract

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, phase-matching condition is relevant even for this sub-wavelength structure. Furthermore, we identify a geometric factor which was not identified before. We support our analysis with numerical simulations.