Boundary element method for surface nonlinear optics of nanoparticles

We present the frequency-domain boundary element formulation for solving surface second-harmonic generation from nanoparticles of virtually arbitrary shape and material. We use the Rao-Wilton-Glisson basis functions and Galerkin's testing, which leads to very accurate solutions for both near and far fields. This is verified by a comparison to a solution obtained via multipole expansion for the case of a spherical particle. The frequency-domain formulation allows the use of experimentally measured linear and nonlinear material parameters or the use of parameters obtained using ab-initio principles. As an example, the method is applied to a non-centrosymmetric L-shaped gold nanoparticle to illustrate the formation of surface nonlinear polarization and the second-harmonic radiation properties of the particle. This method provides a theoretically well-founded approach for modelling nonlinear optical phenomena in nanoparticles.