Surface second-harmonic generation from surface plasmon waves scattered by metallic nanostructures

We analyze second-harmonic (SH) generation from scattering of surface plasmon polaritons (SPPs) by one-dimensional metallic nanostructures. The electromagnetic field at the fundamental frequency (FF) is calculated by using a formalism based on the reduced Rayleigh equations, in which the arbitrary shape of the nanostructure is accounted for by means of the impedance boundary condition. The near field at the FF, the induced nonlinear-source surface polarization at the SH, and the associated multipole moments up to second order are calculated from this fundamental field. The dependence of near field and radiated optical power at the SH on the SPP wavelength and nanostructure geometry is then investigated.