Surface Integral Method for the Second Harmonic Generation in Metal Nanoparticles

Abstract

Second harmonic (SH) radiation in metal nanoparticles is generated by both nonlocal-bulk and local-surface SH sources, induced by the electromagnetic field at the fundamental frequency. We propose a surface integral equation (SIE) method for evaluating the SH radiation generated by metal nanoparticles with arbitrary shapes, considering all SH sources. We demonstrate that the contribution of the nonlocal-bulk SH sources to the SH electromagnetic field can be taken into account through equivalent surface electric and magnetic currents. We numerically solve the SIE problem by using the Galerkin method and the Rao-Wilton-Glisson basis functions in the framework of the distribution theory. The accuracy of the proposed method is verified by comparison with the SH-Mie analytical solution. As an example of a complex-shaped particle, we investigate the SH scattering by a triangular nano-prism. This method paves the way for a better understanding of the SH generation process in arbitrarily shaped nanoparticles and can also have a high impact in the design of novel nanoplasmonic devices with enhanced SH emission.

References in corpus (2)

• Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions
• Origin of second-harmonic generation enhancement in optical split-ring resonators

Cited by in corpus (8)

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• Revisiting the boundary conditions for second-harmonic generation at metal-dielectric interfaces
• Evidence for cascaded third harmonic generation in non-centrosymmetric gold nanoantennas
• Surface second-harmonic from metallic nanoparticle configurations - a transformation optics approach
• $T$-matrix method for calculation of second-harmonic generation in clusters of spherical particles
• Analytical Theory of Second Harmonic Generation from a Nanoparticle with a Non-Centrosymmetric Geometry
• $\mathcal{T}$-matrix method for computation of second-harmonic generation upon optical wave scattering from clusters of arbitrary particles: Application to nonlinear optical interaction of bound states in the continuum