Revisiting the boundary conditions for second-harmonic generation at metal-dielectric interfaces

Abstract

We study second-harmonic generation (SHG) arising from surface nonlinearity at a metal-dielectric interface using a spectral decomposition method. Since our method avoids the need to consider the generalized boundary condition across the metal-dielectric interface in the presence of a perpendicular surface source, we retrieve the known discontinuity of the tangential component of the electric field ($E_{\parallel }^{2\omega }$) for a general geometry, based on a purely mathematical argument. Further, we reaffirm the standard convention of the implementation of this condition, namely, that the surface dipole source radiates as if placed outside the metal surface for arbitrary geometries. We also study and explain the spectral dependence of the discontinuity of the tangential component of the electric field at second harmonic. Finally, we note that the default settings of the commercial numerical package COMSOL Multiphysics fail to account for the $E_{\parallel }^{2\omega }$-discontinuity. We provide a simple recipe that corrects the boundary condition within these existing settings.

References in corpus (2)

• Origin of optical second-harmonic generation in spherical gold nanoparticles: Local surface and nonlocal bulk contributions
• Second harmonic generation from metallic arrays of rectangular holes

Cited by in corpus (5)

• Surface second-harmonic from metallic nanoparticle configurations - a transformation optics approach
• Optimization of second-harmonic generation from touching plasmonic wires
• Observing the influence of second-harmonic tangential surface source in gold plasmonic nanostructures
• Second-harmonic generation due to coulomb-like interaction in a heterodimer of subwavelength dimensions
• Leveraging Plasmonic Nanocavity Arrays Forming Metasurfaces to Boost Second Harmonic Generation due to Surface Effects