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 (7)

• Second and Third Harmonic Generation in Metal-Based Nanostructures
• 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
• Surface Integral Method for the Second Harmonic Generation in Metal Nanoparticles
• Cascaded Second-order Surface Plasmon Solitons due to Intrinsic Metal Nonlinearity
• Robust Location of Optical Fiber Modes via the Argument Principle Method
• Second harmonic generation from metallic arrays of rectangular holes

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