A surface integral formulation for the second-harmonic generation (SHG) from periodic metallic–dielectric nanostructures is described. This method requires the discretization of the scatterers’ surface in the unit cell only. All the physical quantities involved in this problem are derived in the unit cell by applying specific periodic boundary conditions both at the fundamental and the second-harmonic (SH) frequencies. Both the fundamental and the SH electric fields are computed using the method of moments and periodic Green’s function evaluated with the Ewald’s method. The accuracy of the method is carefully assessed using two specific cases, namely the surface plasmon enhancement of SHG from a gold film and the SHG from L-shaped nanoparticle arrays. These two examples emphasize the accuracy and versatility of the proposed method, which can be applied to a broad range of periodic metallic structures, including plasmonic arrays on arbitrary substrates and metamaterials.
© 2013 Optical Society of America
Original Manuscript: July 18, 2013
Revised Manuscript: August 22, 2013
Manuscript Accepted: September 27, 2013
Published: October 25, 2013
Jérémy Butet, Benjamin Gallinet, Krishnan Thyagarajan, and Olivier J. F. Martin, "Second-harmonic generation from periodic arrays of arbitrary shape plasmonic nanostructures: a surface integral approach," J. Opt. Soc. Am. B 30, 2970-2979 (2013)