Geometric effect on second harmonic generation from gold grating

We numerically investigate second harmonic generation from gold gratings of an ideal rectangular and ladder-shaped cross-section. The SHG efficiency from the gold gratings of the ladder-shaped cross-section is significantly enhanced compared with that from the ideal rectangular cross-section with a maximum enhancement factor of around two. The enhancement is ascribe to the nanostructure dependent local fundamental electric field, the nonlinear sources and thus the far field radiation. Our results have a practical meaning in the explanation of experimental SHG measurement, and the modulation of SHG response in the metallic nanostructure.