Modeling of enhanced second-harmonic generation with phase-matching in periodic subwavelength structure metal film

The recent observation of enhanced optical transmission through a periodic array of subwavelength apertures in a metal film has elicited significant interest both because it represents a novel phenomenon and because it raises the prospect of a series of new applications. Recently, an ~104 increase in conversion efficiency of second harmonic generation (SHG) from a periodically nanostructured silver film structure consisting of a single subwavelength aperture surrounded by a set of concentric surface grooves was reported. Although the phase-matching condition for extraordinary transmission has been discussed by many researchers, the phase-matching conditions of SHG process was neglected in former experiments. In this paper, we design a silver film with two different sets of periods on a quartz substrate with the silver thickness of 20nm in order to excite long-range surface plasma wave that could transmit millimeter-order distance in the metal surface, which greatly contribution to the improvement of the conversion efficiency of SHG for about 102 times. The fundamental light is perpendicularly coupled into the metal film with about 29 percent coupling efficiency, and the direction of the transmitted SH light is also perpendicular to the metal surface. Furthermore, this new type of structure could contribute to high conversion efficiency of SHG for the virtues of low losses, extremely compact structure and easily fabrication process.