A numerical investigation of enhanced backward second-harmonic generation in one-dimensional PIM/NIM structure

Abstract

In this paper, we have demonstrated a numerical investigation of an enhanced backward second-harmonic generation (BSHG) effect in a one-dimensional positive-index material/negative-index material (1D-PIM/NIM) structure with nonlinear deep grating. The 1D-PIM/NIM structure composed of common linear PIM layers and NIM layers, whose electric permittivity and magnetic permeability are described by Drude model for allowing negative refractive index behavior, embedded in nonlinear χ(2) material in periodically arrangement. To model BSHG phenomenon, we have developed a completed set of nonlinear coupled-mode equations (NCMEs) by perturbing nonlinear wave equation by a small factor with appropriate scale following a way of multiple-scale approach (MSA). Then, we have numerically solved the NCMEs to achieve the second-harmonic frequency output and conversion efficiency of backward field. We have also discussed a backward phase-matching (BWPM) condition, which has been satisfied by tuning a fundamental frequency (FF) at ω in a negative refractive index region and second-harmonic (SH) frequency at 2ω in a positive refractive index region, and band-edge local field enhancement condition, which has been created by rearranging PIM and NIM layers in optimal periodic fashion. By using both conditions, a conversion efficiency of BSHG can be dramatically enhanced.