Second-harmonic Generation in Left-handed Metamaterials

Abstract

We study the second-harmonic generation in left-handed metamaterials with a quadratic nonlinear response and demonstrate a novel type of the phase matching between backwardpropagating waves of the fundamental frequency and forward-propagating waves of the second harmonics. We show that under these conditions a surface of the left-handed metamaterial is transformed into an effective mirror totally reflecting the second harmonics generated by an incident wave. We derive and analyze the coupled-mode equations for a semi-infinite nonlinear metamaterial. We also suggest binary metamaterials composed of two types of magnetic resonant elements, and demonstrate that in the nonlinear regime such metamaterials provide unique possibilities for phase-matched parametric interaction and enhanced second-harmonic generation. Show more