Nonlinear Optics with Metamaterials

In all the preceding chapters, we studied the linear properties of optical metamaterials, assuming that the effective electric permittivity e and magnetic permeability μ are independent of the incident light intensity. Indeed, an overwhelming portion of the experimental results on metamaterials reported thus far are exclusively focused on the linear response of metamaterials to external electromagnetic radiation. However, nonlinear effects in metamaterials have become an emerging field of study, particularly among theoretical physicists. A range of nonlinear phenomena in a variety of metamaterials, especially negative-index materials (NIMs), have been theoretically investigated to a considerable extent. The studied topics include general treatments for nonlinear wave propagation and nonlinear Schrodinger equations in NIMs [1, 2], as well as specific nonlinear processes such as second-harmonic generation (SHG) and parametric amplification [3, 4, 5, 6].