Nonlinear optics in metamaterials

Nonlinear optics focuses on the phenomena that arise when intense light interacts with matter. At low intensities, optical response of a material scales linearly with the amplitude of the electric field. However, at high intensities, light-matter interactions become more complicated leading to such fascinating nonlinear effects as self-focusing, soliton propagation, and high-harmonic generation. Although the field of nonlinear optics was developing for many decades since the invention of lasers, nonlinear optical materials available to date are still limited by either slow materials' response time in such phenomena as saturable absorption, photorefractive effect, and thermal nonlinear phenomena, or by relatively low and generally band-limited nonlinear susceptibilities responsible for ultra-fast nonlinear processes. The emergence of metamaterials is likely to revolutionize nonlinear optics, enabling to low-power, compact, and ultra-fast applications of nonlinear optical phenomena. We review a subset of recent progress in theoretical and experimental studies of nonlinear optical properties and phenomena enabled by the unique properties of engineered optical media. We discuss new regimes of nonlinear optical interactions enabled by judiciously designed metamaterials; review fundamental limit of nonlinear optical phenomena and several metamaterial-based approaches to enhancing nonlinearities at optical frequencies; and consider engineered nonlinear properties of soft matter-based nonlinear media.