Nonlinear and electro-optics of nano-dispersed nematic liquid crystals with tunable negative-, zero-, and positive indices

We present a review of recent progress in the studies of the nonlinear- and electro-optics of liquid crystals, particularly in their meta-material forms. An analytical expression for the "ultimate" optical nonlinearity of nematic liquid crystals is obtained, and several routes to realizing such optical nonlinearities are discussed. We also describe two approaches for realizing tunable or reconfigurable negative-zero-positive index materials: (1) planar nano-structured frequency selective surfaces [FSS] containing nematic liquid crystals; (2) core-shell nano-spheres randomly distributed in bulk nematic liquid crystal matrix. Such metamaterials can be designed for applications in the visible-infrared, as well as Terahertz and microwave regimes. These liquid crystalline meta-materials are capable of supra-nonlinearities characterized by refractive index changing coefficients of over 1cm²/watt and microseconds response times.