Chapter 16: Dispersive Shock Waves in Reorientational and Other Optical Media
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia
Nematic liquid crystals are an example of a nonlinear nonlocal optical medium in which rod-like molecules orientate in response to a light beam, or some other applied electric fields. This is because the electric field induces dipoles in the organic molecules. Nematic liquid crystals have received much attention from researchers, as nonlinear effects can be observed over small length scales. A series of elegant experiments have shown that stable optical spatial solitary waves, so-called nematicons, can propagate in nematic liquid crystals [1, 2]. Such solitary waves have generated much interest because of their possible applications as reconfigurable “circuits” for all-optical information processing [3–5].
Nematic liquid crystals are just one example  in a variety of optical dielectrics that support spatial solitary waves (Chapter 1). Other optical media include photorefractives , quadratic media , glasses , thermal media , and colloids . In all these media, solitary waves occur because of a balance between diffraction (in the spatial domain) or dispersion (in the temporal domain) and nonlinear (self-) focusing. In all cases, a nonlinear interaction between the medium and the light alters the refractive index of the medium.
The nonlinear Schrödinger ...