Chapter 15: Vortices in Nematic Liquid Crystals
Fenomenos Nonlineales y Mecánica, Department of Mathematics and Mechanics, Universidad Nacional Autónoma de México, Mexico D.F., Mexico
School of Mathematics and Applied Statistics, University of Wollongong , Wollongong, New South Wales, Australia
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh , Scotland, United Kingdom
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia
The study of optical vortices has a long history in both linear and nonlinear media. The book by Kivshar and Agrawal  provides a complete review of this extensive work for vortex propagation in local media. Although this extensive body of knowledge for vortex propagation in local media exists, the vortex evolution in nonlocal media, such as thermal nonlinear media and nematic liquid crystals, has been studied only recently . Another recent topic of study is vortex-type structures in coupled waveguides, which provide an underlying lattice for the vortex propagation and lead to a discrete analog of a vortex . It is the purpose of this chapter to describe the main analytical tools for the asymptotic analysis of the stability and propagation of optical vortices in nonlocal, nonlinear media, with an emphasis on nematic liquid crystals. To this end, we begin ...