Optical Spin Vortex in Nonlinear Anisotropic Media

A theoretical study is given of a new type of optical vortex in nonlinear anisotropic media. This is called an ``optical spin vortex'', which is realized as a special solution of the two-component non-linear Schr\"{o}dinger equation. The existence of spin vortex is inherent in the spin texture that is caused by the anisotropy of dielectric tensor, where a role of spin is played by the Stokes vector. By introducing the effective Lagrangian governing the non-linear Schr\"{o}dinger equation, we derive the evolution equation for the motion of spin vortex, which exhibits a clear distinction from the conventional singular vortex inherent in the phase function that is described by the single component complex field.