Chapter 8 - Vortex Solitons

Abstract

Optical vortex solitons represent a generalization of the concept of spatial dark solitons to two transverse dimensions. A vortex soliton is associated with the self-trapping of a phase singularity embedded within a broad optical beam in a self-defocusing medium. Experimentally, vortex solitons appear in a natural way through the transverse instability of dark-soliton stripes in a nonlinear bulk medium. Unlike the spinning solitons, which carry an angular momentum and require a self-focusing medium, the vortex solitons exist only in self-defocusing nonlinear media (n 2 < 0). Optical vortex solitons are sometimes described as the stable, black, and self-guided beams of circular symmetry. Vortex solitons can be generalized to include the polarization properties of light, and two such generalizations are possible. Firstly, two optical fields of different polarizations can have a vortex-like structure. This kind of double-vortex soliton is known to exist in other fields. Secondly, a vortex of one polarization can guide the optical field of another polarization, giving rise to the two-dimensional generalization of the bright-dark soliton pairs. Vortex solitons can also be generalized to include the temporal dimension. Such an extension leads to the concept of optical bullets in the context of bright solitons.