Nonuniformly Filled Vortex Rings in Nonlinear Optics

Vortex rings in ferromagnets

Vortex ring solutions are presented for the Landau-Lifshitz equation, which models the dynamics of a three-dimensional ferromagnet. The vortex rings propagate at constant speed along their symmetry axis and are characterized by the integer-valued Hopf charge. They are stable to axial perturbations, but it is demonstrated that an easy axis anisotropy results in an instability to perturbations wh...

Nonlinear Optics Basics: Kramers-Krönig Relations in Nonlinear Optics

Monopole-antimonopole and Vortex Rings

The SU(2) Yang-Mills-Higgs theory supports the existence of monopoles, antimonopoles, and vortex rings. In this paper, we would like to present new exact static antimonopole-monopole-antimonopole (A-M-A) configurations. The net magnetic charge of these configurations is always negative one, whilst the net magnetic charge at the origin is always positive one for all positive integer values of th...

Wave optics of Liesegang rings.

Liesegang rings refract and reflect at the interface between the regions of the same gel but of different thickness. The incident and the refracted rings obey a refraction law analogous to the Snell's law of classical optics, with a reverse of the spacing coefficient being a counterpart of the refraction index. The wavelike behavior of the rings at the interface is explained by geometrical argu...

Monopoles, Antimonopoles and Vortex Rings

Introduction Defects, classical solutions of spontaneously broken gauge theories, where the Higgs field vanishes at points, lines or surfaces, are relevant in particle physics and cosmology. Monopoles, for instance, represent zero-dimensional defects, vortex solutions or strings are associated with one-dimensional defects, domain walls represent two-dimensional defects. Here we present new clas...