Dynamics of spherically symmetric vortex of laser radiation in a nonlinear medium

The possibility of realization of a spherically symmetric vortex of the electromagnetic field in a homogeneous isotropic medium is analyzed. It was shown that the vortex could emerge by the interaction of the vector spherical harmonic with the nonlinear medium having a negative linear permittivity. As a result the nonlinear refractive index becomes the valid value in a small volume near the centre. The radial-gradient distribution of the nonlinear refractive index acts as a spherical microcavity induced in the nonlinear medium. Within this volume a set of undamped vector spherical harmonics forms the spherical symmetric structure of the electromagnetic field of a soliton type. This structural resonance has quite discrete energy values. Mechanisms and conditions of self-organization of the spherically symmetric vortex are discussed on a basis of nonlinear-optical and quantum-mechanical approaches. Dynamics and stability of the spherically symmetric vortex in the nonlinear medium are discussed.