Polygons of quantized vortices in nonlinear photonic waveguides

Abstract

In a nonlinear optical waveguide with defocusing Kerr-type nonlinearity, we discuss the existence of a type of stationary nonlinear waves with propagation-invariant density profiles, consisting of vortices located at the vertices of a regular polygon with or without an anti-vortex at its center. These polygons rotate around the center of the system and we provide approximate expressions for their angular velocity. We have computed the evolution of the vortex structures and discuss their stability and the fate of the instabilities that can unravel the regular polygon configurations. Such instabilities can be driven by the instability of the vortices themselves, by vortex-antivortex annihilation or by the eventual breaking of the symmetry due to the motion of the vortices.