“Capillary” structures in transversely trapped nonlinear optical beams

A mathematical analogy between paraxial optics with two circular polarizations of light in a defocusing Kerr medium with positive dispersion, binary Bose–Einstein condensates of cold atoms in the phase separation regime, and hydrodynamics of two immiscible compressible liquids can help in theoretical search for unknown three-dimensional coherent optical structures. In this work, transversely trapped (by a smooth profile of the refractive index) light beams are considered and new numerical examples are presented, including a “floating drop”, a precessing longitudinal optical vortex with an inhomogeneous profile of filling with the second component, and the combination of a drop and a vortex filament. Filled vortices that are perpendicular to the beam axis and propagate at large distances have also been simulated.