Self-Trapping of Three-Dimensional Spatiotemporal Solitary Waves in Self-Focusing Kerr Media

We theoretically demonstrate that Kerr media under self-focusing nonlinearity support three-dimensional spatiotemporal solitary waves in various patterns, such as necklace-, disk-, and vortex-ring shapes. The structures of these solitons are defined by the set of radial, orbital, and azimuthal quantum numbers, (n,l,m), respectively.