Spatiotemporal optical vortex solitons: Dark solitons with transverse and tilted phase line singularities

Vortex solitons (dark solitons) are described in self-defocusing Kerr media whose phase line singularity is not parallel to the propagation direction, but is perpendicular or tilted almost arbitrary angles, depending on the medium linear dispersion. These solitons broaden the so-called spatiotemporal optical vortices recently observed in experiments to the nonlinear realm, opening new perspectives in practical applications of optical vortices.