Dark solitary vortices in defocusing media

The existence and robustness of dark vortices in bi-dispersive and/or normally dispersive self-defocusing nonlinear media is demonstrated. The underlying equation is the bi-dispersive three-dimensional nonlinear Schrdinger equation. The dark vortices are investigated numerically as well as variationally. These vortices can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between diffraction and nonlinearity. Linear stability analysis predicts that for fairly long propagation distances these objects are subject to a very weak transverse instability (in the temporal domain). On this basis the maximum growth rate of the instability is estimated. However, numerical simulations depict that 3D vortices are robust objects. Instability is observed only in the case where the vortex is subjected to relatively strong transverse perturbation. Furthermore, in our simulation is observed that a dark vortex does not break into vortices of a lower vorticity. The variational approach predicts that the synenergy content (the finite ambient energy that remains when the infinite energy of the dark object is excluded) of a vortex of high vorticity is lower than the sum of the synenergies of unitary vortices with the same pedestal. Such vortex solitary objects can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity such as specific AlGaAs alloys.