Scientific-Practical Material Research Centre, Belarus

\begin{abstract} Spatio-temporal localization conditions of high-power femtosecond singular pulses in Kerr medium depending on topological charge and the ratio of input pulse power to critical one are studied. The underlying physical mechanism for the stable propagation of the vortex is the dynamic competition between the Kerr self-focusing, defocusing caused by photoinduced plasma and anomalous group velocity dispersion (GVD). Two-scale variational approach predicts the stability and the robustness of light bullets with topological charge in fused silica at anomalous GVD effect. However, according to our estimations the stability region originated from plasma impact is very narrow. If the initial radius and duration of vortex pulse is detuned from their stationary values, then such a pulse oscillates under propagation. At this, the pulse duration and its radius may oscillate in phase or in antiphase. Numerical calculations confirming in general the results of variational analysis demonstrate more soft conditions for vortex light bullet formation. The values of transverse and temporal radii of input singular pulse may be quite attainable in experiment. High intensive vortex filamentation in media with normal and anomalous GVD is investigated numerically. For normal GVD numerical calculations reveal the earlier stages of its filamentation which include temporal profile reshaping and splitting of the ring structure into three subrings along the radial direction. The outer and inner subrings of almost equal intensities still retain the original shape of vortex. Reshaping is observed in central part of the doughnut ring. When the vortex propagates, the filaments appear in the central ring, and the less intense peripheral rings disappear. \end{abstract}