(3+1)-dimensional superluminal spatiotemporal optical solitons and vortices at weak light level

A scheme is proposed to produce (3+1)-dimensional superluminal spatiotemporal optical solitons and vortices in a coherent atomic system working in an active Raman gain regime. It is shown that the evolution of the envelope of a signal field obeys a modified (3+1)-dimensional nonlinear Schrödinger equation, which includes dispersion, diffraction, and Kerr nonlinearity. Various solutions of light bullets, light vortices, light-bullet trains, and light-vortex trains are presented, which display many interesting characters, including superluminal propagating velocity and extremely low generating power. In addition, they can be easily manipulated in a controllable way. Stabilization of such high-dimensional superluminal light bullets and vortices can be realized using the trapping potential formed by an additional far-detuned laser field.