Propagation of spatiotemporal optical vortex beams in electromagnetically-induced transparency media

Electromagnetically induced transparency (EIT) is a fundamental effect in quantum optics, providing a versatile platform for quantum technologies. A growing frontier is the integration of EIT with structured light, particularly vortex beams. Extending this to the spatiotemporal domain, we herein study the propagation and evolution of spatiotemporal optical vortex (STOV) beams in an EIT medium. We derive an analytical solution for the evolved STOV field and its stability criterion, and analyze the propagation dynamics with a primary focus on the evolution of the phase singularity. Following the splitting of the initial multi-charge STOV phase singularity upon propagation, the dynamics of the resultant first-order phase singularities are governed by the interplay of first-order loss dispersion (FLD), second-order loss dispersion (SLD), and group velocity dispersion (GVD) of the EIT medium. FLD dictates their overall directional shift, while SLD governs their mutual separation. Under normal GVD, the phase singularities evolve into parallel π-phase step lines and subsequently undergo a topological charge reversal; under zero GVD, only π-phase step lines are formed without topological charge reversal; both transitions are absent under anomalous GVD. These transitions occur in the far zone when the STOV's center frequency lies within the EIT window, whereas around the absorption peak, they occur at a distance just prior to the critical point beyond which the field collapses. Furthermore, we establish the condition under which the splitting of the initial multi-charge STOV phase singularity is entirely suppressed throughout propagation. STOVs carry intrinsic transverse orbital angular momentum (OAM), providing a new, orthogonal dimension for photonic encoding beyond the conventional longitudinal OAM of spatial optical vortices. Integrating STOVs with EIT merges this robust quantum resource with a platform for coherent dispersion engineering, enabling high-dimensional quantum information processing in a vastly expanded state space that combines both longitudinal and transverse OAM.