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Optics Express

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

Jinze Wu, Lai Wei, Nan Huo, Xiaojin Yin, Jinhong Liu, Jinhong Li

Published May 8, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.1364/oe.596868

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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.
Electromagnetically induced transparency (EIT) is an important phenomenon in quantum optics, and has a wide range of applications in the fields of quantum information processing and quantum precision metrology. Recently, with the rapid progress of the generation and detection of structured light, the EIT with structured light has attracted enormous interests and offers new and novel functionalities and applications. Here, we theoretically study the propagation and evolution of Gaussian vortex beams, a typical type of structured light, in an EIT medium with Λ-type three-level atoms. Based on the generalized Huygens-Fresnel principle, we derive the analytical expressions of fully and partially coherent Gaussian vortex beams propagating in the EIT medium, and study the evolution of the intensity and phase distributions of the beams and their dependencies on parameters such topological charge, coherence length, Rabi frequency, etc. It is shown that both the fully and partially coherent Gaussian vortex beams undergo focusing and diverging periodically during propagation. The phase singularity of the fully coherent beam keeps unchanged, while the phase singularity of the partially coherent beam experiences splitting and recombination periodically. In addition, new phase singularities with opposite topological charge are generated in the latter case. Our results not only advance the study of the interaction between structured light and coherent media, but also pave the avenue for manipulating structured light via EIT.
In the burgeoning field of light-matter interactions, angular momentum has emerged as a pivotal factor, driving innovative research directions. This study delves into the interaction dynamics between vortex lights and an electromagnetically induced transparency (EIT) medium, with a primary focus on elucidating the underlying mechanism of angular momentum transfer. Through comprehensive theoretical analysis and numerical simulations, it is demonstrated that when the probe field carries orbital angular momentum (OAM), the dispersion and absorption characteristics of the EIT medium undergo periodic modulation. This modulation is intricately determined by the azimuthal phase and topological charge of the beam. Notably, the OAM in the driving field exerts no such influence on the medium's properties. Leveraging vortex phase plates (VPPs) or spatial light modulators (SLMs) to manipulate the tunable OAM enables dynamic control over the EIT effect. This breakthrough not only deepens our understanding of light-matter interactions at the quantum level but also unlocks new avenues for high-dimensional quantum information processing and advanced optical communication technologies.
Spatiotemporal optical vortices (STOVs) are structured light featuring a phase singularity in the spatiotemporal domain, exhibiting unique topology that couples spatial and temporal dimensions. To date, amplification of STOVs remains unexplored, and their wavelength tunability is limited by available light sources. In this work, we present the theoretical analysis and experimental demonstration of optical parametric amplification (OPA) of STOVs. The pulse energy of the STOV signal is enhanced by a factor of 60, while its spatiotemporal structure is robustly preserved. The generated idler inherits the phase-conjugated STOV topology with the opposite topological charge, governed by simultaneous conservation of energy, linear momentum, and spatiotemporal orbital angular momentum. The intrinsic wavelength-conversion capability of OPA further provides a route towards spectrally tunable STOV generation, spanning from visible to near-infrared wavelength regimes. This work paves the way toward further development of multi-stage amplification architectures, facilitating applications of wavelength-tunable spatiotemporally structured light at ultrahigh intensities.
We investigate the propagation of an optical vector vortex weakly interacting with a coherently prepared atomic medium (phaseonium) in a three-level ΛΛΛ configuration. The vector beam consists of vortex pulse pairs with right- and left-circular polarizations, corresponding to opposite spin angular momentum (SAM), and carrying opposite orbital angular momentum (OAM) charges ±l\pm l±l. We show that during the propagation of the vortex pairs, analytically obtained in the linear regime, the medium inherits the topology of the vortex pair, mapping the OAM onto a spatially structured atomic coherence. This mapping produces 2∣l∣−2|l|-2∣l∣−fold azimuthal transparency structures that reshape the beam intensity from a ring into a petal-like pattern. The OAM-structured atomic coherence induces a corresponding optical anisotropy within the medium, which feeds back into the propagating vector beam, resulting in optical spin-orbit coupling manifested as SAM exchange, rotation, and evolution of polarization textures. Depending on the initial ground-state population of the phaseonium, the polarization state evolves between left-circular, linear, and right-circular polarizations.
We investigate coherent orbital-angular-momentum (OAM) transfer and dispersion-controlled light propagation in a ladder-type Er³⁺: YAG three-level system. Using the density-matrix formalism and coupled Maxwell-Bloch equations, we derive analytical expressions for the probe and generated beams that explicitly incorporate Er³⁺-ion concentration. We show that an incident vortex-carrying probe beam transfers its OAM to a generated signal beam through a concentration-dependent sum-frequency nonlinear process, with complete phase and topological-charge preservation. By analyzing conversion efficiency, spatial phase, and intensity distributions, we identify an optimal Er³⁺ concentration (3%) that maximizes vortex-transfer efficiency. Furthermore, the absorption and dispersion spectra of the probe and generated beams reveal the mechanism underpinning the vortex transfer and indicate the potential for concentration-selectable transitions between fast and slow propagation regimes. These results establish Er³⁺: YAG as a viable solid-state platform for coherent manipulation of structured light, enabling efficient vortex-beam frequency conversion and dispersion engineering, with potential relevance to classical and quantum OAM-based communication protocols, wavelength-compatible OAM interfaces, and slow-light photonic signal processing.
We theoretically investigate coherent orbital-angular-momentum (OAM) transfer and dispersion-controlled light propagation in a ladder-type Er YAG three-level system. Using the density-matrix formalism and coupled Maxwell-Bloch equations, we derive analytical expressions for the probe and generated beams that explicitly incorporate Er ion concentration. We show that an incident vortex-carrying probe beam transfers its OAM to a generated signal beam through a concentration-dependent sum-frequency nonlinear process, with complete phase and topological-charge preservation. By analyzing conversion efficiency, spatial phase, and intensity distributions, we identify an optimal Er concentration (3 percent) that maximizes vortex-transfer efficiency. Furthermore, the absorption and dispersion spectra of the probe and generated beams reveal the mechanism underpinning the vortex transfer and demonstrate tunable transitions between fast and slow regimes. These results establish Er YAG as a viable solid-state platform for the coherent manipulation of structured light, enabling efficient vortex-beam frequency conversion and dispersion engineering for applications in high-dimensional quantum communication, wavelength-compatible OAM interfaces, and slow-light photonic signal processing.