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Journal of Applied Physics

Spatial modulation of refractive index in a dense atomic ensemble using Laguerre–Gaussian beams

Peng Chen, Kang Zheng, Rui‐Bo Jin, Chunling Ding, Xiangying Hao

Published Apr 24, 2023• 4 citations
Publisher

Abstract

We propose a scheme to investigate the spatial modulation of the refractive index in a dense atomic ensemble under the action of the Laguerre–Gaussian (LG) beams. Theoretical derivations based on a density-matrix approach associated with numerical simulations are utilized to study the behaviors of the index of refraction, showing that the azimuthal and radial mode indices (i.e., l 2 and p 2) of the LG beams significantly affect the real and imaginary parts of the refractive index. To be specific, the number of the dispersive peaks is determined by ( p 2 + 1 ) | l 2 |, and there are 2 | l 2 | lossless petals in conjunction with p 2 concentric absorption rings centered on the vortex center. Furthermore, by tuning the phase values of the electric and magnetic components of the electromagnetic field, the index of refraction can be drastically tuned from negative to zero to positive and accompanied by periodic absorption and amplification. This investigation provides a powerful tool for manipulating the index of refraction through a nonlinear interaction between atoms and the vortex beams and suggests potential applications in optical switching, logic gates, and optical storage with spatially varying refractive indices.

DOI
10.1063/5.0145999

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We propose a scheme to investigate the spatial modulation of the refractive index in a dense atomic ensemble under the action of the Laguerre–Gaussian (LG) beams. Theoretical derivations based on a density-matrix approach associated with numerical simulations are utilized to study the behaviors of the index of refraction, showing that the azimuthal and radial mode indices (i.e., l 2 and p 2) of the LG beams significantly affect the real and imaginary parts of the refractive index. To be specific, the number of the dispersive peaks is determined by ( p 2 + 1 ) | l 2 |, and there are 2 | l 2 | lossless petals in conjunction with p 2 concentric absorption rings centered on the vortex center. Furthermore, by tuning the phase values of the electric and magnetic components of the electromagnetic field, the index of refraction can be drastically tuned from negative to zero to positive and accompanied by periodic absorption and amplification. This investigation provides a powerful tool for manipulating the index of refraction through a nonlinear interaction between atoms and the vortex beams and suggests potential applications in optical switching, logic gates, and optical storage with spatially varying refractive indices.
Abstract We have studied two-dimensional absorption, gain, and corresponding refractive index profiles in a ladder-type three-level atomic system interacting with three coherent fields. One is a weak probe field considered as a plane wave, while the other two are the control fields taken as two Laguerre–Gaussian doughnut beams. Position dependence of two vortex beams induces the spatially modulated coherence at the condition of resonance, which enables us to obtain space-dependent absorption, transparency, gain without inversion (GWI), and refractive index enhancement in the present scheme. The azimuthal modulation of coherence effects is attributed to the presence of optical angular momentum of the vortex beams. Under the influence of an additional travelling wave field with the presence of two vortex beams, the present model leads us to obtain an ultra-large enhancement of refractive index at the resonant detuning of the fields. This phenomenon makes the atom-field system to play the equivalent role of a high-refractive-index prism. The role of near dipole–dipole (NDD) interaction on the modulation of position-dependent coherence effects has also been investigated. It has been shown that, without any inclusion of the travelling wave field in the system, the phenomenon of resonant enhancement of refractive index may also occur in the presence of NDD effect. The new way of generating spatially controlled GWI and nonlinear refractive index enhancement is specific to the present model. This work seems to be useful for finding its applications in spatially modulated coherence controlled electromagnetically induced transparency-based quantum devices like quantum optical memory, switches, and quantum logic gates, where the refractive index switching phenomenon is a prerequisite.
Abstract We study high-resolution atomic localization in a multilevel atomic system driven simultaneously by a Gaussian and a Laguerre–Gaussian (LG) beam. The coexistence of the two fields creates a hybrid coupling landscape in which the Gaussian beam supplies radial confinement, while the LG beam contributes an orbital angular momentum (OAM)-dependent azimuthal modulation. By solving the steady-state density-matrix equations, we show that the resulting localization patterns contain mixed spatial harmonics whose structure is set by the topological charge, beam waist, and probe detuning. The OAM index determines the angular symmetry of the localized absorption features, whereas the beam waist controls their radial extent. Probe detuning provides an additional tuning mechanism that alters the contrast and geometry of the localization regions. These results highlight how structured light fields can be used to engineer controllable spatial localization in atomic media, with relevance to precision metrology, spatially resolved quantum control, and structured-light sensing.
A spatial light modulator (SLM) has been used to create high quality Laguerre–Gaussian (LG) light beams, which have been used to study the guiding of cold rubidium atoms. The SLM allows real-time variation of the hollow guiding beam and permits direct comparison of the guided atom fluxes for different LG modes with minimal adjustment of the other optical components. It is demonstrated that, by increasing the azimuthal index l of the Laguerre–Gaussian beam, the radiation pressure pushing the trapped atoms may be reduced while maintaining the same guided flux. This is the first comparative study of hollow beam atom guiding, and further demonstrates the versatility of the SLM for studies in atom optics.
Recently, the generation and detection of structured light field have drawn a great deal of attention, due to their importance in high-capacity optical data storage and quantum technology. In this letter, we explore the azimuthal modulation of optical transparency in a four-level double-V type quantum system near a plasmonic nanostructure. A Laguerre-Gaussian beam and the interaction of the system with free-space vacuum modes have been employed to create the phase-dependent absorption of a non-vortex probe field. First, we demonstrate how to identify the azimuthal index associated with the conventional LG beam via measuring the probe absorption so that the phase information of such a beam gets encoded on the spatially-dependent absorption profile with angularly-distributed lobes. Also, a spatially-varying optical transparency can be formed, due to the periodic variation of the absorption spectrum. Then, asymmetrical Laguerre-Gaussian beams are used to extend the selective spatial transparency mechanism to asymmetric spatially-structured windows, allowing for optical manipulation of spatial modes at arbitrary positions. Moreover, we investigate the influence of the asymmetric parameter on the features of the spatial inhomogeneities and show how the beams enable us to imprint the phase information of the orbital angular momentum at a desired position.
We studied Fresnel diffraction of a Laguerre-Gaussian beam LGp,l{\text{LG}}_{p,l}LGp,l​ with arbitrary azimuthal lll and radial ppp indices on a grating induced during its Raman interaction with a spatially periodic pump field in an atomic medium. The diffraction pattern turned out to be more complex than the classical Talbot effect observed when a plane wave illuminates a two-dimensional grating. The simulation results show that, under certain conditions, at distances corresponding to the classical Talbot planes (integer and fractional), periodic amplitude-phase distributions appear. The diffraction patterns are not a probe-field image in the induced grating plane, but a regular array of vortex annular-shaped microbeams with an inhomogeneous intensity distribution depending on the lll and ppp indices and with a topological charge equal to that of the initial probe beam. The intensity and spatial distribution of diffraction patterns can be controlled by Raman amplification in the induced grating by varying the pump-field intensity or the Raman detuning.
Abstract This research investigates the intricate interplay between Gaussian beams and atomic media, introducing a novel approach by incorporating a Kerr field and spatially dependent refractive index. The study employs a Gaussian probe field as the primary interaction medium with the atomic ensemble, while simultaneously introducing two control fields. One of these control fields acts as a Kerr field, imparting a unique modulation on the propagation characteristics of the Gaussian beam. The key parameters under scrutiny encompass the probe field detuning (∆P /γ), as well as the Rabi frequencies and detunings of the control fields (Ω1,2/γ, ∆1,2/γ). Further exploration involves transforming one of the control fields into a Gaussian beam, resulting in the creation of a spatially dependent refractive index within the atomic medium. The investigation focuses on the spatial coordinates x/ω0 and y/ω0, where ω0 represents the Gaussian beam waist. This intricate configuration provides a unique platform for studying the manipulation and control of light propagation in atomic media. The research not only sheds light on fundamental interactions in quantum optics but also opens avenues for potential applications in quantum information processing and precision measurement. The outcomes of this study contribute valuable insights into the dynamics of Gaussian beams in complex atomic environments, with potential implications for quantum technology and communication.