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Optics Letters

Propagation of optical vortices in a nonlinear atomic medium with a photonic band gap

Zhaoyang Zhang, Danmeng Ma, Yiqi Zhang, Mingtao Cao, Zhongfeng Xu, Yanpeng Zhang

Published Mar 1, 2017• 46 citations
Publisher

Abstract

We experimentally generate a vortex beam through a four-wave mixing (FWM) process after satisfying the phase-matching condition in a rubidium atomic vapor cell with a photonic band gap (PBG) structure. The observed FWM vortex can also be viewed as the reflected part of the launched probe vortex from the PBG. Further, we investigate the propagation behaviors, including the spatial shift and splitting of the probe and FWM vortices in the medium with enhanced Kerr nonlinearity induced by electromagnetically induced transparency. This Letter can be useful for better understanding and manipulating the applications involving the interactions between optical vortices and the medium.

DOI
10.1364/ol.42.001059

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We experimentally generate a vortex beam through a four-wave mixing (FWM) process after satisfying the phase-matching condition in a rubidium atomic vapor cell with a photonic band gap (PBG) structure. The observed FWM vortex can also be viewed as the reflected part of the launched probe vortex from the PBG. Further, we investigate the propagation behaviors, including the spatial shift and splitting of the probe and FWM vortices in the medium with enhanced Kerr nonlinearity induced by electromagnetically induced transparency. This Letter can be useful for better understanding and manipulating the applications involving the interactions between optical vortices and the medium.
Considering the fact that the orbital angular momentum of light can be transferred through light-matter interactions, we experimentally induced a dressed vortex four-wave mixing (FWM) with the interaction between a vortex probe beam and an inverted Y-type four-level atomic system with a photonic band gap. Further, the Kerr-nonlinearity-modulated propagation behaviors of the probe and the dressed FWM vortices are investigated, including the spatial shift, splitting, and incompleteness of the vortex shape. Strikingly, the propagation behaviors of the vortex beams can be influenced by the interaction between the nonlinear phase and the spiral phase. This study would promote the development of optical computing and information processing science related to the interactions between optical vortices and samples.
We experimentally observe a vortex six-wave mixing (SWM), namely, enhanced four-wave mixing (FWM), signal with its orbital angular momentum transferred from a vortex probe via a photonic band gap (PBG) structure in a hot rubidium vapor cell. By analyzing spatial images and interference patterns, on the one hand, we demonstrate spatial shift and splitting of the images as well as shift of phase singularity for the probe transmission signal under the nonlinear phase of different dressing fields; on the other hand, we observe defocusing and shift of the images as well as shift of phase singularity for the reflected vortex SWM signal by scanning the frequency detuning of a related field. Moreover, we find the interference patterns of the vortex probe can be switched from parallel shape to spiral shape by changing its incident angle. Also, we further research the spiral interference patterns of the transmitted signal by scanning the probe detuning, observing that the number of forks changes with the detuning. We consider the transmitted signal as a combined beam of the linear probe and nonlinear FWM, which are separated under Kerr effect. It is the separation that causes the fork number to change with probe detuning. Our studies are useful for better understanding and manipulation of optical vortices and have wide applications in quantum communication and information processing.
Abstract We experimentally observe the vortex six-wave mixing (SWM) signal carrying orbital angular momentum in a photonic band gap structure. First, we scan the probe detuning and the detuning of the dressing field to find an explanation for the intensity variation of four-wave mixing (FWM) intensity and the shift of forks in interference patterns. Then we change the power of the coupling field and obtain SWM images as well as its interference patterns to investigate the propagation characteristics, including spatial shift and splitting. We observe a change of fork quantity when decreasing the incident angle of the probe field. We suppose that the reflected signal is a combination of a linear probe and a nonlinear vortex FWM signal. By changing the incident angle of the field, the overlap condition between fields have changed correspondingly and the cross-Kerr effect of the coupling field on the linear vortex probe and third-order FWM become different, causing a separation in the center of the two components, which brings the inducement of additional forks.
The dressed four-wave mixing (FWM) in a four-level 85 Rb atomic system, experimentally demonstrated in this paper, is comprised by two coexisting processes. One is emission signal due to enhanced nonlinear via electromagnetically induced transparency (EIT). The other is the Bragg reflection of probe beam because of the created photonic band gap (PBG), which is affected by both linear and third-order nonlinear susceptibility. Moreover, we have demonstrated that different experimental parameters can significantly influence the measured signal with flexibly controlled PBG. These studies are found useful for understanding the fundamental mechanisms in generated FWM processing.
Abstract We experimentally observe the interference patterns of vortex probe transmission signal (PTS) and vortex four-wave mixing (FWM). By changing the difference in the divergences of two optical beams, the spiral interference patterns of the probe beam and the reference Gaussian probe beam can be obtained. It is found that in the interference patterns of vortex PTS, the shifting of the fork can be regulated by blocking different dressing fields and tuning the probe frequency. When the two-photon resonance condition is satisfied, the shift of the fork is the weakest since the strongest probe field intensity induces the weak nonlinear phase shift. In addition, we realize that the relationship between the intensities of the vortex FWM signal and the probe field is not monotonic, because both the intensity of probe field and the dressing effect will affect the intensity of the vortex FWM signal. We also find that the spatial modulations including shifting and splitting are also regulated by the intensity of the probe field and the coupling field. Here, the explanation of these phenomena is presented by the transition of the nonlinear refraction index. Finally, we realize that the singularity overlap or separation between the linear probe and the third-order vortex FWM will lead to the change of fork quantity. Our research is helpful to understand and manipulate optical vortices and can be widely used in quantum computation and communication.
We experimentally demonstrate dressed multi-wave mixing (MWM) and the reflection of the probe beam due to electromagnetically induced absorption (EIA) grating can coexist in a five-level atomic ensemble. The reflection is derived from the photonic band gap (PBG) of EIA grating, which is much broader than the PBG of EIT grating. Therefore, EIA-type PBG can reflect more energy from probe than EIT-type PBG does, which can effectively affect the MWM signal. The EIA-type as well as EIT-type PBG can be controlled by multiple parameters including the frequency detunings, propagation angles and powers of the involved light fields. Also, the EIA-type PBG by considering both the linear and third-order nonlinear refractive indices is also investigated. The theoretical analysis agrees well with the experimental results. This investigation has potential applications in all-optical communication and information processing.