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Spatial Structure and Propagation of Vortex Four-Wave Mixing Signal

Ma Xiaoyu, Sang Suling, Zhao Guohui

Published Nov 21, 2025• 0 citations
Publisher

Abstract

Abstract The spatial structure and propagation of vortex Four-Wave mixing (FWM) generated in a cascade three-level atomic system when Laguerre-Gaussian (LG) beams are used as the incident pump fields are studied. Firstly, by solving the third-order density matrix elements in the steady state, the intensity expression of the vortex FWM signal is obtained. Next, their spatial image and phase during the propagation process are researched. It is shown that with the increase of propagation distance, its image of the intensity tends to a Gaussian beam, and the center of the spot gradually deviates from the original optical singularity. Furthermore, after superposing multiple topological charge (TC) numbers, the intensity and phase images present entirely different light spots at various positions. The TC number can rapidly increase the capacity of the signal for carrying information. This type of signal can be utilized in quantum communication and information, offering a scalable light source for high-dimensional quantum storage.

DOI
10.21203/rs.3.rs-7296934/v1

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Abstract The spatial structure and propagation of vortex Four-Wave mixing (FWM) generated in a cascade three-level atomic system when Laguerre-Gaussian (LG) beams are used as the incident pump fields are studied. Firstly, by solving the third-order density matrix elements in the steady state, the intensity expression of the vortex FWM signal is obtained. Next, their spatial image and phase during the propagation process are researched. It is shown that with the increase of propagation distance, its image of the intensity tends to a Gaussian beam, and the center of the spot gradually deviates from the original optical singularity. Furthermore, after superposing multiple topological charge (TC) numbers, the intensity and phase images present entirely different light spots at various positions. The TC number can rapidly increase the capacity of the signal for carrying information. This type of signal can be utilized in quantum communication and information, offering a scalable light source for high-dimensional quantum storage.
Abstract The coherent control of orbital angular momentum four-wave mixing (OAM-FWM) signal in a cascaded three-level atomic system by multiple parameters of incident lights is studied. Firstly, based on the Laguerre–Gaussian beam, the expressions for the intensity and phase of the FWM signal loaded with OAM were derived by solving the density matrix equation in the steady state. Then, through coordinate transformation, the spatial distribution construction of the OAM-FWM signal was completed. And the spatial structure of intensity and phase distribution are investigated respectively. It is shown that the Rabi frequency and detuning can effectively control the output OAM-FWM signal. Finally, we further study the phase distribution of multiple topological charge (TC) numbers in the FWM process, considering the conservation of OAM. As a result, the signal can also be regulated by multiple TC numbers. The constructed OAM-FWM signal which has enhanced the information storage capacity, could be widely used in optical communication and quantum information research.
Abstract We have proposed a double scheme for the efficient generation and control of spatial four-wave mixing (FWM)-induced ultraviolet light via optical angular momentum transfer from a vortex-field (Laguerre–Gaussian (LG) beam) applied once to the excited transition of the first two-photon ladder and then in the uppermost transition of the three-photon ladder in the FWM-loop configuration of a five-level atomic excitation mechanism. In both the LG-cases, at the conditions of resonant and off-resonant detunings of the two coherent fields with high Rabi frequencies guiding the multi-photon excitation route in the system, it has been shown that the vortex FWM light can propagate either in the superluminal or in the subluminal regime depending upon ‘turned-off’ and ‘turned-on’ conditions of a Raman field outside the FWM-loop, respectively. Such switching phenomenon is the most interesting outcome of the present study along with the significant phase-twisting effects as manifested in the helical phase patterns in both the LG-cases. Thus, the practical implementation of the present model under a cold atomic environment paves up a novel way of obtaining structured high-dimensional light transfer process based on the mechanism of nonlinear photonics, which might have potential applications in quantum information processing and technology in the near future.
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.
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.
We investigate the steady-state optical response of a Laguerre-Gaussian vortex cavity system integrated with cold atoms featuring a double-ΛΛΛ energy level structure. Within this hybrid system, the atoms are driven by cavity mode and three coherent vortex beams, each carrying independent orbital angular momentum (OAM). We first check the steady-state output spectrum of the hybrid system in the passive/active case (without/with external cavity driving). Our findings reveal that the optomechanically induced transparency (OMIT) spectrum is modulated by the OAM difference (Δℓℏ)(Δ\ell\hbar)(Δℓℏ) from the atomic component throughout the four-wave mixing (FWM) process. The resulting loop phase (ΔℓθΔ\ellθΔℓθ) can achieve a switching effect on the absorption and gain behavior of the hybrid system for the probe beam. Additionally, the group delay, indicative of fast/slow light phenomena, is also tuned by ΔℓΔ\ellΔℓ. We further display how the atomic OAM modulates the periodicity of the output spot pattern in the hybrid system. This research provides valuable insights into the modulation of optical responses in Laguerre-Gaussian vortex cavity systems.
We present a theoretical analysis of the spatial shape (transverse and longitudinal) of two degenerate four-wave mixing (FWM) signals induced by fields Ea and Eb, with nonuniform transverse profiles, and wave-vectors ka and kb. The two signals are generated in a cold sample of two-level atoms, in the forward directions 2ka − kb and 2kb − ka. In all cases, the transverse shapes of the generated signals (both near- and far-field) are dictated by the projection of the nonlinear coherence onto the Laguerre-Gaussian (LG) function space. Our calculations show that the longitudinal profile of each generated beam is affected by the spectral characteristics of the medium, described by the third order nonlinear susceptibility. For Gaussian incident fields with equal detunings from resonance, the FWM beam shapes are completely symmetric, with an asymmetry induced by different detunings of incident fields. By considering incident beams with LG distributions, the topological charge conservation determines the orbital angular momentum of each signal and the longitudinal profiles show similar behaviors to the case with Gaussian beams. The phase discontinuities of LG modes reveal a rotation and distortion of the phase distribution of the FWM beams caused by the detunings. We discuss for selected configurations, the relations between both generated beams and their propagation properties. We also present preliminary experimental results of the power spectra of the two FWM signals generated in our magneto-optical trap of rubidium atoms.