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Photonics Research

Enhancement of phase conjugation degenerate four-wave mixing using a Bessel beam

Qian Zhang, Xuemei Cheng, Haowei Chen, Bo He, Zhaoyu Ren, Ying Zhang, Jintao Bai

Published Feb 12, 2018• 13 citations
Publisher

Abstract

We report on the enhancement of phase conjugation degenerate four-wave mixing (DFWM) in hot atomic Rb vapor by using a Bessel beam as the probe beam. The Bessel beam was generated using cross-phase modulation based on the thermal nonlinear optical effect. Our results demonstrated that the DFWM signal generated by the Bessel beam is about twice as large as that generated by the Gaussian beam, which can be attributed to the extended depth and tight focusing features of the Bessel beam. We also found that a DFWM signal with reasonable intensity can be detected even when the Bessel beam encounters an obstruction on its way, thanks to the self-healing property of the Bessel beam. This work not only indicates that DFWM using a Bessel beam would be of great potential in the fields of high-fidelity communication, adaptive optics, and so on, but also suggests that a Bessel beam would be of significance to enhance the nonlinear process, especially in thick and scattering media.

DOI
10.1364/prj.6.000162

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Optics Express•Oct 4, 2017•20 citations
We report on the enhancement of phase conjugation degenerate four-wave mixing (DFWM) in hot atomic Rb vapor by using a Bessel beam as the probe beam. The Bessel beam was generated using cross-phase modulation based on the thermal nonlinear optical effect. Our results demonstrated that the DFWM signal generated by the Bessel beam is about twice as large as that generated by the Gaussian beam, which can be attributed to the extended depth and tight focusing features of the Bessel beam. We also found that a DFWM signal with reasonable intensity can be detected even when the Bessel beam encounters an obstruction on its way, thanks to the self-healing property of the Bessel beam. This work not only indicates that DFWM using a Bessel beam would be of great potential in the fields of high-fidelity communication, adaptive optics, and so on, but also suggests that a Bessel beam would be of significance to enhance the nonlinear process, especially in thick and scattering media.
Nonlinear atomic media are promising substitutes for spatial light modulators (SLMs) owing to the high tunability and fast response. We demonstrate the generation of high-order Bessel-like beam based on cross-phase modulation in 85 Rb atoms. The atomic medium, whose refractive index is spatially modulated by the focused Gaussian pump beam, acts as a nonlinear focusing lens for the Laguerre-Gaussian probe beam. As a result, the probe beam carries the nonlinear phase shift and is converted into a Bessel-like mode in far-field diffraction. The superior self-healing ability of the generated high-order Bessel-like beam is verified by inserting an obstruction in the beam path, and its high tunability is investigated in terms of the pump beam power and vapor temperature. Furthermore, this novel beam is used in an obstruction-immune rotation sensor to measure the angular velocity. Nonlinear atomic medium as a novel SLM promises considerable application prospects in modulating the light field structure.
We report on an experimental generation of Airy beams by four-wave mixing (FWM) in atomic vapor cells. This is achieved by using a non-degenerate FWM process, which occurs with two Gaussian pump beams and one Airy signal beam in hot Rubidium vapor. After satisfying the phase matching condition, a FWM field with the profile of an Airy beam can be generated. In our experiment, the diffraction-free and self-healing behaviors of the generated FWM beam are examined. The results shown that the generated FWM beam is an Airy beam. The nonlinear generation process can be extended to other configurations in the atomic medium, which will be useful for manipulation and application of Airy beams in atomic systems.
One more promising application of the four-wave mixing process is the correction of arbitrary phase aberrations in an optical beam. In such applications, the fidelity as well as the efficiency of the phase-conjugation process needs to be considered in practice. The process which has received the most extensive attention to date is degenerate four-wave mixing (DFWM). The nonlinear interaction in this case is known to result in a perfect phase-conjugate provided high-quality pump beams are available and competing effects such as local self-focusing (or defocusing) can be neglected.
We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the 3s2S1∕23s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}3s2S1∕2​, F=2F=2F=2, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, F=3F=3F=3, mF=3{m}_{F}=3mF​=3 transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.
We propose a new method to generate Bessel-like beam using cross-phase modulation. The hot rubidium atomic sample is shown to have the ability to vary a Gaussian beam (probe beam) into a Bessel-like beam when the sample is illuminated with a counter-propagating Gaussian beam (pump beam) tuned close to the atomic resonances. It is demonstrated that the Bessel-like beam exhibits self-healing after encountering an obstruction on the beam path. The parameters of the Bessel-like beam are found to be easily adjusted by the pump beam power and sample temperature. Moreover, this method is even applicable to the probe beam of low power, having more practical value than the method using self-phase modulation which needs high input beam power. The merits of variable parameter, no requirement for input beam power, simple setup, and low cost would make this method of significance in a variety of applications, especially in those areas where Bessel beam power is needed to be low and parameter to be adjusted easily without changing the setup.