• Photonics Research
  • Vol. 11, Issue 9, 1553 (2023)
Yanke Li1, Yu Zou1, Sheng Liu1、3、*, Peng Li1、2、4、*, Bingyan Wei1、5、*, and Jianlin Zhao1、2
Author Affiliations
  • 1Key Laboratory of Light Field Manipulation and Information Acquisition, Ministry of Industry and Information Technology, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi’an 710129, China
  • 2Collaborative Innovation Center of Light Manipulation and Applications, Shandong Normal University, Jinan 250358, China
  • 3e-mail: shengliu@nwpu.edu.cn
  • 4e-mail: pengli@nwpu.edu.cn
  • 5e-mail: wbyxz@nwpu.edu.cn
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    DOI: 10.1364/PRJ.488561 Cite this Article Set citation alerts
    Yanke Li, Yu Zou, Sheng Liu, Peng Li, Bingyan Wei, Jianlin Zhao. Linear and nonlinear photonic spin Hall effect induced by analog circular birefringence of Bessel-like beams[J]. Photonics Research, 2023, 11(9): 1553 Copy Citation Text show less

    Abstract

    The spin Hall effect of a light beam is essentially a product of circular birefringence but is rarely demonstrated. Here, we provide a scheme for initiating off-axis circular birefringence based on the spin-dependent wave vector bifurcation of Bessel beams via a single liquid crystal Pancharatnam–Berry phase element. The tilted Bessel beam shows a detectable photonic spin Hall effect. By introducing the nonlinear propagation trajectories, the spin Hall effect is greatly enhanced. More surprisingly, the two spin states exactly propagate along the scaled trajectories, enabling flexible control of the spin separation. This phenomenon is also applicable to other Bessel-like beams with nonlinear trajectories, which have been already reported.
    δ=(1+kr22k02)KYzk0.

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    δ±=(1+kr±22k02)KYzk0.

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    Δδ=|δ+δ|=2ΔkkrKYzk03.

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    δ=n=1Ncnzn.

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    KYkzδz=kzn=1Ncnzn1.

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    KY=n=1Ncnrn1kznkrn1.

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    KY=n=1NCn±rn1kz±nkr±n1,

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    δ±=n=1NCnzn=sδ±n=1Ncn(zsz±)n,

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    Δδ=|δ+δ|=2n=1Ncnzn[m=1(n+1)/2(n1)!(n2m)!(2m1)!(Δkkr)2m1+o(krΔkk02)].

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    δ={f1(z),z<Lf2(z),zL.

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    δ={A[1+sin(2πzT)],z<L0,zL,(C1)

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    Yanke Li, Yu Zou, Sheng Liu, Peng Li, Bingyan Wei, Jianlin Zhao. Linear and nonlinear photonic spin Hall effect induced by analog circular birefringence of Bessel-like beams[J]. Photonics Research, 2023, 11(9): 1553
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