• Photonics Research
  • Vol. 7, Issue 11, 1273 (2019)
Wenjin Long1, Jintao Pan1, Xinyi Guo2, Xiaohe Liu2, Haolin Lin2, Huadan Zheng1, Jianhui Yu1、4, Heyuan Guan1, Huihui Lu1, Yongchun Zhong2, Shenhe Fu2, Li Zhang3, Wenguo Zhu1、2、*, and Zhe Chen1
Author Affiliations
  • 1Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Jinan University, Guangzhou 510632, China
  • 2Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
  • 3School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528000, China
  • 4e-mail: kensomyu@gmail.com
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    DOI: 10.1364/PRJ.7.001273 Cite this Article Set citation alerts
    Wenjin Long, Jintao Pan, Xinyi Guo, Xiaohe Liu, Haolin Lin, Huadan Zheng, Jianhui Yu, Heyuan Guan, Huihui Lu, Yongchun Zhong, Shenhe Fu, Li Zhang, Wenguo Zhu, Zhe Chen. Optimized weak measurement of orbital angular momentum-induced beam shifts in optical reflection[J]. Photonics Research, 2019, 7(11): 1273 Copy Citation Text show less

    Abstract

    Tiny but universal beam shifts occur when a polarized light beam is reflected upon a planar interface. Although the beam shifts of Gaussian beams have been measured by the weak measurement technique, the weak measurement for orbital angular momentum (OAM)-induced spatial shifts of vortex beams is still missing. Here, by elaborately choosing the preselection and postselection states, the tiny OAM-induced Goos–H nchen and Imbert–Fedorov shifts are amplified at an air–prism interface. The maximum shifts along directions both parallel and perpendicular to the incident plane are theoretically predicted and experimentally verified with optimal preselection and postselection states. These maximum shifts can be used to determine the OAM of vortex beams.
    GH=[0χpχs0],(1)

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    IF=[γp00γs],(2)

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    |φf=ψpost|exp[ig(GHP^x+IFP^y)]|ψpre|φi.(3)

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    Xw=φf|X^|φf=g[Re(AwGH)+Im(AwIF)],(4)

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    Yw=φf|Y^|φf=g[Re(AwIF)Im(AwIF)],(5)

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    Xw=k0rp2Im(γp)rs2Im(γs)Δ(rp2+rs2),(6)

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    Yw=k0rsrp[Im(χp)Im(χs)]Δ(rp2+rs2),(7)

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    E˜={[α(rpkxk0rp)+βMkyk0]|H+[β(rskxk0rs)+αMkyk0]|V}φ˜,(8)

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    E˜{[α(rpkxk0rp)+βMkyk0]i[β(rskxk0rs)+αMkyk0]ei2ϕ}φ˜(cosϕ2|H+sinϕ2|V).(9)

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    Xw={αβrprs[Im(γpei2ϕ2)Im(γsei2ϕ2)]+αβ[rp2Im(γp)+rs2Im(γs)]+rprs[α2Re(γpei2ϕ2)β2Re(γsei2ϕ2)]}/k0W,(10)

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    Yw={rprs[α2Im(γsei2ϕ2)β2Im(γpei2ϕ2)]+[α2rp2Im(χp)+β2rs2Im(χs)]+αβrprs[Re(χsei2ϕ2)+Re(χpei2ϕ2)]}/k0W,(11)

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    W=α2rp2+β2rs2+2αβrprssin2ϕ2+(||+1)[(αrpχp)2+(βrsχs)2+2αrpβrsIm(χp*χse2iϕ2)+rp2γp2(α2+β22αβrsin2ϕ)]/k02w02.(12)

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    Wenjin Long, Jintao Pan, Xinyi Guo, Xiaohe Liu, Haolin Lin, Huadan Zheng, Jianhui Yu, Heyuan Guan, Huihui Lu, Yongchun Zhong, Shenhe Fu, Li Zhang, Wenguo Zhu, Zhe Chen. Optimized weak measurement of orbital angular momentum-induced beam shifts in optical reflection[J]. Photonics Research, 2019, 7(11): 1273
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