• Photonics Research
  • Vol. 5, Issue 2, 92 (2017)
Chengquan Mi1, Shizhen Chen1, Xinxing Zhou2, Kai Tian1, Hailu Luo1、*, and Shuangchun Wen1
Author Affiliations
  • 1Laboratory for Spin Photonics, School of Physics and Electronics, Hunan University, Changsha 410082, China
  • 2Synergetic Innovation Center for Quantum Effects and Applications, College of Physics and Information Science, Hunan Normal University, Changsha 410081, China
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    DOI: 10.1364/PRJ.5.000092 Cite this Article Set citation alerts
    Chengquan Mi, Shizhen Chen, Xinxing Zhou, Kai Tian, Hailu Luo, Shuangchun Wen. Observation of tiny polarization rotation rate in total internal reflection via weak measurements[J]. Photonics Research, 2017, 5(2): 92 Copy Citation Text show less

    Abstract

    In this paper, we examine the tiny polarization rotation effect in total internal reflection due to the spin–orbit interaction of light. We find that the tiny polarization rotation rate will induce a geometric phase gradient, which can be regarded as the physical origin of photonic spin Hall effect. We demonstrate that the spin-dependent splitting in position space is related to the polarization rotation in momentum space, while the spin-dependent splitting in momentum space is attributed to the polarization rotation in position space. Furthermore, we introduce a quantum weak measurement to determine the tiny polarization rotation rate. The rotation rate in momentum space is obtained with 118 nm, which manifests itself as a spatial shift, and the rotation rate in position space is achieved with 38 μrad/λ, which manifests itself as an angular shift. The investigation of the polarization rotation characteristics will provide insights into the photonic spin Hall effect and will enable us to better understand the spin–orbit interaction of light.
    |H(ki,r)=|P(ki,r)kiyki,rcotθi,r|S(ki,r),(1)

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    |V(ki,r)=|S(ki,r)+kiyki,rcotθi,r|P(ki,r).(2)

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    |H(ki)rp(|H(kr)+kiyδrH|V(kr)),(3)

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    |V(ki)rs(|V(kr)kiyδrV|H(kr)),(4)

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    δrH=[1+|rs|exp(iφs)|rp|exp(iφp)]cotθiki,(5)

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    δrV=[1+|rp|exp(iφp)|rs|exp(iφs)]cotθiki.(6)

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    Re[δrH]=[1+|rs||rp|cos(φsφp)]cotθiki,(7)

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    Im[δrH]=|rs||rp|sin(φsφp)cotθiki,(8)

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    Re[δrV]=[1+|rp||rs|cos(φpφs)]cotθiki,(9)

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    Im[δrV]=|rp||rs|sin(φpφs)cotθiki.(10)

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    |Φ=w02πexp[w02(kix2+kiy2)4],(11)

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    |ψrH=rp|Hkry(rp+rs)cotθiki|V=rp2[(1+ikryδrH)|++(1ikryδrH)|]rp2[exp(ikryδrH)|++exp(ikryδrH)|].(12)

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    |ψrH=rpexp(iφp)2[exp(ikryRe[δrH])|++exp(ikryRe[δrH])|].(13)

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    ΦG=σkryRe[δrH],(14)

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    y±H=ΦGkry=σRe[δrH].(15)

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    |ψrH=rpexp(iφp)2[exp(ikrIm[δrH]zRyr)|++exp(+ikrIm[δrH]zRyr)|].(16)

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    ΦG=σkrIm[δrH]zRyr.(17)

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    ΔkryH=ΦGyr=σkrIm[δr]zR.(18)

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    y±H=Re[δrH]±zrIm[δrH]zR.(19)

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    y±V=Re[δrV]±zrIm[δrV]zR.(20)

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    (cosγsinγ)=exp(+iφG)|++exp(iφG)|,(21)

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    |Φf=ψf|exp(iσkryδrH,V)|ψi|Φi=ψf|1+iσkryδH,V|ψi|Φiψf|ψi(1+ikryδrH,Vψf|σ|ψiψf|ψi)|Φi=ψf|ψi(1+ikryAwδH,V)|Φi.(22)

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    Aw=ψf|σ|ψiψf|ψi,(23)

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    Im[AwδrH,V]=Re[Aw]Im[δrH,V]+Im[Aw]Re[δrH,V].(24)

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    |ψi=cos(Θ+2α2)|++eiΦsin(Θ+2α2)|,(25)

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    |ψf=sin(Θ2)|+ei(Φ+2β)cos(Θ2)|,(26)

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    Aw=sin2αcos2αcos2β1+isin2βcos2αcos2αcos2β1.(27)

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    ywH,V=zrkrΦf|kry|ΦfΦf|Φf.(28)

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    ywH,V=zrzRRe[δrH,V]cotβ.(29)

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    ywH,V=zrzRIm[δrH,V]cotα.(30)

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    Chengquan Mi, Shizhen Chen, Xinxing Zhou, Kai Tian, Hailu Luo, Shuangchun Wen. Observation of tiny polarization rotation rate in total internal reflection via weak measurements[J]. Photonics Research, 2017, 5(2): 92
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