• Optical Instruments
  • Vol. 41, Issue 5, 17 (2019)
Yuan REN and Chunhui HUANG*
Author Affiliations
  • College of Physics and Information Engineering, Fuzhou University, Fuzhou 350116, China
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    DOI: 10.3969/j.issn.1005-5630.2019.05.003 Cite this Article
    Yuan REN, Chunhui HUANG. Depolarization measurement and correction of polarized light normally incident on the corner cube[J]. Optical Instruments, 2019, 41(5): 17 Copy Citation Text show less

    Abstract

    In order to solve the depolarization effect of the corner cube, an elliptically polarized light correction scheme with the external wave plates is proposed. The modified formula of the corner cube with a tilted solid ridgeline is summarized, and a polarized light correction model with clockwise and counter-clockwise reflection paths is established. The analysis of the model shows that two half-wave plates and one retarder can keep the polarization state of the incident ray equal to that of the emerging ray. Based on the model, by using a 1 064 nm laser, the correction experiment on the BK7 glass corner cube whose solid ridgeline is placed vertically in clockwise and counter-clockwise reflection paths is carried out. When the angle between the polarized direction and the horizontal direction of the linearly polarized incident light varies from 90° to 0°, the maximum absolute value of the ellipticity of the light in depolarization is corrected from 35° to 5°. When the incident light is with the approximately circular polarization, its ellipticity drops from 44° to 40° after correction.
    $\left[ {PS} \right] = \left[ {cosθsinθsinθcosθ} \right]\left[ {PS} \right] = {{ J}_{\rm r}}(\theta )\left[ {PS} \right]$(1)

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    ${{ J}_{\rm R}} = \left[ {exp(iδp)00exp(iδs)} \right]$(2)

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    ${{ J}_{123}} = {{ J}_{\rm r}}( - \frac{{2\pi }}{3}){{ J}_{\rm R3}}{{ J}_{\rm r}}(\frac{\pi }{3}){{ J}_{\rm R2}}{{ J}_{\rm r}}( - \frac{\pi }{3}){{ J}_{\rm R1}}{{ J}_{\rm r}}( - \frac{\pi }{3})$(3)

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    ${{ J}_{321}} = {{ J}_{\rm r}}( - \frac{\pi }{3}){{ J}_{\rm R1}}{{ J}_{\rm r}}( - \frac{\pi }{3}){{ J}_{\rm R2}}{{ J}_{\rm r}}(\frac{\pi }{3}){{ J}_{\rm R3}}{{ J}_{\rm r}}( - \frac{{2\pi }}{3})$(4)

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    ${{ J}_{213}} = {{ J}_{\rm r}}(\frac{{2\pi }}{3}){{ J}_{321}}{{ J}_{\rm r}}(\frac{{2\pi }}{3})$(5)

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    ${{ J}_{132}} = {{ J}_{\rm r}}( - \frac{{2\pi }}{3}){{ J}_{321}}{{ J}_{\rm r}}( - \frac{{2\pi }}{3})$(6)

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    ${{ J}_{231}} = {{ J}_{\rm r}}( - \frac{{2\pi }}{3}){{ J}_{123}}{{ J}_{\rm r}}( - \frac{{2\pi }}{3})$(7)

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    ${{ J}_{312}} = {{ J}_{\rm r}}(\frac{{2\pi }}{3}){{ J}_{123}}{{ J}_{\rm r}}(\frac{{2\pi }}{3})$(8)

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    ${{ J}_{123}}(\gamma ) = {{ J}_{\rm r}}(\gamma ){{ J}_{123}}{{ J}_{\rm r}}(\gamma )$(9)

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    $ {{E}_{\rm o}}={{ J}_{N}} {{ J}_{N-1}} \cdots {{ J}_{2}} {{ J}_{1}} {{E}_{\rm i}} $ (10)

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    $ {{{ J}}_{N}} {{{ J}}_{N-1}} \cdots {{{ J}}_{2}} {{{ J}}_{1}}={{I}} $ (11)

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    ${{ J}_{123}} = \left[ {0.0088+0.9594i0.2338+0.1576i0.2338+0.1576i0.8926+0.3518i} \right]$(12)

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    $E123_1=[E123x1E123y1]=[0.971520.23698+8.3267×10017i],E123_2=[E123x2E123y2]=[0.23698+1.9429×10016i0.97152]$ ()

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    ${{ V}_\pi } = \left[ {0.971520.236980.236980.97152} \right] = \frac{1}{{\sqrt {{\rm{0}}{\rm{.9715}}{{\rm{2}}^2} + {\rm{0}}{\rm{.2369}}{{\rm{8}}^2}} }}\left[ {0.971520.236980.236980.97152} \right]$(13)

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    $ JA=VπJ123Vπ=[0.06585+0.99783i1.1582×106+7.8065×107i1.1582×106+7.8065×107i0.94963+0.31337i][0.06585+0.99783i000.94963+0.31337i]=[e1.5049i00e2.8229i] $ (14)

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    $JAD0=D0JA=D0VπJ123Vπ=VπJ123VπD0e2.8229iI=I$ (15)

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    ${{ J}_\pi }(\theta ) = \left[ {cos2θsin2θsin2θcos2θ} \right]$(16)

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    ${{ J}_0}(\delta ) = \left[ {eiδ001} \right]$(17)

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    $Jπ(θ)J123Jπ(θ)J0(δ)=J0(δ)Jπ(θ)J123Jπ(θ)=I$ (18)

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    $Jπ(πθ)J321Jπ(πθ)J0(δ)=J0(δ)Jπ(πθ)J321Jπ(πθ)=I$ (19)

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    $Jπ(2π3θ)J213Jπ(π3θ)J0(δ)=J0(δ)Jπ(2π3θ)J213Jπ(π3θ)=I$ (20)

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    $Jπ(π3θ)J132Jπ(2π3θ)J0(δ)=J0(δ)Jπ(π3θ)J132Jπ(2π3θ)=I$ (21)

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    $Jπ(π3+θ)J231Jπ(2π3+θ)J0(δ)=J0(δ)Jπ(π3+θ)J231Jπ(2π3+θ)=I$ (22)

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    $Jπ(2π3+θ)J312Jπ(π3+θ)J0(δ)=J0(δ)Jπ(2π3+θ)J312Jπ(π3+θ)=I$ (23)

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    $Jπ(θγ2)J123(γ)Jπ(θ+γ2)J0(δ)=J0(δ)Jπ(θγ2)J123(γ)Jπ(θ+γ2)=I$ (24)

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    ${{ J}_{132}}(\frac\pi{6}) = {{ J}_{\rm r}}(\frac\pi{6}){{ J}_{132}}{{ J}_{\rm r}}(\frac\pi{6})$(25)

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    ${{ J}_{231}}(\frac\pi{6}) = {{ J}_{\rm r}}(\frac\pi{6}){{ J}_{231}}{{ J}_{\rm r}}(\frac\pi{6})$(26)

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    $Jπ(π4θ)J132(π6)Jπ(3π4θ)J0(δ)=J0(δ)Jπ(π4θ)J132(π6)Jπ(3π4θ)=I$ (27)

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    $Jπ(π4+θ)J231(π6)Jπ(3π4+θ)J0(δ)=J0(δ)Jπ(π4+θ)J231(π6)Jπ(3π4+θ)=I$ (28)

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    Yuan REN, Chunhui HUANG. Depolarization measurement and correction of polarized light normally incident on the corner cube[J]. Optical Instruments, 2019, 41(5): 17
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