Abstract

We propose a method for measuring the full polarization states of a light field by using hybrid polarization-angular multiplexing digital holography based on geometric phase. Through acquiring the geometric phase distribution of the whole light field by only recording a composite hologram, and according to quantitative relationship between the geometric phase and polarization state, the Stokes parameters of a light field can be calculated. Compared with other methods, this method can be used to obtain the complex amplitude information of the light field simultaneously without requiring other complex devices or elements to be adjusted, thus enabling dynamic polarization state measurement. The measurement results of the light fields generated by standard polarized optical elements, vortex half-wave retarder, and liquid crystal depolarizer verified this method’s feasibility and validity.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2018 (2)

T. Malhotra, R. Gutiérrez-Cuevas, J. Hassett, M. R. Dennis, A. N. Vamivakas, and M. A. Alonso, “Measuring Geometric Phase without Interferometry,” Phys. Rev. Lett. 120(23), 233602 (2018).
[Crossref] [PubMed]

T. Xi, J. Di, Y. Li, S. Dai, C. Ma, and J. Zhao, “Measurement of ultrafast combustion process of premixed ethylene/oxygen flames in narrow channel with digital holographic interferometry,” Opt. Express 26(22), 28497–28504 (2018).
[Crossref] [PubMed]

2017 (5)

2016 (5)

2015 (1)

2013 (1)

H. A. Tsai and Y. L. Lo, “Phase-based method in heterodyne-modulated ellipsometer,” Appl. Phys. B 113(4), 537–542 (2013).
[Crossref]

2011 (1)

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

2010 (1)

2008 (1)

S. Ippolito, “Polarized high-resolution imaging,” Nat. Photonics 2(5), 273–274 (2008).
[Crossref]

2007 (1)

2006 (1)

M. Yokota, Y. Terui, and I. Yamaguchi, “Analysis of polarization state by digital holography with polarization modulation,” Opt. Rev. 13(6), 405–409 (2006).
[Crossref]

2002 (2)

T. Colomb, P. Dahlgren, D. Beghuin, E. Cuche, P. Marquet, and C. Depeursinge, “Polarization imaging by use of digital holography,” Appl. Opt. 41(1), 27–37 (2002).
[Crossref] [PubMed]

U. Schnars and W.P.O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

1999 (3)

1994 (2)

1992 (1)

H. Kimura, M. Yamamoto, M. Yanagihara, T. Maehara, and T. Namioka, “Full polarization measurement of synchrotron radiation with use of soft x-ray multilayers,” Rev. Sci. Instrum. 63(1), 1379–1382 (1992).
[Crossref]

1987 (2)

G. E. Jellison, “Four-channel polarimeter for time-resolved ellipsometry,” Opt. Lett. 12(10), 766–768 (1987).
[Crossref] [PubMed]

M. V. Berry, “The Adiabatic Phase and Pancharatnam’s Phase for Polarized Light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
[Crossref]

1985 (2)

1984 (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 392(1802), 45–57 (1984).
[Crossref]

1977 (1)

1956 (1)

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Ind. Acad. Sci.A 44(5), 247–262 (1956).
[Crossref]

Alfano, R. R.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Alonso, M. A.

T. Malhotra, R. Gutiérrez-Cuevas, J. Hassett, M. R. Dennis, A. N. Vamivakas, and M. A. Alonso, “Measuring Geometric Phase without Interferometry,” Phys. Rev. Lett. 120(23), 233602 (2018).
[Crossref] [PubMed]

Azzam, R. M. A.

Bazhenov, V. Y.

Beghuin, D.

Berry, H. G.

Berry, M. V.

M. V. Berry, “The Adiabatic Phase and Pancharatnam’s Phase for Polarized Light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
[Crossref]

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. Lond. A Math. Phys. Sci. 392(1802), 45–57 (1984).
[Crossref]

Bevilacqua, F.

Buller, G. S.

Chen, M.

Chen, P.

Chen, X.

Cheng, H.

S. Liu, L. Han, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “A method for simultaneously measuring polarization and phase of arbitrarily polarized beams based on Pancharatnam-Berry phase,” Appl. Phys. Lett. 110(17), 171112 (2017).
[Crossref]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[Crossref] [PubMed]

Cheng, Z. J.

Choi, Y.

Colomb, T.

Cuche, E.

Dahlgren, P.

Dai, S.

Dennis, M. R.

T. Malhotra, R. Gutiérrez-Cuevas, J. Hassett, M. R. Dennis, A. N. Vamivakas, and M. A. Alonso, “Measuring Geometric Phase without Interferometry,” Phys. Rev. Lett. 120(23), 233602 (2018).
[Crossref] [PubMed]

Depeursinge, C.

Di, J.

Edmiston, C.

Gabrielse, G.

Garcia, M.

Ge, S.

Gerardot, B. D.

Gori, F.

Gruev, V.

Guo, C. S.

Gutiérrez-Cuevas, R.

T. Malhotra, R. Gutiérrez-Cuevas, J. Hassett, M. R. Dennis, A. N. Vamivakas, and M. A. Alonso, “Measuring Geometric Phase without Interferometry,” Phys. Rev. Lett. 120(23), 233602 (2018).
[Crossref] [PubMed]

Han, L.

Hassett, J.

T. Malhotra, R. Gutiérrez-Cuevas, J. Hassett, M. R. Dennis, A. N. Vamivakas, and M. A. Alonso, “Measuring Geometric Phase without Interferometry,” Phys. Rev. Lett. 120(23), 233602 (2018).
[Crossref] [PubMed]

Hu, W.

Ippolito, S.

S. Ippolito, “Polarized high-resolution imaging,” Nat. Photonics 2(5), 273–274 (2008).
[Crossref]

Javidi, B.

Jellison, G. E.

Jüptner, W.

Jüptner, W.P.O.

U. Schnars and W.P.O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Kang, Y. G.

Kim, B.-M.

Kimura, H.

H. Kimura, M. Yamamoto, M. Yanagihara, T. Maehara, and T. Namioka, “Full polarization measurement of synchrotron radiation with use of soft x-ray multilayers,” Rev. Sci. Instrum. 63(1), 1379–1382 (1992).
[Crossref]

Kremer, P. E.

Kulikovskaya, O. A.

Kumar, S.

Lee, K. J.

Li, E.

Li, P.

Li, Y.

Liu, S.

S. Liu, L. Han, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “A method for simultaneously measuring polarization and phase of arbitrarily polarized beams based on Pancharatnam-Berry phase,” Appl. Phys. Lett. 110(17), 171112 (2017).
[Crossref]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[Crossref] [PubMed]

Liu, X.

Livingston, A. E.

Lo, Y. L.

H. A. Tsai and Y. L. Lo, “Phase-based method in heterodyne-modulated ellipsometer,” Appl. Phys. B 113(4), 537–542 (2013).
[Crossref]

Lu, Y.

Ma, C.

Ma, Y.

Maehara, T.

H. Kimura, M. Yamamoto, M. Yanagihara, T. Maehara, and T. Namioka, “Full polarization measurement of synchrotron radiation with use of soft x-ray multilayers,” Rev. Sci. Instrum. 63(1), 1379–1382 (1992).
[Crossref]

Malhotra, T.

T. Malhotra, R. Gutiérrez-Cuevas, J. Hassett, M. R. Dennis, A. N. Vamivakas, and M. A. Alonso, “Measuring Geometric Phase without Interferometry,” Phys. Rev. Lett. 120(23), 233602 (2018).
[Crossref] [PubMed]

Marinov, R.

Marquet, P.

Milione, G.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Murata, S.

Namioka, T.

H. Kimura, M. Yamamoto, M. Yanagihara, T. Maehara, and T. Namioka, “Full polarization measurement of synchrotron radiation with use of soft x-ray multilayers,” Rev. Sci. Instrum. 63(1), 1379–1382 (1992).
[Crossref]

Nitanai, E.

Nolan, D. A.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Nomura, T.

Numata, T.

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Ind. Acad. Sci.A 44(5), 247–262 (1956).
[Crossref]

Park, K.

Ren, X.

Schnars, U.

U. Schnars and W.P.O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33(2), 179–181 (1994).
[Crossref] [PubMed]

Sun, W.

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, “Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light,” Phys. Rev. Lett. 107(5), 053601 (2011).
[Crossref] [PubMed]

Taghizadeh, M. R.

Taranenko, V. B.

Terui, Y.

M. Yokota, Y. Terui, and I. Yamaguchi, “Analysis of polarization state by digital holography with polarization modulation,” Opt. Rev. 13(6), 405–409 (2006).
[Crossref]

Tsai, H. A.

H. A. Tsai and Y. L. Lo, “Phase-based method in heterodyne-modulated ellipsometer,” Appl. Phys. B 113(4), 537–542 (2013).
[Crossref]

Vail, A.

Vamivakas, A. N.

T. Malhotra, R. Gutiérrez-Cuevas, J. Hassett, M. R. Dennis, A. N. Vamivakas, and M. A. Alonso, “Measuring Geometric Phase without Interferometry,” Phys. Rev. Lett. 120(23), 233602 (2018).
[Crossref] [PubMed]

Wang, B. Y.

Wei, B.

Wen, D.

Williams, P. A.

Xi, T.

Xie, M.

Yamaguchi, I.

M. Yokota, Y. Terui, and I. Yamaguchi, “Analysis of polarization state by digital holography with polarization modulation,” Opt. Rev. 13(6), 405–409 (2006).
[Crossref]

Yamamoto, M.

H. Kimura, M. Yamamoto, M. Yanagihara, T. Maehara, and T. Namioka, “Full polarization measurement of synchrotron radiation with use of soft x-ray multilayers,” Rev. Sci. Instrum. 63(1), 1379–1382 (1992).
[Crossref]

Yan, X.

Yanagihara, M.

H. Kimura, M. Yamamoto, M. Yanagihara, T. Maehara, and T. Namioka, “Full polarization measurement of synchrotron radiation with use of soft x-ray multilayers,” Rev. Sci. Instrum. 63(1), 1379–1382 (1992).
[Crossref]

Yang, T. D.

Yang, Y.

Yokota, M.

M. Yokota, Y. Terui, and I. Yamaguchi, “Analysis of polarization state by digital holography with polarization modulation,” Opt. Rev. 13(6), 405–409 (2006).
[Crossref]

Yue, F.

Yue, Q. Y.

Zhang, J.

Zhang, L.

Zhang, Y.

S. Liu, L. Han, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “A method for simultaneously measuring polarization and phase of arbitrarily polarized beams based on Pancharatnam-Berry phase,” Appl. Phys. Lett. 110(17), 171112 (2017).
[Crossref]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[Crossref] [PubMed]

Zhao, J.

T. Xi, J. Di, Y. Li, S. Dai, C. Ma, and J. Zhao, “Measurement of ultrafast combustion process of premixed ethylene/oxygen flames in narrow channel with digital holographic interferometry,” Opt. Express 26(22), 28497–28504 (2018).
[Crossref] [PubMed]

C. Ma, Y. Li, J. Zhang, P. Li, T. Xi, J. Di, and J. Zhao, “Lateral shearing common-path digital holographic microscopy based on a slightly trapezoid Sagnac interferometer,” Opt. Express 25(12), 13659–13667 (2017).
[Crossref] [PubMed]

S. Liu, L. Han, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “A method for simultaneously measuring polarization and phase of arbitrarily polarized beams based on Pancharatnam-Berry phase,” Appl. Phys. Lett. 110(17), 171112 (2017).
[Crossref]

J. Di, Y. Li, M. Xie, J. Zhang, C. Ma, T. Xi, E. Li, and J. Zhao, “Dual-wavelength common-path digital holographic microscopy for quantitative phase imaging based on lateral shearing interferometry,” Appl. Opt. 55(26), 7287–7293 (2016).
[Crossref] [PubMed]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[Crossref] [PubMed]

J. Zhang, C. Ma, S. Dai, J. Di, Y. Li, T. Xi, and J. Zhao, “Transmission and total internal reflection integrated digital holographic microscopy,” Opt. Lett. 41(16), 3844–3847 (2016).
[Crossref] [PubMed]

J. Zhao, X. Yan, W. Sun, and J. Di, “Resolution improvement of digital holographic images based on angular multiplexing with incoherent beams in orthogonal polarization states,” Opt. Lett. 35(20), 3519–3521 (2010).
[Crossref] [PubMed]

Appl. Opt. (5)

Appl. Phys. B (1)

H. A. Tsai and Y. L. Lo, “Phase-based method in heterodyne-modulated ellipsometer,” Appl. Phys. B 113(4), 537–542 (2013).
[Crossref]

Appl. Phys. Lett. (1)

S. Liu, L. Han, P. Li, Y. Zhang, H. Cheng, and J. Zhao, “A method for simultaneously measuring polarization and phase of arbitrarily polarized beams based on Pancharatnam-Berry phase,” Appl. Phys. Lett. 110(17), 171112 (2017).
[Crossref]

J. Mod. Opt. (1)

M. V. Berry, “The Adiabatic Phase and Pancharatnam’s Phase for Polarized Light,” J. Mod. Opt. 34(11), 1401–1407 (1987).
[Crossref]

Meas. Sci. Technol. (1)

U. Schnars and W.P.O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–R101 (2002).
[Crossref]

Nat. Photonics (1)

S. Ippolito, “Polarized high-resolution imaging,” Nat. Photonics 2(5), 273–274 (2008).
[Crossref]

Opt. Express (6)

Opt. Lett. (10)

J. Zhao, X. Yan, W. Sun, and J. Di, “Resolution improvement of digital holographic images based on angular multiplexing with incoherent beams in orthogonal polarization states,” Opt. Lett. 35(20), 3519–3521 (2010).
[Crossref] [PubMed]

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24(5), 291–293 (1999).
[Crossref] [PubMed]

J. Zhang, C. Ma, S. Dai, J. Di, Y. Li, T. Xi, and J. Zhao, “Transmission and total internal reflection integrated digital holographic microscopy,” Opt. Lett. 41(16), 3844–3847 (2016).
[Crossref] [PubMed]

R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10(7), 309–311 (1985).
[Crossref] [PubMed]

G. E. Jellison, “Four-channel polarimeter for time-resolved ellipsometry,” Opt. Lett. 12(10), 766–768 (1987).
[Crossref] [PubMed]

F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. 24(9), 584–586 (1999).
[Crossref] [PubMed]

R. M. A. Azzam, “Rotating-detector ellipsometer for measurement of the state of polarization of light,” Opt. Lett. 10(9), 427–429 (1985).
[Crossref] [PubMed]

P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, and J. Zhao, “Generation of perfect vectorial vortex beams,” Opt. Lett. 41(10), 2205–2208 (2016).
[Crossref] [PubMed]

V. Y. Bazhenov, O. A. Kulikovskaya, and V. B. Taranenko, “Nonlinear coherent polarimetry for measuring the complex nonlinear index,” Opt. Lett. 19(6), 381–383 (1994).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 Schematic of the proposed PAMDH system based on geometric phase. BE: beam expander; L: lens; P: polarizer; S: sample; HWP: half-wave plate; NPBS1-NPBS2: non-polarized beam splitters; PBS1-PBS2: polarized beam splitters; M1-M3: mirrors; NDF: neutral density filter; MO: microscope objective; TL: tube lens.
Fig. 2
Fig. 2 Theoretical model for measuring polarization state based on geometric phase
Fig. 3
Fig. 3 (a) Composite hologram recorded by PAMDH system and the details of hologram. (b) Spatial spectra of the hologram.
Fig. 4
Fig. 4 Measurement results of Stokes parameters. (a) Comparison of measured and theoretical value; (b) positions on the Poincare’s sphere of the measured polarization states; (c) result of 30 measurements corresponding to a linear polarization beam with θ = π/6.
Fig. 5
Fig. 5 (a) Setup for generating elliptically polarized light; (b) Positions on the Poincare’s sphere of the measured polarization states; (c) Comparison of measured and theoretical values.
Fig. 6
Fig. 6 (a) Measurement results of Stokes parameters for the first order radial vector beam. (b) The elliptical polarization distribution calculated by Stokes parameters.
Fig. 7
Fig. 7 Measurement results of Stokes parameters for the LC depolarizer. (a) Micrograph of the LC depolarizer; (b) dynamic phase distribution of the LC depolarizer; (c1) Stokes parameters distribution of linear incident polarized beam with θ = π/4; (c2) Stokes parameters distribution of left-handed circularly polarized incident beam.

Tables (1)

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Table 1 Measurement results of linear polarization beam with θ = π/6

Equations (14)

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I = | E O + E R H + E R V | 2 = | E O H | 2 + | E O V | 2 + | E R H | 2 + | E R V | 2 + E O H E R H * + E O V E R V * + E O H * E R H + E O V * E R V = I H + I V ,
I H = | E O H | 2 + | E R H | 2 + 2 | E O H | | E R H | cos φ H ,
I V = | E O V | 2 + | E R V | 2 + 2 | E O V | | E R V | cos φ V .
I O H = | E O H | 2 = I O cos 2 ( O H / 2 ) ,
I O V = | E O V | 2 = I O sin 2 ( O H / 2 ) .
2 χ 1 = π / 2 O H = π / 2 2 arc tan | E O V | / | E O H | .
φ H = φ H d + φ H p b ,
φ V = φ V d + φ V p b .
2 ψ 1 = ( φ H φ V ) ( φ H d φ V d ) .
E H = β | E O H | | E R H | exp ( i φ H ) ,
E V = β | E O V | | E R V | exp ( i φ V ) .
2 ψ 1 = arg ( E H / E V ) Δ φ ,
2 χ 1 = π / 2 2 arc tan | E V | / | E H | .
{ S 1 = sin 2 χ 1 S 2 = cos 2 χ 1 cos 2 ψ 1 S 3 = cos 2 χ 1 sin 2 ψ 1 .

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