Abstract

A new polarimeter is presented which gives time-resolved measurements of both the optic-axis angle and the linear phase retardation for modulated birefringent optical devices. It is suitable for characterizing dynamic waveplate devices based on liquid crystal and other materials. It is fully automated and requires no angular alignment of the device under test. The system has an absolute angle error of < ± 0.3° and a retardance error of < ± 0.44°, with considerably better relative accuracy. The method has been tested with a chiral nematic liquid crystal device exhibiting flexoelectro-optic switching at 3 kHz in the uniform lying helix mode. These results represent the first time-resolved tilt-angle and phase retardation measurements for a liquid crystal device operating at fast switching frequencies.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Full Article  |  PDF Article
OSA Recommended Articles
Flexoelectro-optic liquid crystal analog phase-only modulator with a 2π range and 1  kHz switching

Julian A. J. Fells, Xiuze Wang, Steve J. Elston, Chris Welch, Georg H. Mehl, Martin J. Booth, and Stephen M. Morris
Opt. Lett. 43(18) 4362-4365 (2018)

High speed liquid crystal over silicon display based on the flexoelectro-optic effect

Jing Chen, Stephen M. Morris, Timothy D. Wilkinson, Jon P. Freeman, and Harry J. Coles
Opt. Express 17(9) 7130-7137 (2009)

Full-field characterization of a twisted nematic liquid-crystal device using equivalence theorem of a unitary optical system

Chih-Jen Yu, Yao-Teng Tseng, Kuei-Chu Hsu, and Chien Chou
Appl. Opt. 51(2) 238-244 (2012)

References

  • View by:
  • |
  • |
  • |

  1. P. Rudquist, L. Komitov, and S. T. Lagerwall, “Volume-stabilized ULH structure for the flexoelectro-optic effect and the phase-shift effect in cholesterics,” Liq. Cryst. 24(3), 329–334 (1998).
    [Crossref]
  2. T. J. Gould, D. Burke, J. Bewersdorf, and M. J. Booth, “Adaptive optics enables 3D STED microscopy in aberrating specimens,” Opt. Express 20(19), 20998–21009 (2012).
    [Crossref] [PubMed]
  3. A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express 18(20), 21090–21099 (2010).
    [Crossref] [PubMed]
  4. J. Chen, S. M. Morris, T. D. Wilkinson, J. P. Freeman, and H. J. Coles, “High speed liquid crystal over silicon display based on the flexoelectro-optic effect,” Opt. Express 17(9), 7130–7137 (2009).
    [Crossref] [PubMed]
  5. J. S. Patel and R. B. Meyer, “Flexoelectric electro-optics of a cholesteric liquid crystal,” Phys. Rev. Lett. 58(15), 1538–1540 (1987).
    [Crossref] [PubMed]
  6. R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2(6), 148–150 (1978).
    [Crossref] [PubMed]
  7. S. R. M. Robertson, “Measuring birefringence properties using a wave plate and an analyzer,” Appl. Opt. 22(14), 2213–2216 (1983).
    [Crossref] [PubMed]
  8. P. A. Williams, A. H. Rose, and C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36(25), 6466–6472 (1997).
    [Crossref] [PubMed]
  9. K.-C. Lim and J. T. Ho, “Apparatus for high-resolution birefringence measurement in liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 47(3–4), 173–177 (1978).
    [Crossref]
  10. I. G. Wood and A. M. Glazer, “Ferroelastic phase transition in BiVO4. I. Birefringence measurements using the rotating-analyser method,” J. Appl. Cryst. 13(3), 217–223 (1980).
    [Crossref]
  11. J. Etxebarria, A. Remón, M. J. Tello, T. A. Ezcurra, M. A. Pérez-Jubindo, and T. Sierra, “A new method for high accuracy tilt angle measurements in ferroelectric liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 150(1), 257–263 (1987).
  12. C. Noot, S. P. Perkins, and H. J. Coles, “Tilt angle measurement of low molar mass organosiloxane liquid crystals,” Ferroelectrics 244(1), 331–338 (2000).
    [Crossref]
  13. G. Baur, V. Wittwer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56A(2), 142–144 (1976).
    [Crossref]
  14. S.-T. Wu, U. Efron, and L. D. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt. 23(21), 3911–3915 (1984).
    [Crossref] [PubMed]
  15. P. Rudquist, M. Buivydas, L. Komitov, and S. T. Lagerwall, “Linear electro-optic effect based on flexoelectricity in a cholesteric with sign change of dielectric anisotropy,” J. Appl. Phys. 76(12), 7778–7783 (1994).
    [Crossref]
  16. R. C. Jones, “A new calculus for the treatment of optical systems I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31(7), 488–493 (1941).
    [Crossref]
  17. J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttg.) 76(2), 67–71 (1987).
  18. Specifications, “WPQ05M-546 - Ø1/2” Mounted Zero-Order, Quarter-Wave Plate, 546 nm,” (Thorlabs Inc.) https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=7234
  19. S. J. Elston, “Flexoelectricity in nematic domain walls,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 011701 (2008).
    [Crossref] [PubMed]
  20. A. Varanytsia and L.-C. Chien, “Giant flexoelectro-optic effect with liquid crystal dimer CB7CB,” Sci. Rep. 7, 41333 (2017).
    [Crossref] [PubMed]
  21. J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
    [Crossref]
  22. B. I. Outram and S. J. Elston, “Determination of flexoelectric coefficients in nematic liquid crystals using the crystal rotation method,” Liq. Cryst. 39(2), 149–156 (2012).
    [Crossref]
  23. B. I. Outram and S. J. Elston, “Flexoelectric and dielectric in-plane switching behaviour of Grandjean liquid-crystal structures,” EPL 99(3), 37007 (2012).
    [Crossref]
  24. H. Chen, R. Zhu, J. Zhu, and S.-T. Wu, “A simple method to measure the twist elastic constant of a nematic liquid crystal,” Liq. Cryst. 42(12), 1738–1742 (2015).
    [Crossref]

2017 (1)

A. Varanytsia and L.-C. Chien, “Giant flexoelectro-optic effect with liquid crystal dimer CB7CB,” Sci. Rep. 7, 41333 (2017).
[Crossref] [PubMed]

2015 (1)

H. Chen, R. Zhu, J. Zhu, and S.-T. Wu, “A simple method to measure the twist elastic constant of a nematic liquid crystal,” Liq. Cryst. 42(12), 1738–1742 (2015).
[Crossref]

2012 (3)

B. I. Outram and S. J. Elston, “Determination of flexoelectric coefficients in nematic liquid crystals using the crystal rotation method,” Liq. Cryst. 39(2), 149–156 (2012).
[Crossref]

B. I. Outram and S. J. Elston, “Flexoelectric and dielectric in-plane switching behaviour of Grandjean liquid-crystal structures,” EPL 99(3), 37007 (2012).
[Crossref]

T. J. Gould, D. Burke, J. Bewersdorf, and M. J. Booth, “Adaptive optics enables 3D STED microscopy in aberrating specimens,” Opt. Express 20(19), 20998–21009 (2012).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2008 (1)

S. J. Elston, “Flexoelectricity in nematic domain walls,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 011701 (2008).
[Crossref] [PubMed]

2005 (1)

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

2000 (1)

C. Noot, S. P. Perkins, and H. J. Coles, “Tilt angle measurement of low molar mass organosiloxane liquid crystals,” Ferroelectrics 244(1), 331–338 (2000).
[Crossref]

1998 (1)

P. Rudquist, L. Komitov, and S. T. Lagerwall, “Volume-stabilized ULH structure for the flexoelectro-optic effect and the phase-shift effect in cholesterics,” Liq. Cryst. 24(3), 329–334 (1998).
[Crossref]

1997 (1)

1994 (1)

P. Rudquist, M. Buivydas, L. Komitov, and S. T. Lagerwall, “Linear electro-optic effect based on flexoelectricity in a cholesteric with sign change of dielectric anisotropy,” J. Appl. Phys. 76(12), 7778–7783 (1994).
[Crossref]

1987 (3)

J. S. Patel and R. B. Meyer, “Flexoelectric electro-optics of a cholesteric liquid crystal,” Phys. Rev. Lett. 58(15), 1538–1540 (1987).
[Crossref] [PubMed]

J. Etxebarria, A. Remón, M. J. Tello, T. A. Ezcurra, M. A. Pérez-Jubindo, and T. Sierra, “A new method for high accuracy tilt angle measurements in ferroelectric liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 150(1), 257–263 (1987).

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttg.) 76(2), 67–71 (1987).

1984 (1)

1983 (1)

1980 (1)

I. G. Wood and A. M. Glazer, “Ferroelastic phase transition in BiVO4. I. Birefringence measurements using the rotating-analyser method,” J. Appl. Cryst. 13(3), 217–223 (1980).
[Crossref]

1978 (2)

K.-C. Lim and J. T. Ho, “Apparatus for high-resolution birefringence measurement in liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 47(3–4), 173–177 (1978).
[Crossref]

R. M. A. Azzam, “Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal,” Opt. Lett. 2(6), 148–150 (1978).
[Crossref] [PubMed]

1976 (1)

G. Baur, V. Wittwer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56A(2), 142–144 (1976).
[Crossref]

1941 (1)

Azzam, R. M. A.

Baur, G.

G. Baur, V. Wittwer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56A(2), 142–144 (1976).
[Crossref]

Bernabeu, E.

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttg.) 76(2), 67–71 (1987).

Berreman, D. W.

G. Baur, V. Wittwer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56A(2), 142–144 (1976).
[Crossref]

Bewersdorf, J.

Booth, M. J.

Buivydas, M.

P. Rudquist, M. Buivydas, L. Komitov, and S. T. Lagerwall, “Linear electro-optic effect based on flexoelectricity in a cholesteric with sign change of dielectric anisotropy,” J. Appl. Phys. 76(12), 7778–7783 (1994).
[Crossref]

Burke, D.

Chen, H.

H. Chen, R. Zhu, J. Zhu, and S.-T. Wu, “A simple method to measure the twist elastic constant of a nematic liquid crystal,” Liq. Cryst. 42(12), 1738–1742 (2015).
[Crossref]

Chen, J.

Chien, L.-C.

A. Varanytsia and L.-C. Chien, “Giant flexoelectro-optic effect with liquid crystal dimer CB7CB,” Sci. Rep. 7, 41333 (2017).
[Crossref] [PubMed]

Coles, H. J.

J. Chen, S. M. Morris, T. D. Wilkinson, J. P. Freeman, and H. J. Coles, “High speed liquid crystal over silicon display based on the flexoelectro-optic effect,” Opt. Express 17(9), 7130–7137 (2009).
[Crossref] [PubMed]

C. Noot, S. P. Perkins, and H. J. Coles, “Tilt angle measurement of low molar mass organosiloxane liquid crystals,” Ferroelectrics 244(1), 331–338 (2000).
[Crossref]

Efron, U.

Elston, S. J.

B. I. Outram and S. J. Elston, “Determination of flexoelectric coefficients in nematic liquid crystals using the crystal rotation method,” Liq. Cryst. 39(2), 149–156 (2012).
[Crossref]

B. I. Outram and S. J. Elston, “Flexoelectric and dielectric in-plane switching behaviour of Grandjean liquid-crystal structures,” EPL 99(3), 37007 (2012).
[Crossref]

S. J. Elston, “Flexoelectricity in nematic domain walls,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 011701 (2008).
[Crossref] [PubMed]

Etxebarria, J.

J. Etxebarria, A. Remón, M. J. Tello, T. A. Ezcurra, M. A. Pérez-Jubindo, and T. Sierra, “A new method for high accuracy tilt angle measurements in ferroelectric liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 150(1), 257–263 (1987).

Ezcurra, T. A.

J. Etxebarria, A. Remón, M. J. Tello, T. A. Ezcurra, M. A. Pérez-Jubindo, and T. Sierra, “A new method for high accuracy tilt angle measurements in ferroelectric liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 150(1), 257–263 (1987).

Freeman, J. P.

Gauza, S.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Gil, J. J.

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttg.) 76(2), 67–71 (1987).

Glazer, A. M.

I. G. Wood and A. M. Glazer, “Ferroelastic phase transition in BiVO4. I. Birefringence measurements using the rotating-analyser method,” J. Appl. Cryst. 13(3), 217–223 (1980).
[Crossref]

Gould, T. J.

Hess, L. D.

Ho, J. T.

K.-C. Lim and J. T. Ho, “Apparatus for high-resolution birefringence measurement in liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 47(3–4), 173–177 (1978).
[Crossref]

Jesacher, A.

Jones, R. C.

Komitov, L.

P. Rudquist, L. Komitov, and S. T. Lagerwall, “Volume-stabilized ULH structure for the flexoelectro-optic effect and the phase-shift effect in cholesterics,” Liq. Cryst. 24(3), 329–334 (1998).
[Crossref]

P. Rudquist, M. Buivydas, L. Komitov, and S. T. Lagerwall, “Linear electro-optic effect based on flexoelectricity in a cholesteric with sign change of dielectric anisotropy,” J. Appl. Phys. 76(12), 7778–7783 (1994).
[Crossref]

Lagerwall, S. T.

P. Rudquist, L. Komitov, and S. T. Lagerwall, “Volume-stabilized ULH structure for the flexoelectro-optic effect and the phase-shift effect in cholesterics,” Liq. Cryst. 24(3), 329–334 (1998).
[Crossref]

P. Rudquist, M. Buivydas, L. Komitov, and S. T. Lagerwall, “Linear electro-optic effect based on flexoelectricity in a cholesteric with sign change of dielectric anisotropy,” J. Appl. Phys. 76(12), 7778–7783 (1994).
[Crossref]

Li, J.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Lim, K.-C.

K.-C. Lim and J. T. Ho, “Apparatus for high-resolution birefringence measurement in liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 47(3–4), 173–177 (1978).
[Crossref]

Lu, R.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Meyer, R. B.

J. S. Patel and R. B. Meyer, “Flexoelectric electro-optics of a cholesteric liquid crystal,” Phys. Rev. Lett. 58(15), 1538–1540 (1987).
[Crossref] [PubMed]

Morris, S. M.

Noot, C.

C. Noot, S. P. Perkins, and H. J. Coles, “Tilt angle measurement of low molar mass organosiloxane liquid crystals,” Ferroelectrics 244(1), 331–338 (2000).
[Crossref]

Outram, B. I.

B. I. Outram and S. J. Elston, “Flexoelectric and dielectric in-plane switching behaviour of Grandjean liquid-crystal structures,” EPL 99(3), 37007 (2012).
[Crossref]

B. I. Outram and S. J. Elston, “Determination of flexoelectric coefficients in nematic liquid crystals using the crystal rotation method,” Liq. Cryst. 39(2), 149–156 (2012).
[Crossref]

Patel, J. S.

J. S. Patel and R. B. Meyer, “Flexoelectric electro-optics of a cholesteric liquid crystal,” Phys. Rev. Lett. 58(15), 1538–1540 (1987).
[Crossref] [PubMed]

Pérez-Jubindo, M. A.

J. Etxebarria, A. Remón, M. J. Tello, T. A. Ezcurra, M. A. Pérez-Jubindo, and T. Sierra, “A new method for high accuracy tilt angle measurements in ferroelectric liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 150(1), 257–263 (1987).

Perkins, S. P.

C. Noot, S. P. Perkins, and H. J. Coles, “Tilt angle measurement of low molar mass organosiloxane liquid crystals,” Ferroelectrics 244(1), 331–338 (2000).
[Crossref]

Remón, A.

J. Etxebarria, A. Remón, M. J. Tello, T. A. Ezcurra, M. A. Pérez-Jubindo, and T. Sierra, “A new method for high accuracy tilt angle measurements in ferroelectric liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 150(1), 257–263 (1987).

Robertson, S. R. M.

Rose, A. H.

Rudquist, P.

P. Rudquist, L. Komitov, and S. T. Lagerwall, “Volume-stabilized ULH structure for the flexoelectro-optic effect and the phase-shift effect in cholesterics,” Liq. Cryst. 24(3), 329–334 (1998).
[Crossref]

P. Rudquist, M. Buivydas, L. Komitov, and S. T. Lagerwall, “Linear electro-optic effect based on flexoelectricity in a cholesteric with sign change of dielectric anisotropy,” J. Appl. Phys. 76(12), 7778–7783 (1994).
[Crossref]

Sierra, T.

J. Etxebarria, A. Remón, M. J. Tello, T. A. Ezcurra, M. A. Pérez-Jubindo, and T. Sierra, “A new method for high accuracy tilt angle measurements in ferroelectric liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 150(1), 257–263 (1987).

Tello, M. J.

J. Etxebarria, A. Remón, M. J. Tello, T. A. Ezcurra, M. A. Pérez-Jubindo, and T. Sierra, “A new method for high accuracy tilt angle measurements in ferroelectric liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 150(1), 257–263 (1987).

Varanytsia, A.

A. Varanytsia and L.-C. Chien, “Giant flexoelectro-optic effect with liquid crystal dimer CB7CB,” Sci. Rep. 7, 41333 (2017).
[Crossref] [PubMed]

Wang, C. M.

Wen, C.-H.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Wilkinson, T. D.

Williams, P. A.

Wittwer, V.

G. Baur, V. Wittwer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56A(2), 142–144 (1976).
[Crossref]

Wood, I. G.

I. G. Wood and A. M. Glazer, “Ferroelastic phase transition in BiVO4. I. Birefringence measurements using the rotating-analyser method,” J. Appl. Cryst. 13(3), 217–223 (1980).
[Crossref]

Wu, S.-T.

H. Chen, R. Zhu, J. Zhu, and S.-T. Wu, “A simple method to measure the twist elastic constant of a nematic liquid crystal,” Liq. Cryst. 42(12), 1738–1742 (2015).
[Crossref]

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

S.-T. Wu, U. Efron, and L. D. Hess, “Birefringence measurements of liquid crystals,” Appl. Opt. 23(21), 3911–3915 (1984).
[Crossref] [PubMed]

Zhu, J.

H. Chen, R. Zhu, J. Zhu, and S.-T. Wu, “A simple method to measure the twist elastic constant of a nematic liquid crystal,” Liq. Cryst. 42(12), 1738–1742 (2015).
[Crossref]

Zhu, R.

H. Chen, R. Zhu, J. Zhu, and S.-T. Wu, “A simple method to measure the twist elastic constant of a nematic liquid crystal,” Liq. Cryst. 42(12), 1738–1742 (2015).
[Crossref]

Appl. Opt. (3)

EPL (1)

B. I. Outram and S. J. Elston, “Flexoelectric and dielectric in-plane switching behaviour of Grandjean liquid-crystal structures,” EPL 99(3), 37007 (2012).
[Crossref]

Ferroelectrics (1)

C. Noot, S. P. Perkins, and H. J. Coles, “Tilt angle measurement of low molar mass organosiloxane liquid crystals,” Ferroelectrics 244(1), 331–338 (2000).
[Crossref]

J. Appl. Cryst. (1)

I. G. Wood and A. M. Glazer, “Ferroelastic phase transition in BiVO4. I. Birefringence measurements using the rotating-analyser method,” J. Appl. Cryst. 13(3), 217–223 (1980).
[Crossref]

J. Appl. Phys. (1)

P. Rudquist, M. Buivydas, L. Komitov, and S. T. Lagerwall, “Linear electro-optic effect based on flexoelectricity in a cholesteric with sign change of dielectric anisotropy,” J. Appl. Phys. 76(12), 7778–7783 (1994).
[Crossref]

J. Disp. Technol. (1)

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive indices of liquid crystals for display applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

J. Opt. Soc. Am. (1)

Liq. Cryst. (3)

P. Rudquist, L. Komitov, and S. T. Lagerwall, “Volume-stabilized ULH structure for the flexoelectro-optic effect and the phase-shift effect in cholesterics,” Liq. Cryst. 24(3), 329–334 (1998).
[Crossref]

B. I. Outram and S. J. Elston, “Determination of flexoelectric coefficients in nematic liquid crystals using the crystal rotation method,” Liq. Cryst. 39(2), 149–156 (2012).
[Crossref]

H. Chen, R. Zhu, J. Zhu, and S.-T. Wu, “A simple method to measure the twist elastic constant of a nematic liquid crystal,” Liq. Cryst. 42(12), 1738–1742 (2015).
[Crossref]

Mol. Cryst. Liq. Cryst. (Phila. Pa.) (2)

J. Etxebarria, A. Remón, M. J. Tello, T. A. Ezcurra, M. A. Pérez-Jubindo, and T. Sierra, “A new method for high accuracy tilt angle measurements in ferroelectric liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 150(1), 257–263 (1987).

K.-C. Lim and J. T. Ho, “Apparatus for high-resolution birefringence measurement in liquid crystals,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 47(3–4), 173–177 (1978).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Optik (Stuttg.) (1)

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,” Optik (Stuttg.) 76(2), 67–71 (1987).

Phys. Lett. (1)

G. Baur, V. Wittwer, and D. W. Berreman, “Determination of the tilt angles at surfaces of substrates in liquid crystal cells,” Phys. Lett. 56A(2), 142–144 (1976).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

S. J. Elston, “Flexoelectricity in nematic domain walls,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(1), 011701 (2008).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

J. S. Patel and R. B. Meyer, “Flexoelectric electro-optics of a cholesteric liquid crystal,” Phys. Rev. Lett. 58(15), 1538–1540 (1987).
[Crossref] [PubMed]

Sci. Rep. (1)

A. Varanytsia and L.-C. Chien, “Giant flexoelectro-optic effect with liquid crystal dimer CB7CB,” Sci. Rep. 7, 41333 (2017).
[Crossref] [PubMed]

Other (1)

Specifications, “WPQ05M-546 - Ø1/2” Mounted Zero-Order, Quarter-Wave Plate, 546 nm,” (Thorlabs Inc.) https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=7234

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 Diagrammatic representation of the measurement system; L:Laser, P1: input polarizer, QWP: quarter-wave plate (on a motorized rotation mount), DUT: device under test, AFG: arbitrary function generator, P2 output polarizer (on a motorized rotation mount), PD: photodetector.
Fig. 2
Fig. 2 Simulated measurement error for (a) angle of the optic-axis and (b) retardance; (− − blue) LCP input, (−∙−∙ red) RCP input, (— black) combined LCP/RCP inputs; (i) DUT 0.4284λ, QWP error λ/400; (ii) DUT 0.4284λ, QWP error λ/400, QWP angle error 0.4°; (iii) DUT 0.4284 λ, QWP error λ/400, QWP angle error 0.4° and 0.07° error switching from LCP to RCP; (iv) DUT 0.49 λ, QWP error λ/500.
Fig. 3
Fig. 3 Photo-detector voltage versus analyzer angle, θ, for test wave plate angles of φ = 0-40° in 10° increments; (− − blue) LCP input, (−∙−∙ red) RCP input.
Fig. 4
Fig. 4 Experimental calibration results using test wave plate on a motorized rotation mount; (a) error in measured angle from actual angle; (b) error in retardance (from nominal value of 154.217°); (− − blue) LCP input, (−∙−∙ red) RCP input, (— black) combined LCP/RCP inputs, (∙∙∙∙∙∙ black) limits of manufacturer’s retardance tolerance specification.
Fig. 5
Fig. 5 The chiral nematic LC device used to validate the measurement system; (a) illustration of the ULH mode, (b) illustration of the flexoelectro-optic effect, (c) polarizing optical microscope images for sample with mean optic-axis at 22.5° to the axis of one of the polarizers, under an applied 1 kHz square-wave: (i) ± 5 V, (ii) ± 10 V, (iii) ± 15 V, (iv) ± 20 V. The device consists of 3.5 wt% chiral dopant (R5011) in the nematic host E7. The thickness of the device was 4.82 µm and measurements were taken at 25°C. The discontinuities in the structure are due to the presence of spacer beads.
Fig. 6
Fig. 6 Experimental time-resolved measurement data for a dynamically switched flexoelectro-optic LC device. (a) input voltage waveform; (b) tilt-angle, (c) linear birefringence; (d) loss change. The chiral nematic LC device consists of 3.5 wt% chiral dopant (R5011) in the nematic host E7. The thickness of the device was 4.82 μm and measurements were taken at 25°C.
Fig. 7
Fig. 7 Experimentally measured tilt-angle as a function of time for applied voltages from 0– ± 10 V in ± 1 V increments at a temperature of 25°C and an applied frequency of 3 kHz.
Fig. 8
Fig. 8 Plot of tan(φt) as a function of the electric field amplitude applied to the sample; ( × blue) data using the new time-resolved method; (○ red) data acquired using the microscope technique.
Fig. 9
Fig. 9 Change in the linear birefringence with electric field applied to the flexoelectro-optic LC device. (○ blue) data using the new time-resolved method, (— red) theoretical curve from Eq. (19).

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

S( θ,t )= 1 2 S 0 [ 1+sin( δ( t ) )sin( 2θ2φ( t ) ) ]
I( nT )= 1 M m=0 M1 sin( 2 θ m )S( θ m ,nT )
Q( nT )= 1 M m=0 M1 cos( 2 θ m )S( θ m ,nT )
φ M ( nT )= 1 2 tan 1 ( Q( nT ) I( nT ) )
δ M ( nT )= sin 1 ( 2 [ Q ( nT ) 2 +I ( nT ) 2 ] 1/2 S( nT ) ¯ )
S( nT ) ¯ = 1 M m=0 M1 S( θ m ,nT )
S L ( θ,t )= S 0 | P( θ ) W D ( δ( t ),φ( t ) ) W Q ( π/2 +є,π/4 + ζ L ) E H | 2
S R ( θ,t )= S 0 | P( θ ) W D ( δ( t ),φ( t ) ) W Q ( π/2 +є,π/4 + ζ R ) E H | 2
W D,Q ( γ,β )=[ cos( γ/2 )+jcos2βsin( γ/2 ) jsin2βsin( γ/2 ) jsin2βsin( γ/2 ) cos( γ/2 )jcos2βsin( γ/2 ) ] 
S L ( θ,t )= 1 2 S 0 [ 1+sin( δ( t ) )sin( 2θ2φ( t ) )+є R 1 ( θ,t )+ ζ L R 2 ( θ,t ) ]
S R ( θ,t )= 1 2 S 0 [ 1sin( δ( t ) )sin( 2θ2φ( t ) )+є R 1 ( θ,t )+ ζ R R 2 ( θ,t ) ]
R 1 ( θ,t )=sin( 2θ2φ( t ) )sin2φ( t )cosδ( t )cos( 2θ2φ( t ) )cos2φ( t )
R 2 ( θ,t )=2cos( 2θ2φ( t ) )[ sin( 2φ( t ) )cos( δ( t ) )+sin( δ( t ) ) ] +2sin( 2θ2φ( t ) )+2cos( 2φ( t ) )sin( δ( t ) )
φ 45,e,max =±| є 2sin δ n |
I( nT )= 1 2M m=0 M1 sin( 2 θ m )[ S L ( θ m ,nT ) S R ( θ m ,nT ) ]
Q( nT )= 1 2M m=0 M1 cos( 2 θ m )[ S L ( θ m ,nT ) S R ( θ m ,nT ) ]
S( nT ) ¯ = 1 2M m=0 M1 [ S L ( θ m ,nT )+ S R ( θ m ,nT ) ]
tan( φ t )= e 1 e 3 K 11 + K 33 p 2π E A
Δ n u = ( n e 2 + n o 2 2 ) 1/2 [ 1 Δε ε 0 p 2 32 K 22 π 2 ( n e 2 n o 2 n e 2 + n o 2 ) E A 2 ] 1/2 n o
S M ( θ,t )= 1 2 S 0 | P( θ )[ W D ( δ( t ), φ ¯ ( t )+ 1 2 Δφ ) E LC + W D ( δ( t ), φ ¯ ( t ) 1 2 Δφ ) E LC ]  | 2
S M ( θ,t )= 1 2 S 0 [ 1+sin( δ( t ) )sin( 2θ2 φ ¯ ( t ) )cosΔφ sin 2 ( δ(t)/2 ) sin 2 Δφ ]

Metrics