Abstract

A rigorous analysis is presented of the diffraction efficiency of a polarization-insensitive surface-stabilized ferroelectric liquid-crystal (SSFLC) phase grating, taking full account of the internal structure of the ferroelectric liquid-crystal layer. When no field is applied, the twisted director profile in the relaxed state gives an optimum diffraction efficiency for a device thickness between the half-wave-plate and the full-wave-plate conditions. The influence of the magnitude of the spontaneous polarization and applied ac fields are investigated, and it is shown that the diffraction efficiency of a binary SSFLC phase grating can be strongly enhanced with the technique of ac stabilization.

© 2003 Optical Society of America

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  1. R. M. Turner, D. A. Jared, G. D. Sharp, K. M. Johnson, “Optical correlator using very-large-scale integrated circuit/ferroelectric-liquid-crystal electrically addressed spatial light modulators,” Appl. Opt. 32,3094–3101 (1993).
    [CrossRef] [PubMed]
  2. T. D. Wilkinson, Y. Petillot, R. J. Mears, J. L. de Bougrenet de la Tocnaye, “Scale-invariant optical correlators using ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 34,1885–1890 (1995).
    [CrossRef] [PubMed]
  3. S. E. Broomfield, M. A. Neil, E. G. Paige, “Programmable multiple-level phase modulation that uses ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 34,6652–6665 (1995).
    [CrossRef] [PubMed]
  4. R. J. Mears, W. A. Crossland, M. P. Dames, J. R. Collington, M. C. Parker, S. T. Warr, T. D. Wilkinson, A. B. Davey, “Telecommunications applications of ferroelectric liquid-crystal smart pixels,” IEEE J. Sel. Top. Quantum Electron. 2,35–46 (1996).
    [CrossRef]
  5. W. A. Crossland, I. G. Manolis, M. M. Redmond, K. L. Tan, T. D. Wilkinson, M. J. Holmes, T. R. Parker, H. H. Chu, J. Croucher, V. A. Handerek, S. T. Warr, B. Robertson, I. G. Bonas, R. Franklin, C. Stace, H. J. White, R. A. Woolley, G. Henshal, “Holographic switching: the ROSES demonstrator,” J. Lightwave Technol. 18,1845–1854 (2000).
    [CrossRef]
  6. C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
    [CrossRef]
  7. S. Warr, R. Mears, “Polarization-insensitive operation of ferroelectric liquid crystal devices,” Electron. Lett. 31,714–716 (1995).
    [CrossRef]
  8. S. Warr, R. Mears, “Polarisation insensitive diffractive FLC systems,” Ferroelectrics 181,53–59 (1996).
    [CrossRef]
  9. S. E. Broomfield, M. A. Neil, E. G. Paige, G. G. Yang, “Programmable binary phase-only device based on ferroelectric liquid crystal SLM,” Electron. Lett. 28,26–28 (1992).
    [CrossRef]
  10. J. S. Patel, J. W. Goodby, “Alignment of liquid crystals which exhibit cholesteric to smectic* phase transitions,” J. Appl. Phys. 59, 2355–2360 (1986).
    [CrossRef]
  11. CS2005 is the trade name for a commercial high-tilt ferroelectric LC material available from Lixon Department, CHISSO Corporation, Chuo-ku, Tokyo, Japan.
  12. J. Newton, H. Coles, P. Hodge, J. Hannington, “Synthesis and properties of low-molar-mass liquid-crystalline siloxane derivatives,” J. Mater. Chem. 4,869–874 (1994).
    [CrossRef]
  13. N. A. Clark, S. T. Lagerwall, “Sub-millisecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36,899–901 (1980).
    [CrossRef]
  14. D. C. O’Brien, R. J. Mears, T. D. Wilkinson, W. A. Cross-land, “Dynamic holographic interconnects that use ferroelectric spatial light modulators,” Appl. Opt. 33,2795–2803 (1994).
    [CrossRef]
  15. J. C. Jones, M. J. Towler, J. R. Hughes, “Fast, high contrast ferroelectric liquid crystal displays and the role of dielectric biaxiality,” Displays 14,86–93 (1993).
    [CrossRef]
  16. N. A. Clark, T. P. Reiker, “Smectic C chevron, a planar liquid-crystal defect—implications for the surface stabilized ferroelectric liquid crystal geometry,” Phys. Rev. A 37, 1053–1056 (1988).
    [CrossRef] [PubMed]
  17. M. H. Anderson, J. C. Jones, E. P. Raynes, M. J. Towler, “Optical studies of thin layers of smectic C materials,” J. Phys. D 24,338–342 (1991).
    [CrossRef]
  18. E. P. Raynes, R. J. Tough, “The guiding of plane polarized-light by twisted liquid-crystal layers,” Mol. Cryst. Liq. Cryst. 2,139–145 (1985).
  19. C. L. Xu, W. P. Huang, J. Chrostowski, S. K. Chaudhuri, “A full-vectorial beam propagation method for anisotropic waveguides,” J. Lightwave Technol. 12,1926–1931 (1994).
    [CrossRef]
  20. E. E. Kriezis, S. J. Elston, “Wide-angle beam propagation method for liquid-crystal device calculations,” Appl. Opt. 39,5707–5714 (2000).
    [CrossRef]
  21. J. Z. Xue, N. A. Clark, “Stroboscopic microscopy of ferroelectric liquid crystals,” Phys. Rev. E 48,2043–2054 (1993).
    [CrossRef]
  22. C. V. Brown, J. C. Jones, “Accurate determination of the temperature- and frequency-dependent smectic C biaxial permittivity tensor,” J. Appl. Phys. 86,3333–3341 (1999).
    [CrossRef]
  23. C. V. Brown, J. C. Jones, M. S. Bancroft, “Detailed simulation of the Goldstone mode response of FLCs in the surface stabilized geometry,” Ferroelectrics 245,743–751 (2000).
    [CrossRef]
  24. J. C. Jones, E. P. Raynes, M. J. Towler, J. R. Sambles, “Dielectric biaxiality in smectic C host systems,” Mol. Cryst. Liq. Cryst. 199,277–285 (1991).
    [CrossRef]
  25. M. J. Towler, J. R. Hughes, F. C. Saunders, “Switching behavior of smectic C* liquid crystals,” Ferroelectrics 113,453–465 (1991).
    [CrossRef]
  26. SCE8* and SCE13* are the trade names for pitch-compensated, low-tilt commercial ferroelectric LC mixtures developed by BDH Ltd., Poole, Dorset, UK.
  27. M. H. Lu, K. A. Grandall, C. Rosemblatt, “Polarization induced renormalization of the B(1) elastic modulus in a ferroelectric liquid-crystal,” Phys. Rev. Lett. 68,3575–3578 (1992).
    [CrossRef] [PubMed]
  28. K. Okano, “Electrostatic contribution to the distortion free-energy density of ferroelectric liquid crystals,” Jpn. J. Appl. Phys. 25,846–847 (1986).
    [CrossRef]
  29. D. C. Ulrich, “Domain formation and switching in ferroelectric liquid crystals,” Ph.D. dissertation (University of Oxford, Oxford, UK., 1995).
  30. J. E. Maclennan, N. A. Clark, M. J. Handschy, M. R. Meadows, “Director orientation in chevron surface-stabilized ferroelectric liquid crystal cells,” Liq. Cryst. 7,753–785 (1990).
    [CrossRef]
  31. R. Blacker, K. Lewis, I. Mason, I. Sage, C. Webb, “Nano-phase polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 329,799–810 (1999).
    [CrossRef]
  32. T. Vallius, P. Vahimaa, J. Turunen, Y. Svirko, “Polarization diffractive optics of chiral nanogratings,” in Proceedings of International Quantum Electronics Conference, Moscow, Russia (2002).

2000 (3)

1999 (2)

C. V. Brown, J. C. Jones, “Accurate determination of the temperature- and frequency-dependent smectic C biaxial permittivity tensor,” J. Appl. Phys. 86,3333–3341 (1999).
[CrossRef]

R. Blacker, K. Lewis, I. Mason, I. Sage, C. Webb, “Nano-phase polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 329,799–810 (1999).
[CrossRef]

1996 (2)

S. Warr, R. Mears, “Polarisation insensitive diffractive FLC systems,” Ferroelectrics 181,53–59 (1996).
[CrossRef]

R. J. Mears, W. A. Crossland, M. P. Dames, J. R. Collington, M. C. Parker, S. T. Warr, T. D. Wilkinson, A. B. Davey, “Telecommunications applications of ferroelectric liquid-crystal smart pixels,” IEEE J. Sel. Top. Quantum Electron. 2,35–46 (1996).
[CrossRef]

1995 (3)

1994 (3)

J. Newton, H. Coles, P. Hodge, J. Hannington, “Synthesis and properties of low-molar-mass liquid-crystalline siloxane derivatives,” J. Mater. Chem. 4,869–874 (1994).
[CrossRef]

D. C. O’Brien, R. J. Mears, T. D. Wilkinson, W. A. Cross-land, “Dynamic holographic interconnects that use ferroelectric spatial light modulators,” Appl. Opt. 33,2795–2803 (1994).
[CrossRef]

C. L. Xu, W. P. Huang, J. Chrostowski, S. K. Chaudhuri, “A full-vectorial beam propagation method for anisotropic waveguides,” J. Lightwave Technol. 12,1926–1931 (1994).
[CrossRef]

1993 (3)

J. C. Jones, M. J. Towler, J. R. Hughes, “Fast, high contrast ferroelectric liquid crystal displays and the role of dielectric biaxiality,” Displays 14,86–93 (1993).
[CrossRef]

J. Z. Xue, N. A. Clark, “Stroboscopic microscopy of ferroelectric liquid crystals,” Phys. Rev. E 48,2043–2054 (1993).
[CrossRef]

R. M. Turner, D. A. Jared, G. D. Sharp, K. M. Johnson, “Optical correlator using very-large-scale integrated circuit/ferroelectric-liquid-crystal electrically addressed spatial light modulators,” Appl. Opt. 32,3094–3101 (1993).
[CrossRef] [PubMed]

1992 (2)

S. E. Broomfield, M. A. Neil, E. G. Paige, G. G. Yang, “Programmable binary phase-only device based on ferroelectric liquid crystal SLM,” Electron. Lett. 28,26–28 (1992).
[CrossRef]

M. H. Lu, K. A. Grandall, C. Rosemblatt, “Polarization induced renormalization of the B(1) elastic modulus in a ferroelectric liquid-crystal,” Phys. Rev. Lett. 68,3575–3578 (1992).
[CrossRef] [PubMed]

1991 (3)

J. C. Jones, E. P. Raynes, M. J. Towler, J. R. Sambles, “Dielectric biaxiality in smectic C host systems,” Mol. Cryst. Liq. Cryst. 199,277–285 (1991).
[CrossRef]

M. J. Towler, J. R. Hughes, F. C. Saunders, “Switching behavior of smectic C* liquid crystals,” Ferroelectrics 113,453–465 (1991).
[CrossRef]

M. H. Anderson, J. C. Jones, E. P. Raynes, M. J. Towler, “Optical studies of thin layers of smectic C materials,” J. Phys. D 24,338–342 (1991).
[CrossRef]

1990 (1)

J. E. Maclennan, N. A. Clark, M. J. Handschy, M. R. Meadows, “Director orientation in chevron surface-stabilized ferroelectric liquid crystal cells,” Liq. Cryst. 7,753–785 (1990).
[CrossRef]

1988 (1)

N. A. Clark, T. P. Reiker, “Smectic C chevron, a planar liquid-crystal defect—implications for the surface stabilized ferroelectric liquid crystal geometry,” Phys. Rev. A 37, 1053–1056 (1988).
[CrossRef] [PubMed]

1986 (2)

J. S. Patel, J. W. Goodby, “Alignment of liquid crystals which exhibit cholesteric to smectic* phase transitions,” J. Appl. Phys. 59, 2355–2360 (1986).
[CrossRef]

K. Okano, “Electrostatic contribution to the distortion free-energy density of ferroelectric liquid crystals,” Jpn. J. Appl. Phys. 25,846–847 (1986).
[CrossRef]

1985 (1)

E. P. Raynes, R. J. Tough, “The guiding of plane polarized-light by twisted liquid-crystal layers,” Mol. Cryst. Liq. Cryst. 2,139–145 (1985).

1980 (1)

N. A. Clark, S. T. Lagerwall, “Sub-millisecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36,899–901 (1980).
[CrossRef]

Anderson, M. H.

M. H. Anderson, J. C. Jones, E. P. Raynes, M. J. Towler, “Optical studies of thin layers of smectic C materials,” J. Phys. D 24,338–342 (1991).
[CrossRef]

Bancroft, M. S.

C. V. Brown, J. C. Jones, M. S. Bancroft, “Detailed simulation of the Goldstone mode response of FLCs in the surface stabilized geometry,” Ferroelectrics 245,743–751 (2000).
[CrossRef]

Bannister, R. W.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Blacker, R.

R. Blacker, K. Lewis, I. Mason, I. Sage, C. Webb, “Nano-phase polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 329,799–810 (1999).
[CrossRef]

Bonas, I. G.

Broomfield, S. E.

S. E. Broomfield, M. A. Neil, E. G. Paige, “Programmable multiple-level phase modulation that uses ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 34,6652–6665 (1995).
[CrossRef] [PubMed]

S. E. Broomfield, M. A. Neil, E. G. Paige, G. G. Yang, “Programmable binary phase-only device based on ferroelectric liquid crystal SLM,” Electron. Lett. 28,26–28 (1992).
[CrossRef]

Brown, C. V.

C. V. Brown, J. C. Jones, M. S. Bancroft, “Detailed simulation of the Goldstone mode response of FLCs in the surface stabilized geometry,” Ferroelectrics 245,743–751 (2000).
[CrossRef]

C. V. Brown, J. C. Jones, “Accurate determination of the temperature- and frequency-dependent smectic C biaxial permittivity tensor,” J. Appl. Phys. 86,3333–3341 (1999).
[CrossRef]

Cameron, C. D.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Chaudhuri, S. K.

C. L. Xu, W. P. Huang, J. Chrostowski, S. K. Chaudhuri, “A full-vectorial beam propagation method for anisotropic waveguides,” J. Lightwave Technol. 12,1926–1931 (1994).
[CrossRef]

Chrostowski, J.

C. L. Xu, W. P. Huang, J. Chrostowski, S. K. Chaudhuri, “A full-vectorial beam propagation method for anisotropic waveguides,” J. Lightwave Technol. 12,1926–1931 (1994).
[CrossRef]

Chu, H. H.

Clark, N. A.

J. Z. Xue, N. A. Clark, “Stroboscopic microscopy of ferroelectric liquid crystals,” Phys. Rev. E 48,2043–2054 (1993).
[CrossRef]

J. E. Maclennan, N. A. Clark, M. J. Handschy, M. R. Meadows, “Director orientation in chevron surface-stabilized ferroelectric liquid crystal cells,” Liq. Cryst. 7,753–785 (1990).
[CrossRef]

N. A. Clark, T. P. Reiker, “Smectic C chevron, a planar liquid-crystal defect—implications for the surface stabilized ferroelectric liquid crystal geometry,” Phys. Rev. A 37, 1053–1056 (1988).
[CrossRef] [PubMed]

N. A. Clark, S. T. Lagerwall, “Sub-millisecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36,899–901 (1980).
[CrossRef]

Coles, H.

J. Newton, H. Coles, P. Hodge, J. Hannington, “Synthesis and properties of low-molar-mass liquid-crystalline siloxane derivatives,” J. Mater. Chem. 4,869–874 (1994).
[CrossRef]

Collington, J. R.

R. J. Mears, W. A. Crossland, M. P. Dames, J. R. Collington, M. C. Parker, S. T. Warr, T. D. Wilkinson, A. B. Davey, “Telecommunications applications of ferroelectric liquid-crystal smart pixels,” IEEE J. Sel. Top. Quantum Electron. 2,35–46 (1996).
[CrossRef]

Coomber, S. D.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Cresswell, I.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Crossland, W. A.

W. A. Crossland, I. G. Manolis, M. M. Redmond, K. L. Tan, T. D. Wilkinson, M. J. Holmes, T. R. Parker, H. H. Chu, J. Croucher, V. A. Handerek, S. T. Warr, B. Robertson, I. G. Bonas, R. Franklin, C. Stace, H. J. White, R. A. Woolley, G. Henshal, “Holographic switching: the ROSES demonstrator,” J. Lightwave Technol. 18,1845–1854 (2000).
[CrossRef]

R. J. Mears, W. A. Crossland, M. P. Dames, J. R. Collington, M. C. Parker, S. T. Warr, T. D. Wilkinson, A. B. Davey, “Telecommunications applications of ferroelectric liquid-crystal smart pixels,” IEEE J. Sel. Top. Quantum Electron. 2,35–46 (1996).
[CrossRef]

Cross-land, W. A.

Croucher, J.

Dames, M. P.

R. J. Mears, W. A. Crossland, M. P. Dames, J. R. Collington, M. C. Parker, S. T. Warr, T. D. Wilkinson, A. B. Davey, “Telecommunications applications of ferroelectric liquid-crystal smart pixels,” IEEE J. Sel. Top. Quantum Electron. 2,35–46 (1996).
[CrossRef]

Davey, A. B.

R. J. Mears, W. A. Crossland, M. P. Dames, J. R. Collington, M. C. Parker, S. T. Warr, T. D. Wilkinson, A. B. Davey, “Telecommunications applications of ferroelectric liquid-crystal smart pixels,” IEEE J. Sel. Top. Quantum Electron. 2,35–46 (1996).
[CrossRef]

de Bougrenet de la Tocnaye, J. L.

Elston, S. J.

Franklin, R.

Goodby, J. W.

J. S. Patel, J. W. Goodby, “Alignment of liquid crystals which exhibit cholesteric to smectic* phase transitions,” J. Appl. Phys. 59, 2355–2360 (1986).
[CrossRef]

Grandall, K. A.

M. H. Lu, K. A. Grandall, C. Rosemblatt, “Polarization induced renormalization of the B(1) elastic modulus in a ferroelectric liquid-crystal,” Phys. Rev. Lett. 68,3575–3578 (1992).
[CrossRef] [PubMed]

Hallett, P. M.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Handerek, V. A.

Handschy, M. J.

J. E. Maclennan, N. A. Clark, M. J. Handschy, M. R. Meadows, “Director orientation in chevron surface-stabilized ferroelectric liquid crystal cells,” Liq. Cryst. 7,753–785 (1990).
[CrossRef]

Hannington, J.

J. Newton, H. Coles, P. Hodge, J. Hannington, “Synthesis and properties of low-molar-mass liquid-crystalline siloxane derivatives,” J. Mater. Chem. 4,869–874 (1994).
[CrossRef]

Henshal, G.

Hodge, P.

J. Newton, H. Coles, P. Hodge, J. Hannington, “Synthesis and properties of low-molar-mass liquid-crystalline siloxane derivatives,” J. Mater. Chem. 4,869–874 (1994).
[CrossRef]

Holmes, M. J.

Huang, W. P.

C. L. Xu, W. P. Huang, J. Chrostowski, S. K. Chaudhuri, “A full-vectorial beam propagation method for anisotropic waveguides,” J. Lightwave Technol. 12,1926–1931 (1994).
[CrossRef]

Hughes, J. R.

J. C. Jones, M. J. Towler, J. R. Hughes, “Fast, high contrast ferroelectric liquid crystal displays and the role of dielectric biaxiality,” Displays 14,86–93 (1993).
[CrossRef]

M. J. Towler, J. R. Hughes, F. C. Saunders, “Switching behavior of smectic C* liquid crystals,” Ferroelectrics 113,453–465 (1991).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Hui, V. C.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Jared, D. A.

Johnson, K. M.

Jones, J. C.

C. V. Brown, J. C. Jones, M. S. Bancroft, “Detailed simulation of the Goldstone mode response of FLCs in the surface stabilized geometry,” Ferroelectrics 245,743–751 (2000).
[CrossRef]

C. V. Brown, J. C. Jones, “Accurate determination of the temperature- and frequency-dependent smectic C biaxial permittivity tensor,” J. Appl. Phys. 86,3333–3341 (1999).
[CrossRef]

J. C. Jones, M. J. Towler, J. R. Hughes, “Fast, high contrast ferroelectric liquid crystal displays and the role of dielectric biaxiality,” Displays 14,86–93 (1993).
[CrossRef]

M. H. Anderson, J. C. Jones, E. P. Raynes, M. J. Towler, “Optical studies of thin layers of smectic C materials,” J. Phys. D 24,338–342 (1991).
[CrossRef]

J. C. Jones, E. P. Raynes, M. J. Towler, J. R. Sambles, “Dielectric biaxiality in smectic C host systems,” Mol. Cryst. Liq. Cryst. 199,277–285 (1991).
[CrossRef]

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Kriezis, E. E.

Lagerwall, S. T.

N. A. Clark, S. T. Lagerwall, “Sub-millisecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36,899–901 (1980).
[CrossRef]

Lewis, K.

R. Blacker, K. Lewis, I. Mason, I. Sage, C. Webb, “Nano-phase polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 329,799–810 (1999).
[CrossRef]

Lu, M. H.

M. H. Lu, K. A. Grandall, C. Rosemblatt, “Polarization induced renormalization of the B(1) elastic modulus in a ferroelectric liquid-crystal,” Phys. Rev. Lett. 68,3575–3578 (1992).
[CrossRef] [PubMed]

Maclennan, J. E.

J. E. Maclennan, N. A. Clark, M. J. Handschy, M. R. Meadows, “Director orientation in chevron surface-stabilized ferroelectric liquid crystal cells,” Liq. Cryst. 7,753–785 (1990).
[CrossRef]

Manolis, I. G.

Mason, I.

R. Blacker, K. Lewis, I. Mason, I. Sage, C. Webb, “Nano-phase polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 329,799–810 (1999).
[CrossRef]

Meadows, M. R.

J. E. Maclennan, N. A. Clark, M. J. Handschy, M. R. Meadows, “Director orientation in chevron surface-stabilized ferroelectric liquid crystal cells,” Liq. Cryst. 7,753–785 (1990).
[CrossRef]

Mears, R.

S. Warr, R. Mears, “Polarisation insensitive diffractive FLC systems,” Ferroelectrics 181,53–59 (1996).
[CrossRef]

S. Warr, R. Mears, “Polarization-insensitive operation of ferroelectric liquid crystal devices,” Electron. Lett. 31,714–716 (1995).
[CrossRef]

Mears, R. J.

Miller, R.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Minter, V.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Neil, M. A.

S. E. Broomfield, M. A. Neil, E. G. Paige, “Programmable multiple-level phase modulation that uses ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 34,6652–6665 (1995).
[CrossRef] [PubMed]

S. E. Broomfield, M. A. Neil, E. G. Paige, G. G. Yang, “Programmable binary phase-only device based on ferroelectric liquid crystal SLM,” Electron. Lett. 28,26–28 (1992).
[CrossRef]

Newton, J.

J. Newton, H. Coles, P. Hodge, J. Hannington, “Synthesis and properties of low-molar-mass liquid-crystalline siloxane derivatives,” J. Mater. Chem. 4,869–874 (1994).
[CrossRef]

O’Brien, D. C.

Okano, K.

K. Okano, “Electrostatic contribution to the distortion free-energy density of ferroelectric liquid crystals,” Jpn. J. Appl. Phys. 25,846–847 (1986).
[CrossRef]

Paige, E. G.

S. E. Broomfield, M. A. Neil, E. G. Paige, “Programmable multiple-level phase modulation that uses ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 34,6652–6665 (1995).
[CrossRef] [PubMed]

S. E. Broomfield, M. A. Neil, E. G. Paige, G. G. Yang, “Programmable binary phase-only device based on ferroelectric liquid crystal SLM,” Electron. Lett. 28,26–28 (1992).
[CrossRef]

Pain, D. A.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Parker, M. C.

R. J. Mears, W. A. Crossland, M. P. Dames, J. R. Collington, M. C. Parker, S. T. Warr, T. D. Wilkinson, A. B. Davey, “Telecommunications applications of ferroelectric liquid-crystal smart pixels,” IEEE J. Sel. Top. Quantum Electron. 2,35–46 (1996).
[CrossRef]

Parker, T. R.

Patel, J. S.

J. S. Patel, J. W. Goodby, “Alignment of liquid crystals which exhibit cholesteric to smectic* phase transitions,” J. Appl. Phys. 59, 2355–2360 (1986).
[CrossRef]

Petillot, Y.

Raynes, E. P.

M. H. Anderson, J. C. Jones, E. P. Raynes, M. J. Towler, “Optical studies of thin layers of smectic C materials,” J. Phys. D 24,338–342 (1991).
[CrossRef]

J. C. Jones, E. P. Raynes, M. J. Towler, J. R. Sambles, “Dielectric biaxiality in smectic C host systems,” Mol. Cryst. Liq. Cryst. 199,277–285 (1991).
[CrossRef]

E. P. Raynes, R. J. Tough, “The guiding of plane polarized-light by twisted liquid-crystal layers,” Mol. Cryst. Liq. Cryst. 2,139–145 (1985).

Redmond, M. M.

Reiker, T. P.

N. A. Clark, T. P. Reiker, “Smectic C chevron, a planar liquid-crystal defect—implications for the surface stabilized ferroelectric liquid crystal geometry,” Phys. Rev. A 37, 1053–1056 (1988).
[CrossRef] [PubMed]

Robertson, B.

Rosemblatt, C.

M. H. Lu, K. A. Grandall, C. Rosemblatt, “Polarization induced renormalization of the B(1) elastic modulus in a ferroelectric liquid-crystal,” Phys. Rev. Lett. 68,3575–3578 (1992).
[CrossRef] [PubMed]

Sage, I.

R. Blacker, K. Lewis, I. Mason, I. Sage, C. Webb, “Nano-phase polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 329,799–810 (1999).
[CrossRef]

Sambles, J. R.

J. C. Jones, E. P. Raynes, M. J. Towler, J. R. Sambles, “Dielectric biaxiality in smectic C host systems,” Mol. Cryst. Liq. Cryst. 199,277–285 (1991).
[CrossRef]

Saunders, F. C.

M. J. Towler, J. R. Hughes, F. C. Saunders, “Switching behavior of smectic C* liquid crystals,” Ferroelectrics 113,453–465 (1991).
[CrossRef]

Scattergood, D. C.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Sharp, G. D.

Sheerin, D. T.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Slinger, C. W.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Smith, M. J.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Stace, C.

Stanley, M.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

Svirko, Y.

T. Vallius, P. Vahimaa, J. Turunen, Y. Svirko, “Polarization diffractive optics of chiral nanogratings,” in Proceedings of International Quantum Electronics Conference, Moscow, Russia (2002).

Tan, K. L.

Tough, R. J.

E. P. Raynes, R. J. Tough, “The guiding of plane polarized-light by twisted liquid-crystal layers,” Mol. Cryst. Liq. Cryst. 2,139–145 (1985).

Towler, M. J.

J. C. Jones, M. J. Towler, J. R. Hughes, “Fast, high contrast ferroelectric liquid crystal displays and the role of dielectric biaxiality,” Displays 14,86–93 (1993).
[CrossRef]

M. H. Anderson, J. C. Jones, E. P. Raynes, M. J. Towler, “Optical studies of thin layers of smectic C materials,” J. Phys. D 24,338–342 (1991).
[CrossRef]

M. J. Towler, J. R. Hughes, F. C. Saunders, “Switching behavior of smectic C* liquid crystals,” Ferroelectrics 113,453–465 (1991).
[CrossRef]

J. C. Jones, E. P. Raynes, M. J. Towler, J. R. Sambles, “Dielectric biaxiality in smectic C host systems,” Mol. Cryst. Liq. Cryst. 199,277–285 (1991).
[CrossRef]

Turner, R. M.

Turunen, J.

T. Vallius, P. Vahimaa, J. Turunen, Y. Svirko, “Polarization diffractive optics of chiral nanogratings,” in Proceedings of International Quantum Electronics Conference, Moscow, Russia (2002).

Ulrich, D. C.

D. C. Ulrich, “Domain formation and switching in ferroelectric liquid crystals,” Ph.D. dissertation (University of Oxford, Oxford, UK., 1995).

Vahimaa, P.

T. Vallius, P. Vahimaa, J. Turunen, Y. Svirko, “Polarization diffractive optics of chiral nanogratings,” in Proceedings of International Quantum Electronics Conference, Moscow, Russia (2002).

Vallius, T.

T. Vallius, P. Vahimaa, J. Turunen, Y. Svirko, “Polarization diffractive optics of chiral nanogratings,” in Proceedings of International Quantum Electronics Conference, Moscow, Russia (2002).

Warr, S.

S. Warr, R. Mears, “Polarisation insensitive diffractive FLC systems,” Ferroelectrics 181,53–59 (1996).
[CrossRef]

S. Warr, R. Mears, “Polarization-insensitive operation of ferroelectric liquid crystal devices,” Electron. Lett. 31,714–716 (1995).
[CrossRef]

Warr, S. T.

W. A. Crossland, I. G. Manolis, M. M. Redmond, K. L. Tan, T. D. Wilkinson, M. J. Holmes, T. R. Parker, H. H. Chu, J. Croucher, V. A. Handerek, S. T. Warr, B. Robertson, I. G. Bonas, R. Franklin, C. Stace, H. J. White, R. A. Woolley, G. Henshal, “Holographic switching: the ROSES demonstrator,” J. Lightwave Technol. 18,1845–1854 (2000).
[CrossRef]

R. J. Mears, W. A. Crossland, M. P. Dames, J. R. Collington, M. C. Parker, S. T. Warr, T. D. Wilkinson, A. B. Davey, “Telecommunications applications of ferroelectric liquid-crystal smart pixels,” IEEE J. Sel. Top. Quantum Electron. 2,35–46 (1996).
[CrossRef]

Webb, C.

R. Blacker, K. Lewis, I. Mason, I. Sage, C. Webb, “Nano-phase polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 329,799–810 (1999).
[CrossRef]

White, H. J.

Wilkinson, T. D.

Woolley, R. A.

Xu, C. L.

C. L. Xu, W. P. Huang, J. Chrostowski, S. K. Chaudhuri, “A full-vectorial beam propagation method for anisotropic waveguides,” J. Lightwave Technol. 12,1926–1931 (1994).
[CrossRef]

Xue, J. Z.

J. Z. Xue, N. A. Clark, “Stroboscopic microscopy of ferroelectric liquid crystals,” Phys. Rev. E 48,2043–2054 (1993).
[CrossRef]

Yang, G. G.

S. E. Broomfield, M. A. Neil, E. G. Paige, G. G. Yang, “Programmable binary phase-only device based on ferroelectric liquid crystal SLM,” Electron. Lett. 28,26–28 (1992).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

N. A. Clark, S. T. Lagerwall, “Sub-millisecond bistable electro-optic switching in liquid crystals,” Appl. Phys. Lett. 36,899–901 (1980).
[CrossRef]

Displays (1)

J. C. Jones, M. J. Towler, J. R. Hughes, “Fast, high contrast ferroelectric liquid crystal displays and the role of dielectric biaxiality,” Displays 14,86–93 (1993).
[CrossRef]

Electron. Lett. (2)

S. Warr, R. Mears, “Polarization-insensitive operation of ferroelectric liquid crystal devices,” Electron. Lett. 31,714–716 (1995).
[CrossRef]

S. E. Broomfield, M. A. Neil, E. G. Paige, G. G. Yang, “Programmable binary phase-only device based on ferroelectric liquid crystal SLM,” Electron. Lett. 28,26–28 (1992).
[CrossRef]

Ferroelectrics (3)

S. Warr, R. Mears, “Polarisation insensitive diffractive FLC systems,” Ferroelectrics 181,53–59 (1996).
[CrossRef]

C. V. Brown, J. C. Jones, M. S. Bancroft, “Detailed simulation of the Goldstone mode response of FLCs in the surface stabilized geometry,” Ferroelectrics 245,743–751 (2000).
[CrossRef]

M. J. Towler, J. R. Hughes, F. C. Saunders, “Switching behavior of smectic C* liquid crystals,” Ferroelectrics 113,453–465 (1991).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. J. Mears, W. A. Crossland, M. P. Dames, J. R. Collington, M. C. Parker, S. T. Warr, T. D. Wilkinson, A. B. Davey, “Telecommunications applications of ferroelectric liquid-crystal smart pixels,” IEEE J. Sel. Top. Quantum Electron. 2,35–46 (1996).
[CrossRef]

J. Appl. Phys. (2)

J. S. Patel, J. W. Goodby, “Alignment of liquid crystals which exhibit cholesteric to smectic* phase transitions,” J. Appl. Phys. 59, 2355–2360 (1986).
[CrossRef]

C. V. Brown, J. C. Jones, “Accurate determination of the temperature- and frequency-dependent smectic C biaxial permittivity tensor,” J. Appl. Phys. 86,3333–3341 (1999).
[CrossRef]

J. Lightwave Technol. (2)

J. Mater. Chem. (1)

J. Newton, H. Coles, P. Hodge, J. Hannington, “Synthesis and properties of low-molar-mass liquid-crystalline siloxane derivatives,” J. Mater. Chem. 4,869–874 (1994).
[CrossRef]

J. Phys. D (1)

M. H. Anderson, J. C. Jones, E. P. Raynes, M. J. Towler, “Optical studies of thin layers of smectic C materials,” J. Phys. D 24,338–342 (1991).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Okano, “Electrostatic contribution to the distortion free-energy density of ferroelectric liquid crystals,” Jpn. J. Appl. Phys. 25,846–847 (1986).
[CrossRef]

Liq. Cryst. (1)

J. E. Maclennan, N. A. Clark, M. J. Handschy, M. R. Meadows, “Director orientation in chevron surface-stabilized ferroelectric liquid crystal cells,” Liq. Cryst. 7,753–785 (1990).
[CrossRef]

Mol. Cryst. Liq. Cryst. (3)

R. Blacker, K. Lewis, I. Mason, I. Sage, C. Webb, “Nano-phase polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 329,799–810 (1999).
[CrossRef]

J. C. Jones, E. P. Raynes, M. J. Towler, J. R. Sambles, “Dielectric biaxiality in smectic C host systems,” Mol. Cryst. Liq. Cryst. 199,277–285 (1991).
[CrossRef]

E. P. Raynes, R. J. Tough, “The guiding of plane polarized-light by twisted liquid-crystal layers,” Mol. Cryst. Liq. Cryst. 2,139–145 (1985).

Phys. Rev. A (1)

N. A. Clark, T. P. Reiker, “Smectic C chevron, a planar liquid-crystal defect—implications for the surface stabilized ferroelectric liquid crystal geometry,” Phys. Rev. A 37, 1053–1056 (1988).
[CrossRef] [PubMed]

Phys. Rev. E (1)

J. Z. Xue, N. A. Clark, “Stroboscopic microscopy of ferroelectric liquid crystals,” Phys. Rev. E 48,2043–2054 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

M. H. Lu, K. A. Grandall, C. Rosemblatt, “Polarization induced renormalization of the B(1) elastic modulus in a ferroelectric liquid-crystal,” Phys. Rev. Lett. 68,3575–3578 (1992).
[CrossRef] [PubMed]

Other (5)

T. Vallius, P. Vahimaa, J. Turunen, Y. Svirko, “Polarization diffractive optics of chiral nanogratings,” in Proceedings of International Quantum Electronics Conference, Moscow, Russia (2002).

D. C. Ulrich, “Domain formation and switching in ferroelectric liquid crystals,” Ph.D. dissertation (University of Oxford, Oxford, UK., 1995).

SCE8* and SCE13* are the trade names for pitch-compensated, low-tilt commercial ferroelectric LC mixtures developed by BDH Ltd., Poole, Dorset, UK.

C. W. Slinger, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. Cresswell, P. M. Hallett, J. R. Hughes, V. C. Hui, J. C. Jones, R. Miller, V. Minter, D. A. Pain, D. C. Scattergood, D. T. Sheerin, M. J. Smith, M. Stanley, “Progress and prospects for practical electroholographic display systems,” in Practical Holography XV and Holographic Materials VII, S. A. Benton, S. H. Sylvia, T. J. Trout, eds., Proc. SPIE4296, 18–32 (2001).
[CrossRef]

CS2005 is the trade name for a commercial high-tilt ferroelectric LC material available from Lixon Department, CHISSO Corporation, Chuo-ku, Tokyo, Japan.

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Figures (6)

Fig. 1
Fig. 1

Illustration of the FLC diffraction grating geometry.

Fig. 2
Fig. 2

Diffraction efficiencies as a function of the parameter Δnd/λ for the diffraction geometry in Fig. 1: (a) total diffraction efficiency (ηTOT), with the dashed curve corresponding to the Jones calculus and the solid curve corresponding to the VBPM, and (b) first-order diffraction efficiency (η1) calculated by the VBPM.

Fig. 3
Fig. 3

Twist and tilt profiles as a function of distance through the FLC layer. Curves are shown for zero-applied voltage (dashed curve) and for applied ac voltages from 2 to 16 Vac in steps of 2 Vac (solid curves).

Fig. 4
Fig. 4

Diffraction efficiencies as a function of the parameter Δnd/λ for the twist and tilt profiles of Fig. 3: (a) total diffraction efficiency (ηTOT) obtained by the Jones calculus and (b) first-order diffraction efficiency (η1) obtained by the VBPM.

Fig. 5
Fig. 5

Twist and tilt profiles as a function of distance through the FLC layer. Curves are shown for zero spontaneous polarization (dashed curve) and for the values 5, 10, 15, 20, and 25 nC/cm2.

Fig. 6
Fig. 6

Diffraction efficiencies as a function of the parameter Δnd/k for the twist and tilt profiles of Fig. 5: (a) total diffraction efficiency (ηTOT) obtained by the Jones calculus and (b) first-order diffraction efficiency (η1) obtained by the VBPM.

Tables (1)

Tables Icon

Table 1 LC Material Parameters Used throughout the Simulations

Equations (3)

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

η TOT = | E inc | 2 - 1 4 | E 1 + E 2 | 2 | E inc | 2 .
E 1 = J 1 E inc = [ a b - b * a ] E inc ,
E 2 = J 2 E inc = [ a - b b * a ] E inc .

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