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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 11 — Nov. 1, 2007
  • pp: 3467–3477

Modeling liquid-crystal gradient-index lenses

T. C. Kraan, T. van Bommel, and R. A.M. Hikmet  »View Author Affiliations

JOSA A, Vol. 24, Issue 11, pp. 3467-3477 (2007)

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The optical properties of one-dimensional gradient-refractive-index lens arrays based on liquid crystals are studied. We find that it is quite possible, using theoretical methods, to predict angular distributions of the light emanating from such arrays when they are illuminated with collimated monochromatic light. We compare four theoretical methods in relation to experiments. The experimental data and the model, based on a combination of eikonal methods and diffraction, are in close correspondence. Features such as maximal beam width and number of extrema in the angular light distribution are discussed and explained theoretically. We also studied dispersion effects, both experimentally and theoretically, with good agreement between the two.

© 2007 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(080.2710) Geometric optics : Inhomogeneous optical media
(080.2720) Geometric optics : Mathematical methods (general)
(160.3710) Materials : Liquid crystals
(220.3630) Optical design and fabrication : Lenses
(230.3720) Optical devices : Liquid-crystal devices

Original Manuscript: July 6, 2007
Manuscript Accepted: August 30, 2007
Published: October 12, 2007

T. C. Kraan, T. van Bommel, and R. A. M. Hikmet, "Modeling liquid-crystal gradient-index lenses," J. Opt. Soc. Am. A 24, 3467-3477 (2007)

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  1. S. T. Kowel, D. S. Cleverly, and P. G. Kornreich, "Focusing by electrical modulation of refraction in a liquid crystal cell," Appl. Opt. 23, 278-289 (1984). [CrossRef] [PubMed]
  2. S. T. Kowel, P. Kornreich, and A. Nouhi, "Adaptive spherical lens," Appl. Opt. 23, 2774-2777 (1984). [CrossRef] [PubMed]
  3. P. F. Brinkley, S. T. Kowel, and C. Chu, "Liquid crystal adaptive lens: beam translation and field meshing," Appl. Opt. 27, 4578-4586 (1988). [CrossRef] [PubMed]
  4. W. Chan, L. Ning, S. T. Kowel, and P. F. Brinkley, "The liquid crystal adaptive lens: aberration correction," Proc. SPIE 1773, 468-475 (1992). [CrossRef]
  5. N. A. Riza and M. C. DeJule, "Three terminal adaptive nematic liquid-crystal lens device," Opt. Lett. 19, 1013-1015 (1994). [CrossRef] [PubMed]
  6. S. Masuda, S. Takahashi, T. Nose, S. Sato, and H. Ito, "Liquid-crystal microlens with a beam-steering function," Appl. Opt. 36, 4772-4778 (1997). [CrossRef] [PubMed]
  7. W. W. Chan and S. T. Kowel, "Imaging performance of the liquid-crystal adaptive lens with conductive ladder meshing," Appl. Opt. 36, 8958-8969 (1997). [CrossRef]
  8. V. Laude, "Twisted-nematic liquid-crystal pixelated active lens," Opt. Commun. 153, 134-152 (1998). [CrossRef]
  9. A. F. Naumov, G. D. Love, M. Y. Loktev, and F. L. Vladimirov, "Control optimization of spherical modal liquid crystal lenses," Opt. Express 4, 344-352 (1999). [CrossRef]
  10. O. A. Zayakin, M. Y. Loktev, G. Love, and A. Naumov, "Cylindrical adaptive lenses," Proc. SPIE 3983, 112-117 (1999). [CrossRef]
  11. W. Liu, J. Kelly, and J. Chen, "Electro-optical performance of a self-compensating vertically-aligned liquid crystal display mode," Jpn. J. Appl. Phys., Part 1 38, 2779-2784 (1999). [CrossRef]
  12. W. Liu and J. Kelly, "Optical properties of a switchable diffraction grating," Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 358, 199-208 (2001). [CrossRef]
  13. H. Ren, Y.-H. Fan, S. Gauza, and S.-T. Wu, "Tunable-focus cylindrical liquid crystal lens," Jpn. J. Appl. Phys., Part 1 43, 652-653 (2004). [CrossRef]
  14. Y.-H. Lin, H. Ren, K.-H. Fan-Chiang, W.-K. Choi, S. Gauza, X. Zhu, and S.-T. Wu, "Tunable-focus cylindical liquid crystal lenses," Jpn. J. Appl. Phys., Part 1 44, 243-244 (2005). [CrossRef]
  15. M. Ye, B. Wang, and S. Sato, "Liquid-crystal lens with a focal length that is variable in a wide range," Appl. Opt. 43, 6407-6412 (2004). [CrossRef] [PubMed]
  16. B. Apter, E. Bahat-Treidel, and U. Efron, "Continuously controllable, wide-angle liquid crystal beam deflector based on the transversal field effect in a three-electrode cell," Opt. Eng. 44, 054001 (2005). [CrossRef]
  17. H. Ren, Y.-H. Lin, and S.-T. Wu, "Adaptive lens using liquid crystal concentration redistribution," Appl. Phys. Lett. 88, 191116 (2006). [CrossRef]
  18. M.Born and E.Wolf, eds., Principles of Optics (Pergamon, 1959).
  19. M. Kline and I. W. Kay, Electromagnetic Theory and Geometrical Optics (Interscience, 1965).
  20. Y. A. Kravtsov and Y. I. Orlov, Geometrical Optics of Inhomogeneous Media (Springer-Verlag, 1990). [CrossRef]
  21. H. L. Ong, "Optical properties of general twisted nematic liquid crystals," Appl. Phys. Lett. 51, 1398-1400 (1987). [CrossRef]
  22. J. A. Kosmopoulos and H. M. Zenginoglou, "Geometrical optics approach to the nematic liquid crystal grating: numerical results," Appl. Opt. 26, 1714-1721 (1987). [CrossRef] [PubMed]
  23. H. M. Zenginoglou and J. A. Kosmopoulos, "Geometrical optics approach to the nematic liquid crystal grating: leading term formulas," Appl. Opt. 28, 3516-3519 (1989). [CrossRef] [PubMed]
  24. A. L. Rivera, S. M. Chumakov, and K. B. Wolf, "Hamiltonian foundation of geometrical anisotropic optics," J. Opt. Soc. Am. A 12, 1380-1389 (1995). [CrossRef]
  25. W. Shen, J. Zhang, S. Wang, and S. Zhu, "Fermat's principle, the general eikonal equation, and space geometry in a static anisotropic medium," J. Opt. Soc. Am. A 14, 2850-2854 (1997). [CrossRef]
  26. C. G. Parazzoli, B. E. C. Koltenbah, R. B. Greegor, T. A. Lam, and M. H. Tanielan, "Eikonal equation for a general anisotropic or chiral medium: application to a negative-graded index-of-refraction lens with an anisotropic material," J. Opt. Soc. Am. B 23, 439-450 (2006). [CrossRef]
  27. S. C. McClain, L. W. Hillman, and R. A. Chipman, "Polarization ray tracing in anisotropic optically active media. I. Algorithms," J. Opt. Soc. Am. A 10, 2371-2382 (1993). [CrossRef]
  28. S. C. McClain, L. W. Hillman, and R. A. Chipman, "Polarization ray tracing in anisotropic optically active media. II. Theory and physics," J. Opt. Soc. Am. A 10, 2383-2393 (1993). [CrossRef]
  29. G. Panasyuk, J. Kelly, E. C. Gartland, and D. W. Allender, "Geometrical optics approach in liquid crystal films with three-dimensional director variations," Phys. Rev. E 67, 041702 (2003). [CrossRef]
  30. O. Gielkens, Polymer Vision Ltd., High Tech Campus 48, 5656 AE Eindhoven, The Netherlands (personal communication, 2001).
  31. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999).
  32. Mathematica website, http://www.wolfram.com.
  33. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).
  34. ELDIM website, http://www.eldim.fr.
  35. R. A. M. Hikmet, T. van Bommel, and T. C. Kraan, "Study of light distribution through lc field induced lens arrays," submitted to J. Appl. Phys..
  36. Shintech website, http://www.shintech.jp.
  37. J. F. Strömer, E. P. Raynes, and C. V. Brown, "Study of elastic constant ratios in nematic liquid crystals," Appl. Phys. Lett. 88, 051915 (2006). [CrossRef]
  38. B. A. E. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991). [CrossRef]
  39. E. Hecht, Optics, 2nd ed. (Addison Wesley, 1989).
  40. K. Neyts, S. Vermeirsch, S. Vermael, H. de Vleeschouwer, F. Bougrioua, S. Rozanski, D. de Boer, J. van Haaren, and S. Day, "Simulation of refraction, retardation and transmission in liquid crystal displays with slow variations," in Proceedings of the 20th International Display Research Conference (Society for Information Display, 2000), pp. 225-228.

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