Abstract

Abstract: A multigrid computational model has been developed to assess the performance of refractive liquid crystal lenses, which is up to 40 times faster than previous techniques. Using this model, the optimum geometries producing an ideal parabolic voltage distribution were deduced for refractive liquid crystal lenses with diameters from 1 to 9 mm. The ratio of insulation thickness to lens diameter was determined to be 1:2 for small diameter lenses, tending to 1:3 for larger lenses. The model is used to propose a new method of lens operation with lower operating voltages needed to induce specific optical powers. The operating voltages are calculated for the induction of optical powers between + 1.00 D and + 3.00 D in a 3 mm diameter lens, with the speed of the simulation facilitating the optimization of the refractive index profile. We demonstrate that the relationship between additional applied voltage and optical power is approximately linear for optical powers under + 3.00 D. The versatility of the computational simulation has also been demonstrated by modeling of in-plane electrode liquid crystal devices.

© 2012 OSA

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  1. G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
    [CrossRef] [PubMed]
  2. S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
    [CrossRef]
  3. H. W. Ren, D. W. Fox, B. Wu, and S. T. Wu, “Liquid crystal lens with large focal length tunability and low operating voltage,” Opt. Express 15(18), 11328–11335 (2007).
    [CrossRef] [PubMed]
  4. H. W. Ren and S. T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14(23), 11292–11298 (2006).
    [CrossRef] [PubMed]
  5. A. F. Naumov, G. D. Love, M. Y. Loktev, and F. L. Vladimirov, “Control optimization of spherical modal liquid crystal lenses,” Opt. Express 4(9), 344–352 (1999).
    [CrossRef] [PubMed]
  6. M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41(Part 2, No. 5B), L571–L573 (2002).
    [CrossRef]
  7. M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43(35), 6407–6412 (2004).
    [CrossRef] [PubMed]
  8. S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6(6), 471–485 (1999).
    [CrossRef]
  9. G. Q. Li, P. Valley, P. Ayras, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007).
    [CrossRef]
  10. B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” IEEE Photon. Technol. Lett. 18(1), 79–81 (2006).
    [CrossRef]
  11. U. Trottenberg, Multigrid, 1st ed. (Academic Press, London, 2001).

2007 (2)

G. Q. Li, P. Valley, P. Ayras, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007).
[CrossRef]

H. W. Ren, D. W. Fox, B. Wu, and S. T. Wu, “Liquid crystal lens with large focal length tunability and low operating voltage,” Opt. Express 15(18), 11328–11335 (2007).
[CrossRef] [PubMed]

2006 (3)

B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” IEEE Photon. Technol. Lett. 18(1), 79–81 (2006).
[CrossRef]

H. W. Ren and S. T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14(23), 11292–11298 (2006).
[CrossRef] [PubMed]

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

2004 (1)

2002 (1)

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41(Part 2, No. 5B), L571–L573 (2002).
[CrossRef]

1999 (2)

1979 (1)

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[CrossRef]

Ayras, P.

G. Q. Li, P. Valley, P. Ayras, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007).
[CrossRef]

Ayräs, P.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Fox, D. W.

Giridhar, M. S.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Haddock, J. N.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Honkanen, S.

G. Q. Li, P. Valley, P. Ayras, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Kippelen, B.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Li, G.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Li, G. Q.

G. Q. Li, P. Valley, P. Ayras, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007).
[CrossRef]

Loktev, M. Y.

Love, G. D.

Mathine, D. L.

G. Q. Li, P. Valley, P. Ayras, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Meredith, G. R.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Naumov, A. F.

Peyghambarian, N.

G. Q. Li, P. Valley, P. Ayras, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Ren, H. W.

Sato, S.

B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” IEEE Photon. Technol. Lett. 18(1), 79–81 (2006).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43(35), 6407–6412 (2004).
[CrossRef] [PubMed]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41(Part 2, No. 5B), L571–L573 (2002).
[CrossRef]

S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6(6), 471–485 (1999).
[CrossRef]

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[CrossRef]

Schwiegerling, J.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Valley, P.

G. Q. Li, P. Valley, P. Ayras, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007).
[CrossRef]

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Vladimirov, F. L.

Wang, B.

B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” IEEE Photon. Technol. Lett. 18(1), 79–81 (2006).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43(35), 6407–6412 (2004).
[CrossRef] [PubMed]

Williby, G.

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Wu, B.

Wu, S. T.

Ye, M.

B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” IEEE Photon. Technol. Lett. 18(1), 79–81 (2006).
[CrossRef]

M. Ye, B. Wang, and S. Sato, “Liquid-crystal lens with a focal length that is variable in a wide range,” Appl. Opt. 43(35), 6407–6412 (2004).
[CrossRef] [PubMed]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41(Part 2, No. 5B), L571–L573 (2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

G. Q. Li, P. Valley, P. Ayras, D. L. Mathine, S. Honkanen, and N. Peyghambarian, “High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures,” Appl. Phys. Lett. 90(11), 111105 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. Wang, M. Ye, and S. Sato, “Liquid crystal lens with focal length variable from negative to positive values,” IEEE Photon. Technol. Lett. 18(1), 79–81 (2006).
[CrossRef]

Jpn. J. Appl. Phys. (2)

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[CrossRef]

M. Ye and S. Sato, “Optical properties of liquid crystal lens of any size,” Jpn. J. Appl. Phys. 41(Part 2, No. 5B), L571–L573 (2002).
[CrossRef]

Opt. Express (3)

Opt. Rev. (1)

S. Sato, “Applications of liquid crystals to variable-focusing lenses,” Opt. Rev. 6(6), 471–485 (1999).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

G. Li, D. L. Mathine, P. Valley, P. Ayräs, J. N. Haddock, M. S. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103(16), 6100–6104 (2006).
[CrossRef] [PubMed]

Other (1)

U. Trottenberg, Multigrid, 1st ed. (Academic Press, London, 2001).

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Figures (7)

Fig. 1
Fig. 1

An illustration of a RLCL device designed by Ye et al. [9]. The voltage profile across the LC layer is determined by the powering of the active and control electrodes, with the control electrode providing a baseline voltage across the lens and the active electrodes providing additional voltage at the peripheries. Typically a thick LC layer is required of between 50 – 100 µm in order to produce sufficient phase retardation for RLCLs with diameters of several mm. A ratio of 2-3:1 between RLCL diameter and insulation thickness is usually required.

Fig. 2
Fig. 2

Simplified simulation boxes for the modeling of RLCL. Mirror symmetry is applied to the x-boundary. In the case of RLCLs there are set boundaries in the z direction corresponding to the control and ground electrodes.

Fig. 3
Fig. 3

Electric potential calculations for a 3 mm, + 2.00 D RLCL similar to the design shown in Fig. 1 with (a) showing the potential throughout the entire RLCL device, with the bottom 100 µm constituting the LC layer, and (b) showing the potential of the LC layer. The insulating glass layer is ~1.4 mm thick yielding a bell shaped voltage distribution across the LC layer. The calculation used 4 multigrid iteration grids and a 400x150 point final simulation box to ensure high resolution across the LC layer. The average permittivity of the glass and the LC are taken to be 6.7 and 11.5 respectively (the latter measured for 5CB at room temperature).

Fig. 4
Fig. 4

A comparison of insulation thickness voltage profiles for a 1 mm RLCL. Greater insulation thickness results in a better parabolic profile approximation across the optical area, with a 50 µm insulation thickness closest to a parabolic voltage profile. Here, the permittivity of the glass is 6.7 and the average permittivity of 5CB is 11.5.

Fig. 5
Fig. 5

The relationship between insulation thickness against RLCL diameter (a) and operating voltages and optical power of a 3 mm diameter RLCL with a 140 µm thick insulation layer (b). (a) shows a comparison of minimum operational RLCL geometries for 5CB. The general ratio of 2-3:1 of the RLCL diameter to insulation thickness is observed, with a ratio of 2:1 observed at 1 mm and 2 mm, which increases to 3:1 as the RLCL diameter increases. (b) shows an approximately linear relationship between the additional active variable voltage applied and the optical power achieved with a slight reduction in control voltage due the effect of the increased variable voltages on the central area of the lens.

Fig. 6
Fig. 6

The refractive profiles of a + 0.50 D RLCL (a) and a + 3.00 D RLCL (b). The computer model indicates a greater deviation in the peripheries of the optical area (0-30 µm and 270-300 µ) for a stronger lens than in a weaker lens. Lab measurements give a value of ne = 1.698 and ordinary refractive index (no) = 1.535 (at 589 nm) for 5CB. In the case of 5CB, deviations from the idea parabola occur when a change in ne greater than 0.06 is required.

Fig. 7
Fig. 7

A comparison of the electric field between inter-digited in-plane electrodes using the multigrid simulation, with a 5 µm thick LC layer above the electrodes. A smoother electric field was observed in simulations with lower LC to glass electric permittivity ratios, resulting in an improved performance.

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2 φ x 2 ε+ εφ xz + 2 φ z 2 ε+ εφ zx =0,

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