Abstract

In this study, a novel liquid crystal array based on modal control principle is proposed and demonstrated. The advanced device comprises a six striped electrode structure that forms a configurable 2D matrix of optical elements. A simulation program based on the Frank-Oseen equations and modal control theory has been developed to predict the device electrooptic response, that is, voltage distribution, interference pattern and unwrapped phase. A low-power electronics circuit, that generates complex waveforms, has been built for driving the device. A combined variation of the waveform amplitude and phase has provided a high tuning versatility to the device. Thus, the simulations have demonstrated the generation of a liquid crystal prism array with tunable slope. The proposed device has also been configured as an axicon array. Test measurements have allowed us to demonstrate that electrooptic responses, simulated and empirical, are fairly in agreement.

© 2013 Optical Society of America

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References

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  1. Y. H. Lin and M. S. Chen, “A pico projection system with electrically tunable optical zoom ratio adopting two liquid crystal lenses,” J. Disp. Technol.8(7), 401–404 (2012).
    [CrossRef]
  2. V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Q. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electron. Rev.20(3), 260–266 (2012).
    [CrossRef]
  3. A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, and G. Vdovin, “Liquid-crystal adaptive lenses with modal control,” Opt. Lett.23(13), 992–994 (1998).
    [CrossRef] [PubMed]
  4. V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, M. A. Geday, and J. M. Otón, “Electrooptic characterization of tunable cylindrical liquid crystal lenses,” Mol. Cryst. Liq. Cryst.553(1), 211–219 (2012).
    [CrossRef]
  5. G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Y. Loktev, and A. F. Naumov, “Liquid-crystal lenses with a controlled focal length. I. Theory,” Quantum Electron.29(3), 256–260 (1999).
    [CrossRef]
  6. A. F. Naumov, G. D. Love, M. Y. Loktev, and F. L. Vladimirov, “Control optimization of spherical modal liquid crystal lenses,” Opt. Express4(9), 344–352 (1999).
    [CrossRef] [PubMed]
  7. A. K. Kirby, P. J. Hands, and G. D. Love, “Liquid crystal multi-mode lenses and axicons based on electronic phase shift control,” Opt. Express15(21), 13496–13501 (2007).
    [CrossRef] [PubMed]
  8. N. Fraval and J. L. de la Tocnaye, “Low aberrations symmetrical adaptive modal liquid crystal lens with short focal lengths,” Appl. Opt.49(15), 2778–2783 (2010).
    [CrossRef] [PubMed]
  9. S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 2. Experiment,” Quantum Electron.41(1), 65–70 (2011).
    [CrossRef]
  10. S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 1. Theory,” Quantum Electron.41(1), 58–64 (2011).
    [CrossRef]

2012 (3)

Y. H. Lin and M. S. Chen, “A pico projection system with electrically tunable optical zoom ratio adopting two liquid crystal lenses,” J. Disp. Technol.8(7), 401–404 (2012).
[CrossRef]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Q. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electron. Rev.20(3), 260–266 (2012).
[CrossRef]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, M. A. Geday, and J. M. Otón, “Electrooptic characterization of tunable cylindrical liquid crystal lenses,” Mol. Cryst. Liq. Cryst.553(1), 211–219 (2012).
[CrossRef]

2011 (2)

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 2. Experiment,” Quantum Electron.41(1), 65–70 (2011).
[CrossRef]

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 1. Theory,” Quantum Electron.41(1), 58–64 (2011).
[CrossRef]

2010 (1)

2007 (1)

1999 (2)

A. F. Naumov, G. D. Love, M. Y. Loktev, and F. L. Vladimirov, “Control optimization of spherical modal liquid crystal lenses,” Opt. Express4(9), 344–352 (1999).
[CrossRef] [PubMed]

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Y. Loktev, and A. F. Naumov, “Liquid-crystal lenses with a controlled focal length. I. Theory,” Quantum Electron.29(3), 256–260 (1999).
[CrossRef]

1998 (1)

Algorri, J. F.

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, M. A. Geday, and J. M. Otón, “Electrooptic characterization of tunable cylindrical liquid crystal lenses,” Mol. Cryst. Liq. Cryst.553(1), 211–219 (2012).
[CrossRef]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Q. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electron. Rev.20(3), 260–266 (2012).
[CrossRef]

Arregui, X. Q.

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Q. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electron. Rev.20(3), 260–266 (2012).
[CrossRef]

Bennis, N.

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Q. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electron. Rev.20(3), 260–266 (2012).
[CrossRef]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, M. A. Geday, and J. M. Otón, “Electrooptic characterization of tunable cylindrical liquid crystal lenses,” Mol. Cryst. Liq. Cryst.553(1), 211–219 (2012).
[CrossRef]

Chen, M. S.

Y. H. Lin and M. S. Chen, “A pico projection system with electrically tunable optical zoom ratio adopting two liquid crystal lenses,” J. Disp. Technol.8(7), 401–404 (2012).
[CrossRef]

de la Tocnaye, J. L.

Fraval, N.

Geday, M. A.

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, M. A. Geday, and J. M. Otón, “Electrooptic characterization of tunable cylindrical liquid crystal lenses,” Mol. Cryst. Liq. Cryst.553(1), 211–219 (2012).
[CrossRef]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Q. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electron. Rev.20(3), 260–266 (2012).
[CrossRef]

Guralnik, I. R.

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Y. Loktev, and A. F. Naumov, “Liquid-crystal lenses with a controlled focal length. I. Theory,” Quantum Electron.29(3), 256–260 (1999).
[CrossRef]

A. F. Naumov, M. Yu. Loktev, I. R. Guralnik, and G. Vdovin, “Liquid-crystal adaptive lenses with modal control,” Opt. Lett.23(13), 992–994 (1998).
[CrossRef] [PubMed]

Hands, P. J.

Kirby, A. K.

Kotova, S. P.

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 1. Theory,” Quantum Electron.41(1), 58–64 (2011).
[CrossRef]

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 2. Experiment,” Quantum Electron.41(1), 65–70 (2011).
[CrossRef]

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Y. Loktev, and A. F. Naumov, “Liquid-crystal lenses with a controlled focal length. I. Theory,” Quantum Electron.29(3), 256–260 (1999).
[CrossRef]

Lin, Y. H.

Y. H. Lin and M. S. Chen, “A pico projection system with electrically tunable optical zoom ratio adopting two liquid crystal lenses,” J. Disp. Technol.8(7), 401–404 (2012).
[CrossRef]

Loktev, M. Y.

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Y. Loktev, and A. F. Naumov, “Liquid-crystal lenses with a controlled focal length. I. Theory,” Quantum Electron.29(3), 256–260 (1999).
[CrossRef]

A. F. Naumov, G. D. Love, M. Y. Loktev, and F. L. Vladimirov, “Control optimization of spherical modal liquid crystal lenses,” Opt. Express4(9), 344–352 (1999).
[CrossRef] [PubMed]

Loktev, M. Yu.

Love, G. D.

Naumov, A. F.

Otón, J. M.

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, M. A. Geday, and J. M. Otón, “Electrooptic characterization of tunable cylindrical liquid crystal lenses,” Mol. Cryst. Liq. Cryst.553(1), 211–219 (2012).
[CrossRef]

Patlan, V. V.

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 1. Theory,” Quantum Electron.41(1), 58–64 (2011).
[CrossRef]

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 2. Experiment,” Quantum Electron.41(1), 65–70 (2011).
[CrossRef]

Samagin, S. A.

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 2. Experiment,” Quantum Electron.41(1), 65–70 (2011).
[CrossRef]

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 1. Theory,” Quantum Electron.41(1), 58–64 (2011).
[CrossRef]

Sánchez-Pena, J. M.

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, M. A. Geday, and J. M. Otón, “Electrooptic characterization of tunable cylindrical liquid crystal lenses,” Mol. Cryst. Liq. Cryst.553(1), 211–219 (2012).
[CrossRef]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Q. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electron. Rev.20(3), 260–266 (2012).
[CrossRef]

Urruchi, V.

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Q. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electron. Rev.20(3), 260–266 (2012).
[CrossRef]

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, M. A. Geday, and J. M. Otón, “Electrooptic characterization of tunable cylindrical liquid crystal lenses,” Mol. Cryst. Liq. Cryst.553(1), 211–219 (2012).
[CrossRef]

Vdovin, G.

Vdovin, G. V.

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Y. Loktev, and A. F. Naumov, “Liquid-crystal lenses with a controlled focal length. I. Theory,” Quantum Electron.29(3), 256–260 (1999).
[CrossRef]

Vladimirov, F. L.

Appl. Opt. (1)

J. Disp. Technol. (1)

Y. H. Lin and M. S. Chen, “A pico projection system with electrically tunable optical zoom ratio adopting two liquid crystal lenses,” J. Disp. Technol.8(7), 401–404 (2012).
[CrossRef]

Mol. Cryst. Liq. Cryst. (1)

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, N. Bennis, M. A. Geday, and J. M. Otón, “Electrooptic characterization of tunable cylindrical liquid crystal lenses,” Mol. Cryst. Liq. Cryst.553(1), 211–219 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opto-Electron. Rev. (1)

V. Urruchi, J. F. Algorri, J. M. Sánchez-Pena, M. A. Geday, X. Q. Arregui, and N. Bennis, “Lenticular arrays based on liquid crystals,” Opto-Electron. Rev.20(3), 260–266 (2012).
[CrossRef]

Quantum Electron. (3)

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 2. Experiment,” Quantum Electron.41(1), 65–70 (2011).
[CrossRef]

S. P. Kotova, V. V. Patlan, and S. A. Samagin, “Tunable liquid-crystal focusing device. 1. Theory,” Quantum Electron.41(1), 58–64 (2011).
[CrossRef]

G. V. Vdovin, I. R. Guralnik, S. P. Kotova, M. Y. Loktev, and A. F. Naumov, “Liquid-crystal lenses with a controlled focal length. I. Theory,” Quantum Electron.29(3), 256–260 (1999).
[CrossRef]

Supplementary Material (4)

» Media 1: AVI (2021 KB)     
» Media 2: AVI (355 KB)     
» Media 3: AVI (2044 KB)     
» Media 4: AVI (2940 KB)     

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Figures (11)

Fig. 1
Fig. 1

Modal liquid crystal device proposed. Note drawings are not to scale. (a) Electrode layout and (b) device arrangement.

Fig. 2
Fig. 2

Experimental setup for characterizing the electrooptic response of the LC device.

Fig. 3
Fig. 3

Electrode connections of the LC device. (a) Electrode connection and driving signal definitions and (b) top view of the active area.

Fig. 4
Fig. 4

(a) Experimental and (b) simulated interference patterns when 4Vpkpk are applied to the top substrate.

Fig. 5
Fig. 5

(a, c) Experimental and (b, d) simulated unwrapped phase when 4Vpkpk are applied to the top substrate.

Fig. 6
Fig. 6

The Zernike coefficients of an individual optical element for the arrangement whose unwrapped phase is shown in Fig. 5.

Fig. 7
Fig. 7

(a) Voltage distribution, |U1-U2|, for a one-dimensional array of LC prisms. Experimental (first row) and simulated (second row) for (b) the horizontal and (c) vertical distributed interference patterns.

Fig. 8
Fig. 8

Simulation of a LC tunable prism array with independent elements: (a) electrode layout and driving signal definitions and (b) 3D optical phase shift in the active area (Media 1).

Fig. 9
Fig. 9

The phase profiles for both an ideal prism (dashed line) and the proposed prism (solid line) for 6 Vpkpk.

Fig. 10
Fig. 10

Experimental (first row) and simulated (second row) interference patterns for a two-dimensional matrix of tunable LC axicons.

Fig. 11
Fig. 11

A two-dimensional matrix of tunable LC axicons: (a) Experimental interference patterns (Media 2), (b) 2D simulated in XY plane (Media 3) and (c) 3D simulated unwrapped phase (Media 4).

Tables (1)

Tables Icon

Table 1 Batch of measures carried out when an electrical signal is applied to the device with some constant electrical phases and voltage amplitudes in Vpkpk.

Equations (3)

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

s 2 U= R sq C U t + R sq GU
s 2 U= R sq ( G-jωC )U.
{ s U 1 2 = R sq1 ( G-jωC )( U 1 U 2 ) s U 2 2 = R sq2 ( G-jωC )( U 2 U 1 )

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