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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 24809–24818
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Modal liquid crystal array of optical elements

J. F. Algorri, G. D. Love, and V. Urruchi  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 24809-24818 (2013)
http://dx.doi.org/10.1364/OE.21.024809


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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

1. Introduction

In recent years, liquid crystal (LC) devices have increasingly been used in many non-display applications. LC characteristics such as the Frederick’s effect and high birefringence are crucial for constructing small and lightweight devices that can be controlled by low voltages without requiring any mechanical components. By exploiting such characteristics, LC devices have been notably applied in the fields of optical communications as modulators, switches, filters, photonic optical fibers, and so on; adaptive optics for wavefront correction, beam shaping, and optical tweezers; and liquid crystal lenses.

2. Modal device theory

s2U=Rsq(G-jωC)U.
(2)

3. Structure and modal device operation

4. Experimental setup

The experimental setup, based on a commercial interferometer, is shown in Fig. 2
Fig. 2 Experimental setup for characterizing the electrooptic response of the LC device.
. The interference patterns are measured using a Zygo phase shifting interferometer in a double-pass configuration. LC device was placed, in a standard scheme, between a mirror and a linear polarizer. It has only four external contacts, since two couples of electrodes are connected with each other to the same signal in Fig. 3(a)
Fig. 3 Electrode connections of the LC device. (a) Electrode connection and driving signal definitions and (b) top view of the active area.
. The top view of the active area is depicted in Fig. 3(b). Unwrapped phase was directly obtained by the commercial interferometer in graphs in color by means of phase shifting technique.

5. Simulation and experimental results

The results of this work are presented and described in two steps. In a first stage, the validation of simulation program is established by the comparison of some simulations of a basic approach with their respective experimental measure. The simulation program uses the following input parameters about the device structure and the nematic LC features: thickness = 23 µm, K11 = 1.8, K33 = 6, birefringence = 0.18, dielectric anisotropy = 20.1 and resistivity of high-resistivity layer = 12 MΩ/sq. Differences in the two high resistivity layer thickness, achieved in the fabrication process, are negligible. So that, they are considered equal for simplicity in simulation. In a second phase, a set of advanced arrangements are considered. The device layouts are focused fundamentally to create two kinds of arrays: a one-dimensional array of optics elements working as tunable LC prisms and a two-dimensional matrix with a tunable LC axicon array functionality. Here, we describe the experimental results for validation via a comparison with some simulations carried out previously. The general driving scheme consists of the application of four electrical square signals, with until four different electrical phase shifts, to each electrode. These set ups use opposite electrical phase shifts applied to couples of electrodes. It is required to select one electrode of reference for phase; being 0° the phase of that electrode.

5.1 Validation of the simulation program

In this experiment, identical voltage amplitude without electrical phase shifts between electrodes is applied to electrodes of the top substrate (V1 = V2 = 4 Vpkpk). The bottom electrodes are connected to ground (V3 = V4 = 0 Vpkpk). This causes a hyperbolic voltage distribution and small voltage gradients, suffering from several aberrations. Figure 4
Fig. 4 (a) Experimental and (b) simulated interference patterns when 4Vpkpk are applied to the top substrate.
shows a comparison of the interference pattern of the obtained simulations with experimental measurements. The active area shows a surrounding effect caused by the optical glue in the manufacturing process that generates a constant optical phase shift in those zones. This inconvenience causes a light difference in size between experimental and simulated data. Despite this, simulations show acceptable agreement with the experimental results.

Phase unwrapping is realized by a phase-shifting technique from interference patterns. Figure 5
Fig. 5 (a, c) Experimental and (b, d) simulated unwrapped phase when 4Vpkpk are applied to the top substrate.
shows the unwrapped phase in XY and YZ planes. The glass substrate plane is used as the reference XY plane. The phase unwrapping and simulations reveal a peak-to-value optical phase shift over the active area of 1.6λ for λ = 632.8 nm (around 7.5π). The differences between the simulations and the experimental measurements could be caused by deviations in the input parameters considered just like the hypothesis of thickness uniformity of the high resistivity layers, in simulation, or a high sensitivity to temperature of the experimental device.

The comparison of the unwrapped phases, experimental and simulated, validates the capacity of the simulation program to reproduce these profiles. However, the experimental reconstruction of the phase by the Zygo interferometer is not a simple task for this active area due to the restricted resolution of the interference pattern images. That restriction motivated the interference patterns were the only parameter obtained experimentally. On the contrary, simulation program modeled all the parameters such as the voltage distribution or the unwrapped phase and could be considered to test the device and to adjust better-quality wavefronts.

The quality of the optical elements of this arrangement was quantified by the aberration tests. The aberration coefficients were calculated by comparing the phase profile of one optical element with that of a reference sphere whose radius was the maximum phase shift for this approach. The result reveals that this first configuration is restricted mainly by tetrafoil (Z14) and spherical (Z12) aberrations. Figure 6
Fig. 6 The Zernike coefficients of an individual optical element for the arrangement whose unwrapped phase is shown in Fig. 5.
shows a graph with the magnitudes of the 36 Zernike coefficients where the spherical aberration is especially noticeable. The tetrafoil aberration is mainly caused by the square aperture of the active area in this scheme with the substrates arranged so that their electrodes are oriented orthogonal to each other. Finally, some coma aberrations (Z7, Z8) seem less relevant to the phase deviation.

5.2 A one-dimensional array of tunable LC prisms

The result of applying this control is indeed a controllable one-dimensional LC prism array. For controlling the optical phase profile of the optical elements of the whole array simultaneously, only the voltage amplitude is necessary. However, for advanced independent control of each individual stripped-element of the array, electrical signals with phase shifts between all the electrodes are employed. The result of this approach is simulated using the original structure with the six electrodes enabled [see Fig. 8(a)
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).
]; experimental could not be performed by the current electrode setting. Figure 8(b) includes a recorded video of the unwrapped phase for a specific sequence of amplitude and electrical phase shift. Signal frequency was 1 kHz.

The quality of one prism of the one-dimensional array was checked by evaluating the RMS wavefront deviation. An ideal prism has been taken as a reference prism. Figure 9
Fig. 9 The phase profiles for both an ideal prism (dashed line) and the proposed prism (solid line) for 6 Vpkpk.
shows the comparison of both prism profiles for the higher voltage, 6 Vpkpk.

5.3 A two-dimensional matrix of tunable LC axicons

The prospective applications of the LC device proposed for adaptive optics can be performed for converting a parallel laser beam into four rings so as to create a set of four non-diffractive Bessel beams or for focusing a parallel beam into four controllable long focus depths that can be electrically controlled.

The quantification of the optical quality of an axicon of the two-dimensional matrix could be analogously obtained as with the prism arrangement. Two planes, length and width, must be considered, instead of only the width plane. Once more, an ideal axicon could be achieved by optimizing the manufacturing techniques.

6. Conclusions

Acknowledgments

Authors acknowledge funding support from the Spanish Ministerio de Economía y Competitividad (grant no. TEC2009-13991-C02-01) and Comunidad de Madrid (grant no. FACTOTEM2 S2009/ESP/1781). This work was also funded by the Carlos III University (UC3M) under the Researchers Mobility Program.

References and links

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. Express 4(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. Express 15(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]

OCIS Codes
(230.0230) Optical devices : Optical devices
(230.3720) Optical devices : Liquid-crystal devices

ToC Category:
Optical Devices

History
Original Manuscript: August 14, 2013
Revised Manuscript: September 26, 2013
Manuscript Accepted: September 27, 2013
Published: October 9, 2013

Citation
J. F. Algorri, G. D. Love, and V. Urruchi, "Modal liquid crystal array of optical elements," Opt. Express 21, 24809-24818 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-24809


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References

  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]

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