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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 7384–7389
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Sub-millisecond, high stroke phase modulation using polymer network liquid crystals

Gordon D. Love, Andrew K. Kirby, and Robert A. Ramsey  »View Author Affiliations


Optics Express, Vol. 18, Issue 7, pp. 7384-7389 (2010)
http://dx.doi.org/10.1364/OE.18.007384


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Abstract

We describe the production of a high speed, and high stroke, phase modulator using a polymer network liquid crystal device. We present data showing fast response times (sub millisecond) in a device which can operate at visible wavelengths with a simple electrical addressing scheme.

© 2010 OSA

1. Introduction

High-speed phase (and polarization) modulation using liquid crystals (LCs) can be used in a wide variety of applications, including adaptive optics [1

1. M. Langlois, C. D. Saunter, C. N. Dunlop, R. Myers, and G. D. Love, “Multiconjugate adaptive optics: laboratory experience,” Opt. Express 12(8), 1689–1699 (2004). [CrossRef] [PubMed]

,2

2. D. Dayton, S. Browne, J. Gonglewski, and S. Restaino, “Characterization and Control of a Multielement Dual-Frequency Liquid-Crystal Device for High-Speed Adaptive Optical Wave-Front Correction,” Appl. Opt. 40(15), 2345–2355 (2001). [CrossRef] [PubMed]

], switchable lenses [3

3. M. Y. Loktev, V. N. Belopukhov, F. L. Vladimirov, G. V. Vdovin, G. D. Love, and A. F. Naumov, “Wave front control systems based on modal liquid crystal lenses,” Rev. Sci. Instrum. 71(9), 3290–3297 (2000). [CrossRef]

,4

4. M. Ye and S. Sato, “Liquid crystal lens with focus movable along and off axis,” Opt. Commun. 225(4–6), 277–280 (2003). [CrossRef]

], and optical tweezing [5

5. M. Reicherter, S. Zwick, T. Haist, C. Kohler, H. Tiziani, and W. Osten, “Fast digital hologram generation and adaptive force measurement in liquid-crystal-display-based holographic tweezers,” Appl. Opt. 45(5), 888–896 (2006). [CrossRef] [PubMed]

,6

6. P. J. W. Hands, S. A. Tatarkova, A. K. Kirby, and G. D. Love, “Modal liquid crystal devices in optical tweezing: 3D control and oscillating potential wells,” Opt. Express 14(10), 4525–4537 (2006). [CrossRef] [PubMed]

]. In order to achieve analog (continuously variable) phase control. nematic LCs are normally used, but they suffer from the problem of relatively slow switching speeds. For small phase shifts (around half a visible wavelength) the switching speeds are around 10ms, but for larger phase shifts (more than a wave) the response times are slower than 1 second. There is a large body of literature on techniques to produce fast switching LC phase retarders, including pi-cells [7

7. P. J. Bos and K. R. Beran, “The pi-cell, A Fast Liquid-Crystal Optical Switching Device,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 113(1), 329–339 (1984). [CrossRef]

] and the transient nematic effect [8

8. S. T. Wu and C. S. Wu, “High-speed liquid-crystal modulators using transient nematic effect,” J. Appl. Phys. 65(2), 527 (1989). [CrossRef]

] – although both of these techniques involve limiting the range of phase modulation. Ultimately, the slow relaxation (turn-off) times in nematic LCs is because molecular reorientation is caused by the relatively weak elastic interaction with the LC cell’s alignment layer. Dual frequency LCs circumvent this problem by using an electric field to reorient the LC molecules, and hence the cell can be driven off as well as on [2

2. D. Dayton, S. Browne, J. Gonglewski, and S. Restaino, “Characterization and Control of a Multielement Dual-Frequency Liquid-Crystal Device for High-Speed Adaptive Optical Wave-Front Correction,” Appl. Opt. 40(15), 2345–2355 (2001). [CrossRef] [PubMed]

,9

9. C. R. Stein, “A Two-Frequency Coincidence Addressing Scheme for Nematic-Liquid-Crystal Displays,” Appl. Phys. Lett. 19(9), 343 (1971). [CrossRef]

11

11. H. Q. Xianyu, S. T. Wu, and C. L. Lin, “Dual frequency liquid crystals: a review,” Liquid Crystals 36(6), 717–726 (2009). [CrossRef]

]. The control of dual frequency LCs is notoriously difficult, but this can be made simpler by use of either an optical [12

12. V. A. Dorezyuk, A. F. Naumov, and V. I. Shmal’gauzen, “Control of liquid crystal correctors in adaptive optical systems,” Sov. Tech. Phys. 34, 1389 (1989).

] or electrical [13

13. A. K. Kirby and G. D. Love, “Fast, large and controllable phase modulation using dual frequency liquid crystals,” Opt. Express 12(7), 1470–1475 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-7-1470. [CrossRef] [PubMed]

] feedback system. An alternative method involves increasing the effective elastic interaction within the bulk of the LC by introducing a polymer network in the LC material (PNLCs) [14

14. A. Jákli, D. R. Kim, L. C. Chien, and A. Saupe, “Effect of a polymer network on the alignment and the rotational viscosity of a nematic liquid crystal,” J. Appl. Phys. 72(7), 3161 (1992). [CrossRef]

,15

15. Y. H. Fan, H. Ren, and S. T. Wu, “Electrically switchable Fresnel lens using a polymer-separated composite film,” Opt. Express 13(11), 4141–4147 (2005). [CrossRef] [PubMed]

]. In such devices a polymer network is distributed throughout the LC layer and thus the interaction with the elastic restoring forces acting on the LC is stronger and the response times are reduced. Millisecond response times have been reported using PNLCs [16

16. Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233 (2004). [CrossRef]

18

18. B. Wang, G. Zhang, A. Glushchenko, J. L. West, P. J. Bos, and P. F. MacManamon, “Stressed liquid crystal optical phased array for fast tip-tilt awavefront correction,” Appl. Phys. (Berl.) 44, 7754 (2005).

]. The trade-off for an effective increase in spring constants, and hence increased speed, is that increased voltages are required to turn the devices on. For many applications this is not a serious limitation. A more critical problem is that the index mis-match between the polymer network and the liquid crystal material can produce light scattering – and therefore device operation can be limited to the infrared, where the scattering is reduced.

In this paper we report on a fabrication technique that produces a high speed PNLC which shows sub-millisecond response times with a large phase depth and operation at visible wavelengths.

2. Device fabrication

To prepare the polymer-network liquid crystal (PNLC) device we mix together a high loading (typically 80%) of Merck’s E series liquid crystal, namely E7, in a photopolymerizable mixture of both thiol-ene and acrylate monomers at specific concentrations. We have found that both types of polymerization processes give very favorable results in overall device performance. Device characteristics such as response time, contrast ratio and residual retardance are strongly dependent on the concentrations of both step-type and chain-type polymerization processes in the material bulk. The rapid growth of the polymer network utilizing acrylates (chain-type polymerization) is critical in developing network rigidity while the slow growth of the thiol-ene network (step-type polymerization) develops both a highly crosslinked network while still allowing some elasticity in the bulk for the shear deformation process. The mixed LC and photopolymer syrup is then heated above the clearing point and drop filled between two heated ITO (indium-tin-oxide) fused silica substrates separated by aerosol dispersed spacer balls. To initiate the polymerization process the LC device was illuminated with UV-light in a two-step curing process [17

17. J. L. West, G. Zhang, A. Glushchenko, and Y. Reznikov, “Fast birefringent mode stressed liquid crystal,” Appl. Phys. Lett. 86(3), 031111 (2005). [CrossRef]

]. In the initial step, the LC device is exposed to UV-light (365nm) at an intensity of 45 mW/cm2 for 60 minutes while being held at a temperature of 105°C, which is higher than the clearing point for the LC/polymer mixture (~60°C). For the second stage of the cure process the LC device is allowed to cool rapidly into the nematic phase for the LC, then the device is illuminated for an additional 60 minutes at an intensity of 20 mW/cm2 under ambient conditions.

Since the ITO surface has no alignment treatment the device appears opaque after the curing process. After successful UV exposure to the device the LC domains in the polymer network are randomly distributed, as well as randomly aligned (see Fig. 1(a)
Fig. 1 Shearing effects on LC molecular alignment in a PNLC device. (a) Before shear and (b) after shear. The glass substrates are shown in blue, and the ITO electrode as a red layer. The red ellipse schematically show the LC molecules, and the thin black lines represent the polymer network.
). The PNLC scatters light due to the refractive index mis-match between the randomly aligned LC and polymer. For our cured polymer system we have a refractive index of np = 1.525 which is close to the ordinary refractive index of the commercial LC mixture E7, no = 1.522 (λ = 589nm, 25°C). To minimize the off-state scattering events we must align the bulk of the LC. In order to align the LC molecules in a uniform direction, a shearing process is applied to the top substrate while the bottom substrate is held in place. Typical shearing distances are on the order of 300-400μm and are cell gap dependent. The shearing process is done with a precision stage that allows optical feedback of the exact retardance values achieved during the shearing process (see Fig. 1(b)). This allows for both uniform control over the retardance across the clear aperture as well as determining the precise value of retardance at the operational wavelength of the device. As the shearing process nears completion we apply a rapid cure urethane-acrylate around the perimeter of the cell that locks in the LC alignment and optical properties of the device, including uniform retardance, optical transmission and low transmitted wavefront error.

After shearing the LC molecular alignment is such that the index mis-match between the LC and the polymer is minimized and scattering is essentially eliminated except in the shorter wavelengths (< 450nm). Current research is underway for successful device operation in the shorter wavelength regions (350nm- 450nm). For these devices modified curing processes are being developed which eliminate most of the scattering events. Figure 2
Fig. 2 Effect of shearing process on the transmission of a PNLC device between crossed polarizers, as a function of wavelength showing that shearing dramatically reduces the effect of scattering.
shows the effect of the shearing process on minimizing scattering events and the optical transmission on a device with an 8μm cell gap.

Since the shearing force has a gradient distribution, with the maximum force being concentrated along the top substrate and the smaller force being seen on the bottom substrate, it is expected that the bulk of the device will have varying LC tilt angles [19

19. Y. H. Wu, Y. H. Lin, Y. Q. Lu, H. Ren, Y. H. Fan, J. R. Wu, and S. T. Wu, “Submillisecond response variable optical attenuator based on sheared polymer network liquid crystal,” Opt. Express 12(25), 6382–6384 (2004). [CrossRef]

]. Near the top substrate the shearing force is strong so the LC molecular alignment will be nearly parallel to the substrate. Deeper into the bulk of the material the shear force is weaker so the LC molecular alignment is not as pronounced and because of this the LC tilt angle will be larger. This gradient distribution of LC molecular tilt makes some very important, as well as degrading, contributions to the electro-optical properties of the device. As tilt angle increases the threshold behavior of an LC changes considerably, and in our device this tends to smear the threshold behavior of the device. Without this smearing of the threshold behavior the device would have a much higher threshold voltage (5-7 Volts) due to the polymer network, but with the gradient distribution of tilt these PNLCs have a lower threshold (3-5 Volts) allowing for lower driving fields when compared with stretched polymer dispersed liquid crystal devices [20

20. O. A. Aphonin, Y. V. Panina, A. B. Pravdin, and D. A. Yakovlev, “Optical-properties of stretched polymer-dispersed liquid-crystal films,” Liq. Cryst. 15(3), 395–407 (1993). [CrossRef]

]. The degrading aspects of the distribution of molecular tilts is that it does not allow for a definitive dark state between crossed polarizers (null-state – when the device is used as a display, rather than as a phase modulator). This in turn effects the overall contrast ratio of the device. Great lengths were taken to understand this phenomenon and additional processing steps during fabrication minimize this effect and allow for typical devices to achieve 500:1 contrast ratios (again for display applications). Another aspect of the gradient tilt is that it reduces the effective birefringence of the LC layer. This effect is simply compensated for by increasing the cell gap as required.

3. Switching speed results

Response times of LCs are typically quoted either as a time to fully turn on or off, or the time to go from light to dark in a display. For phase modulation applications, typically one needs the switching times from an arbitrary part of phase-voltage response curve to another arbitrary part. Furthermore, these times are often much slower than the full switching times. We produced a PNLC cell with a total stroke of just over 2 waves (at 633nm), and measured the time to switch from an arbitrary part of the stroke range to any other part. The electrical control was a simple 15 KHz AC voltage that was switched from one value to another (i.e. no complicated intermediate switching voltages are needed, such as those used in the transient nematic or dual frequency effects). The results are shown in Fig. 3
Fig. 3 Response time measurements of the PNLC showing the time taken to switch from an arbitrary starting phase (as shown on the x-axis) to an arbitrary end phase (shown on the y-axis). A phase of 0 corresponds to 0 applied voltage. The diagonal (bottom left to top right) values are all zero as then no switching occurs. The maximum response time (for 2 waves switching).
. The average value of the switching speed is 605 μs, and the maximum value (to switch from 2 waves to 0) is only 1.2 ms. This compares with a value of over a second for material E7 in a 10 μm cell. Importantly, these results show that it is possible to switch between arbitrary phase values without any complicated electrical addressing scheme in times typically less than a millisecond.

4. Phase ripple measurements

Nematic LCs are generally driven by AC fields in order to avoid electro-chemical degradation of the LC material. The fact that conventional LC molecules rotate relatively slowly is an advantage in this sense as it means that LC responds to the rms value of the field and the LC does not flip very rapidly in response to the applied field. If one applies a large AC field to a conventional nematic LC cell between polarizers then the transmitted intensity fluctuates. This residual ripple is caused by the LC molecules attempting to follow the applied field - but fortunately the effect is small. When one is dealing with much faster LC materials then this effect will be larger (for a given frequency of the applied voltage). We measured this by placing our PNLC device between crossed polarizers and monitored the intensity of a transmitted HeNe laser on a photodiode recording the amplitude of the residual intensity fluctuations. This was converted into a residual phase fluctuation, by noting that the transmitted intensity, I, of a beam through an LC cell of retardance, δ, at an angle 45° between crossed polarizers is given by I~sin2(δ2). The results are shown in Fig. 4
Fig. 4 Residual phase fluctuations in the PNLC caused by fluctuations in the LC director as it attempts to follow the applied AC field. A fixed amplitude AC voltage was applied to a cell, placed between crossed polarizer’s, corresponding to a particular phase (as indicated on the x-axis) and the resultant intensity ripple on the transmitted light was used to calculate the residual phase ripple, as indicated on the y-axis. The error bars are small compared to the symbol sizes.
. When the phase is zero (which corresponds to no applied voltage) there is clearly no residual ripple, and this increases as the phase (and hence voltage) increases.

The graph extends up to 1.5 waves, at which point the residual was around 22°. Whether or not this is significant depends on the application – but for adaptive optics this corresponds to a peak to valley phase error of approximately λ/16 which is very small. The ripple voltage decreases with increasing applied frequency. However there is a balance to be reached, as if the frequency is increased too much then the performance degrades with other effects such as cell heating and a lack of electro-optical response.

5. Scattering

In this section we present results of scattering measurements. We measured both “static scattering”, i.e. scattering produced when the PNLC has a fixed AC voltage applied to it, and “dynamic scattering”, i.e. scattering produced when the PNLC is switched between two phase values. In both experiments a polarized laser was transmitted through the LC, with the polarization axis aligned with the extraordinary axis, and then focused onto a pinhole in front of a photodiode. There was no polarizer after the cell. Any changes in scattering – as voltages are applied to the cell – will scatter light away from the photodetector, and these will be measured by a decrease in intensity. Our results are therefore referenced to the scattering when no voltage is applied to the cell – and we assume that in this case the scattering is small. The results for both static and dynamic scattering are shown in Fig. 5
Fig. 5 (a) Static scattering and (b) dynamic scattering in a PNLC. The results are normalized to the off state. The error bars are small compared to the symbol sizes.
.

From the graph of static scattering it can be seen that the change in scattering is small. The intensity goes above the normalized value of 1 – given the nature of the polymer/liquid crystal morphology in the cell there are scattering events that occur due to refractive index mismatch in the off state (on the order of 0.075) and as the cell is activated this mismatch becomes less due to LC molecules aligning with the field (on the order of 0.003), causing the intensity to increase. The right hand plot shows the dynamic scattering – i.e. the drop in intensity that occurs whilst the cell switches. Again – whether or not these values are significant depends on the application in mind, but the key point here is that these values are similar to those measured in conventional nematic LC cells.

6. Conclusions

We have demonstrated the fabrication and implementation of a high speed PNLC device which operates at visible wavelengths and which can be controlled simply.

Acknowledgements

Thanks are due to Marc Pritchard at Durham who performed some early experiments on PNLCs and to Tom Baur at Meadowlark Optics.

References and links

1.

M. Langlois, C. D. Saunter, C. N. Dunlop, R. Myers, and G. D. Love, “Multiconjugate adaptive optics: laboratory experience,” Opt. Express 12(8), 1689–1699 (2004). [CrossRef] [PubMed]

2.

D. Dayton, S. Browne, J. Gonglewski, and S. Restaino, “Characterization and Control of a Multielement Dual-Frequency Liquid-Crystal Device for High-Speed Adaptive Optical Wave-Front Correction,” Appl. Opt. 40(15), 2345–2355 (2001). [CrossRef] [PubMed]

3.

M. Y. Loktev, V. N. Belopukhov, F. L. Vladimirov, G. V. Vdovin, G. D. Love, and A. F. Naumov, “Wave front control systems based on modal liquid crystal lenses,” Rev. Sci. Instrum. 71(9), 3290–3297 (2000). [CrossRef]

4.

M. Ye and S. Sato, “Liquid crystal lens with focus movable along and off axis,” Opt. Commun. 225(4–6), 277–280 (2003). [CrossRef]

5.

M. Reicherter, S. Zwick, T. Haist, C. Kohler, H. Tiziani, and W. Osten, “Fast digital hologram generation and adaptive force measurement in liquid-crystal-display-based holographic tweezers,” Appl. Opt. 45(5), 888–896 (2006). [CrossRef] [PubMed]

6.

P. J. W. Hands, S. A. Tatarkova, A. K. Kirby, and G. D. Love, “Modal liquid crystal devices in optical tweezing: 3D control and oscillating potential wells,” Opt. Express 14(10), 4525–4537 (2006). [CrossRef] [PubMed]

7.

P. J. Bos and K. R. Beran, “The pi-cell, A Fast Liquid-Crystal Optical Switching Device,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 113(1), 329–339 (1984). [CrossRef]

8.

S. T. Wu and C. S. Wu, “High-speed liquid-crystal modulators using transient nematic effect,” J. Appl. Phys. 65(2), 527 (1989). [CrossRef]

9.

C. R. Stein, “A Two-Frequency Coincidence Addressing Scheme for Nematic-Liquid-Crystal Displays,” Appl. Phys. Lett. 19(9), 343 (1971). [CrossRef]

10.

H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter, “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25(4), 186 (1974). [CrossRef]

11.

H. Q. Xianyu, S. T. Wu, and C. L. Lin, “Dual frequency liquid crystals: a review,” Liquid Crystals 36(6), 717–726 (2009). [CrossRef]

12.

V. A. Dorezyuk, A. F. Naumov, and V. I. Shmal’gauzen, “Control of liquid crystal correctors in adaptive optical systems,” Sov. Tech. Phys. 34, 1389 (1989).

13.

A. K. Kirby and G. D. Love, “Fast, large and controllable phase modulation using dual frequency liquid crystals,” Opt. Express 12(7), 1470–1475 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-7-1470. [CrossRef] [PubMed]

14.

A. Jákli, D. R. Kim, L. C. Chien, and A. Saupe, “Effect of a polymer network on the alignment and the rotational viscosity of a nematic liquid crystal,” J. Appl. Phys. 72(7), 3161 (1992). [CrossRef]

15.

Y. H. Fan, H. Ren, and S. T. Wu, “Electrically switchable Fresnel lens using a polymer-separated composite film,” Opt. Express 13(11), 4141–4147 (2005). [CrossRef] [PubMed]

16.

Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233 (2004). [CrossRef]

17.

J. L. West, G. Zhang, A. Glushchenko, and Y. Reznikov, “Fast birefringent mode stressed liquid crystal,” Appl. Phys. Lett. 86(3), 031111 (2005). [CrossRef]

18.

B. Wang, G. Zhang, A. Glushchenko, J. L. West, P. J. Bos, and P. F. MacManamon, “Stressed liquid crystal optical phased array for fast tip-tilt awavefront correction,” Appl. Phys. (Berl.) 44, 7754 (2005).

19.

Y. H. Wu, Y. H. Lin, Y. Q. Lu, H. Ren, Y. H. Fan, J. R. Wu, and S. T. Wu, “Submillisecond response variable optical attenuator based on sheared polymer network liquid crystal,” Opt. Express 12(25), 6382–6384 (2004). [CrossRef]

20.

O. A. Aphonin, Y. V. Panina, A. B. Pravdin, and D. A. Yakovlev, “Optical-properties of stretched polymer-dispersed liquid-crystal films,” Liq. Cryst. 15(3), 395–407 (1993). [CrossRef]

OCIS Codes
(120.5060) Instrumentation, measurement, and metrology : Phase modulation
(160.3710) Materials : Liquid crystals

ToC Category:
Optical Devices

History
Original Manuscript: February 12, 2010
Revised Manuscript: March 19, 2010
Manuscript Accepted: March 19, 2010
Published: March 24, 2010

Citation
Gordon D. Love, Andrew K. Kirby, and Robert A. Ramsey, "Sub-millisecond, high stroke phase modulation using polymer network liquid crystals," Opt. Express 18, 7384-7389 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7384


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References

  1. M. Langlois, C. D. Saunter, C. N. Dunlop, R. Myers, and G. D. Love, “Multiconjugate adaptive optics: laboratory experience,” Opt. Express 12(8), 1689–1699 (2004). [CrossRef] [PubMed]
  2. D. Dayton, S. Browne, J. Gonglewski, and S. Restaino, “Characterization and Control of a Multielement Dual-Frequency Liquid-Crystal Device for High-Speed Adaptive Optical Wave-Front Correction,” Appl. Opt. 40(15), 2345–2355 (2001). [CrossRef] [PubMed]
  3. M. Y. Loktev, V. N. Belopukhov, F. L. Vladimirov, G. V. Vdovin, G. D. Love, and A. F. Naumov, “Wave front control systems based on modal liquid crystal lenses,” Rev. Sci. Instrum. 71(9), 3290–3297 (2000). [CrossRef]
  4. M. Ye and S. Sato, “Liquid crystal lens with focus movable along and off axis,” Opt. Commun. 225(4–6), 277–280 (2003). [CrossRef]
  5. M. Reicherter, S. Zwick, T. Haist, C. Kohler, H. Tiziani, and W. Osten, “Fast digital hologram generation and adaptive force measurement in liquid-crystal-display-based holographic tweezers,” Appl. Opt. 45(5), 888–896 (2006). [CrossRef] [PubMed]
  6. P. J. W. Hands, S. A. Tatarkova, A. K. Kirby, and G. D. Love, “Modal liquid crystal devices in optical tweezing: 3D control and oscillating potential wells,” Opt. Express 14(10), 4525–4537 (2006). [CrossRef] [PubMed]
  7. P. J. Bos and K. R. Beran, “The pi-cell, A Fast Liquid-Crystal Optical Switching Device,” Mol. Cryst. Liq. Cryst. (Phila. Pa.) 113(1), 329–339 (1984). [CrossRef]
  8. S. T. Wu and C. S. Wu, “High-speed liquid-crystal modulators using transient nematic effect,” J. Appl. Phys. 65(2), 527 (1989). [CrossRef]
  9. C. R. Stein, “A Two-Frequency Coincidence Addressing Scheme for Nematic-Liquid-Crystal Displays,” Appl. Phys. Lett. 19(9), 343 (1971). [CrossRef]
  10. H. K. Bücher, R. T. Klingbiel, and J. P. VanMeter, “Frequency-addressed liquid crystal field effect,” Appl. Phys. Lett. 25(4), 186 (1974). [CrossRef]
  11. H. Q. Xianyu, S. T. Wu, and C. L. Lin, “Dual frequency liquid crystals: a review,” Liquid Crystals 36(6), 717–726 (2009). [CrossRef]
  12. V. A. Dorezyuk, A. F. Naumov, and V. I. Shmal’gauzen, “Control of liquid crystal correctors in adaptive optical systems,” Sov. Tech. Phys. 34, 1389 (1989).
  13. A. K. Kirby and G. D. Love, “Fast, large and controllable phase modulation using dual frequency liquid crystals,” Opt. Express 12(7), 1470–1475 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-7-1470 . [CrossRef] [PubMed]
  14. A. Jákli, D. R. Kim, L. C. Chien, and A. Saupe, “Effect of a polymer network on the alignment and the rotational viscosity of a nematic liquid crystal,” J. Appl. Phys. 72(7), 3161 (1992). [CrossRef]
  15. Y. H. Fan, H. Ren, and S. T. Wu, “Electrically switchable Fresnel lens using a polymer-separated composite film,” Opt. Express 13(11), 4141–4147 (2005). [CrossRef] [PubMed]
  16. Y. H. Fan, Y. H. Lin, H. Ren, S. Gauza, and S. T. Wu, “Fast-response and scattering free polymer network liquid crystals for infrared light modulators,” Appl. Phys. Lett. 84(8), 1233 (2004). [CrossRef]
  17. J. L. West, G. Zhang, A. Glushchenko, and Y. Reznikov, “Fast birefringent mode stressed liquid crystal,” Appl. Phys. Lett. 86(3), 031111 (2005). [CrossRef]
  18. B. Wang, G. Zhang, A. Glushchenko, J. L. West, P. J. Bos, and P. F. MacManamon, “Stressed liquid crystal optical phased array for fast tip-tilt awavefront correction,” Appl. Phys. (Berl.) 44, 7754 (2005).
  19. Y. H. Wu, Y. H. Lin, Y. Q. Lu, H. Ren, Y. H. Fan, J. R. Wu, and S. T. Wu, “Submillisecond response variable optical attenuator based on sheared polymer network liquid crystal,” Opt. Express 12(25), 6382–6384 (2004). [CrossRef]
  20. O. A. Aphonin, Y. V. Panina, A. B. Pravdin, and D. A. Yakovlev, “Optical-properties of stretched polymer-dispersed liquid-crystal films,” Liq. Cryst. 15(3), 395–407 (1993). [CrossRef]

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