Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine. Ed. J.C. Dainty. Galway, June 2007.

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CONVERGING AND DIVERGING LIQUID CRYSTAL LENSES

A. K. KIRBY, P. J. W. HANDS, G. D. LOVE Durham University, Dept. of Physics,

Durham, DH1 3LE, UK

We report on recent work on the application of liquid crystals to variable lenses. We demonstrate the construction and operation of a novel and simple form of modal LC lens which offers both converging and diverging modes of operation, as well as tip/tilt and astigmatism.

1. Introduction

Considerable work has been carried out in the field of electronically variable lenses (see, e.g. [1-3] and these proceedings). We have reported previously on the design and production of modal liquid crystal (LC) lenses [4-5] and their use as adaptive focus elements. We have recently developed a new LC device which overcomes some of the limitations of the modal LC lens;

• The fabrication of the modal LC lens is complicated by the requirement for a high-resistance electrode, which is normally achieved by depositing an extremely thin layer of Indium Tin Oxide (ITO) onto a glass substrate. Producing the required thickness with good uniformity is problematic, and the deposition process typically has a low yield. The new LC device has a simple construction and requires only medium-resistance ITO coated glass substrates, which are rather easier to manufacture.

• A normal modal LC lens can be driven to provide a positive (converging) lens of variable power. The new device can also be driven to provide a lens which can be varied from positive to negative optical powers. The effective optical throw of the lens, for a given cell thickness, is doubled compared to the modal lens. Correspondingly the relaxation time, for a given lens throw, is reduced by a factor of approximately 4.

Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine. Ed. J.C. Dainty. Galway, June 2007. 2

• The optical power of the device along x- and y-axes can be controlled independently, allowing tip, tilt and limited astigmatic correction.

2. Construction and operation

The basic principle of operation of the device is illustrated in figures 1 and 2. One substrate of the device is grounded (lower electrode, as shown), and time-varying voltages (V1, V2) are applied to the opposite sides of the other (upper) electrode. If the V1 & V2 are out of phase (φ =1800) then the RMS of the field between the upper and lower electrodes takes on the form illustrated by the dashed line in figure 2. The solid line indicates the equivalent optical phase

shift. Figure 1. 1-D schematic and 3D illustration of LC device

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Figure 2. Phase (solid) and voltage (dashed) profiles for ΔφV1-V2 =1800

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Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine. Ed. J.C. Dainty. Galway, June 2007.

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By altering the relative phase and voltages of V1 and V2 (φ) and by the addition of a bias-voltage term the shape and scale of the voltage profile, and hence the phase profile, can be adjusted – particularly the ‘plateau’ in the centre of the phase profile can be eliminated. All liquid crystals exhibit an inversion of the dielectric anisotropy at some driving field frequency. For most materials this ‘crossover frequency’ is impractically high to be of use – typically several MHz, at which frequency dielectric losses in the material cause heating and usually melting, taking the material out of the liquid crystal phase. There do exist some materials, collectively known as dual-frequency liquid crystals, which have a low crossover frequency, typically a few kHz. Using on of these materials (Niopik LC1001), we can produce a negative (diverging lens). The effect of driving with a field frequency above it’s crossover frequency is that the LC molecules will tend to realign normal to the applied field, i.e. in the plane of the cell, whereas in the more conventional case of driving with a field frequency below the crossover frequency, the molecules tend to align with the applied field. In other words, driving with a low frequency causes the cell to switch ‘on’ and driving with a high frequency causes the cell to switch ‘off’. This mechanism is normally used to improve switching times of cells; however it can be used to produce a negative-lens form. If both high and low frequency fields are applied simultaneously, the LC molecules respond essentially to the difference in the torques and settle at an equilibrium position. If the cell is biased using a low-frequency drive voltage with no inter-electrode phase difference (φ =0), and a high-frequency drive voltage with φ=1800 are applied simultaneously, then the voltage difference profile, VLF-VHF, and the corresponding optical phase profile, take on the form shown in figure 3.

Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine. Ed. J.C. Dainty. Galway, June 2007. 4

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Figure 3. Production of negative (diverging) lens, using dual-frequency LC materials. Solid line represents the difference between the low frequency bias voltage and the high-frequency structure voltage. The dashed trace represents the corresponding optical phase profile.

3. Results

Figures 4-6 show interferograms and unwrapped phase profiles for converging lens operation with varying drive voltages.

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Figure 4. Interferogram and unwrapped x- and y- phase profiles for Vrms(x,y)=5.65V, Vrms(bias)=2.12V, φ =1800

Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine. Ed. J.C. Dainty. Galway, June 2007.

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Figure 5. Interferogram and unwrapped x- and y- phase profiles for Vrms(x,y)=5.65V, Vrms(bias)=2.82V, φ =1800

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Figure 6. Interferogram and unwrapped x- and y- phase profiles for Vrms(x,y)=4.60V, Vrms(bias)=3.54V, φ =1800

Both the positive and negative (converging and diverging) lens operation of the device and independent control of x- and y- axes is demonstrated in Figure 7, which shows the production of astigmatism.

Proceedings of the 6th International Workshop on Adaptive Optics for Industry and Medicine. Ed. J.C. Dainty. Galway, June 2007. 6

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Figure 7. Interferogram and unwrapped x- and y- phase profile using drive voltages of VxLF=5.65 rms, VxLF_bias=2.12Vrms, φx =φy =1800, VyLF=6.7 Vrms, VyHF=2.35 Vrms

Acknowledgments

The original idea of this method of addressing LCs was proposed by Dr. Alexander Naumov. His help and enthusiasm for LC adaptive optics is gratefully acknowledged. This work was funded by the EPSRC and the EU Eurocores SONS programme.

References

1. S. Kuiper and H.H.W. Hendricks, ”Variable-focus liquid lens for miniature cameras”. Appl. Phys. Lett. 85(7):1128-1130 (2004)

2. A. Kaplan, N. Friedman, and N. Davidson, “Acousto-optic lens with very fast scanning,” Opt. Lett. 26(14):1078-1080 (2001)

3. L.G. Commander, S.E. Day, and D.R. Selviah,, “Variable focal length microlenses,” Optics Comms. 177:157-170 (2000)

4. A.F. Naumov, G.D. Love, M.Yu. Loktev and F.L. Vladimirov, “Control optimization of spherical modal liquid crystal lenses,” Optics Express 4(9):344-352 (1999)

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