1. Introduction

Lenses with electrically tunable focal length, such as liquid crystal (LC) lenses [1–14] and liquid lenses [15, 16], are currently topics of broad interest. Since there are no moving mechanical parts, they are potentially smaller, lighter, and cheaper than the tunable lenses fabricated using conventional glass lenses. However, it is difficult for these variable-focus lenses to have a large aperture (diameter larger than 10 mm, for example), and their applications are then confined to fields such as in camera phones, for example, where the required aperture is limited to within only a few millimeters. In many applications, however, a larger aperture is expected. Some LC lenses reported by the authors [1, 7, 10], and that by Naumov, et al. using a modal control approach [5] may have large apertures, but it appears that it is not easy to preserve optical quality when focal lengths are changed. The LC lens using a circular-hole-patterned electrode proposed by the authors is simple in structure [6] and exhibits high optical quality, in particular, when it is driven by two voltages [11, 17, 18]. The LC cell will have phase transformations close to those of glass lenses at certain voltage ranges if an appropriate ratio of the hole diameter to the distance of the patterned electrode from the LC layer is ensured. So it is possible, at least in principle, to enlarge the lens aperture by placing a thick glass substrate between the patterned electrode and the LC layer. However, since the driving voltages are nearly linearly proportional to the thickness of the substrate, they may become too high for practical use when a thick substrate is employed. Using high dielectric constant glass substrates may lower the voltages to some extent [19], but they are still too high when a lens with a diameter over 10 mm is fabricated. In this paper, we report the realization of a LC lens with a large aperture but low driving voltages using a thin layer of material of weak conductivity. The employment of weakly conductive layers has been previously used [4, 5] to distribute desired voltage levels to reorient LC directors to form lens distribution. In this work, the conductive layer that smoothes the electric field is independent of the electrodes, so that the use of two-voltage-driving technology [11] to realize a high-quality LC lens is possible. A lens with a diameter of 15 mm is fabricated, and its properties are measured. The driving voltages are only around 10 V_rms, and good lens quality is observed.

2. Liquid crystal lens with a circular-hole-patterned electrode

In a LC lens with a circular-hole-patterned electrode [6, 11], a nearly symmetrical but spatial nonuniform electric field is formed in the LC layer when voltages are applied. The field reorients the LC directors and sets up a nearly symmetrical distribution of refractive index that is changeable with the applied voltages. If the geometrical structure of the cell, in particular the ratio of the hole diameter D to the distance d of the patterned electrode from the LC layer, is appropriate, the LC cell will have phase transformations close to those of conventional glass lenses at certain voltage ranges and becomes a lens with an electrically tunable focal length. The distance d of the hole-patterned electrode and the LC layer is kept by a dielectric material (usually a glass substrate) placed between them. If for a given diameter D the thickness of the glass substrate, that is the distance d, is suitable, a smoothly varying electric field will be distributed in the LC layer in a circular area (hole) approximately equal to that of the circular hole area in the electrode. A lens with almost the same aperture as that of the circular hole in the electrode then is possible. If, on the other hand, d is too large, the gradient of the electric field in the LC layer will become so small that the formation of a lens-like distribution of the refractive index in the LC layer will become impossible. If it is too small, the gradient electric field will be confined only near the boundary, and in the central part of the hole area there will be no necessary electric field to form the desired lens-like distribution of refractive index. There is an optimized ratio of D to d for lens operation. So to fabricate a LC lens with a large diameter, a thick substrate between the hole-patterned electrode and the LC layer is necessary.

The reorientation state of LC directors and hence lens properties are determined by potential differences across the two surfaces of the LC layer. If a thick glass substrate is used for a lens of large aperture, large portions of the applied voltages are dropped on the glass substrate. High driving voltages are needed to maintain required potential differences on the LC layer. For example, a distance d of approximately 800 µm between the patterned electrode and the LC layer and driving voltages of approximately 90 V_rms for a LC layer of 30 µm thickness are required for a LC lens with a diameter of D=2.0 mm [19]. If D becomes 15.0 mm (the same as that of the cell used in this work), d of approximately 6 mm and voltages as high as approximately 270 V_rms for a LC layer of 75 µm thickness would be required.

3. Lowering driving voltages using thin layer of weakly conductive material

The problem of high voltage is solved in this work by placing a layer of material of weak conductivity between the hole-patterned electrode and the LC layer. The nonuniform electric field induced by the hole-patterned electrode in the cell arouses a radial electric current that redistributes the electric charges in the weakly conductive layer. An electric field resulting from the charge redistribution then occurs in the conductive layer, the direction of which is opposite to that of the radial component of the nonuniform electric field created by the patterned electrode. As a result, the abruptly changing potential caused by the patterned electrode is smoothed by the conductive layer. Though the net charge in the conductive layer remains at zero, the redistribution of the charges in the cell caused by the layer flattens the profile of the potential difference across the LC layer. The radial current in the weakly conductive layer is so small that some time is required before the layer becomes equipotential. The symbol of the charges in the two electrodes changes alternately since the cell that is driven by AC voltages. The radial current then periodically changes the flowing direction. If the symbol change of the charges, the speed of which is determined by the frequency f of the driving voltages, takes place before the layer becoming equipotential, there is always a radial current in the conductive layer. A gradient potential distribution in the layer can then be maintained, leading to a gradual distribution of an electric field in the LC layer, which may form a lens-like distribution of refractive index. Then, an LC lens may be possible if amplitude and frequency of the applied voltage are properly adjusted.

 

Fig. 1. (a) Structure of the LC cell. (b) Structure of the patterned electrode.

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4. Experiment

The LC lens used in our experiment is shown in Fig. 1. The cell is driven by two voltages, via indium tin oxide (ITO) electrodes, and its structure is similar to that reported in Ref. [19] except that a chamber of 75 µm thickness between the hole-patterned electrode and the LC layer is formed by glass substrates 2 and 3. The patterned electrode on substrate 3 shown in Fig. 2(b) is composed of an outer part for the V ₁ application and an inner part for the V ₂ application. V ₁ and V ₂ are sine waves and are in phase. There is a circular hole of D=15 mm diameter in the center of the outer part. The inner part of the circular shape of 14 mm diameter and concentric with the circular hole is surrounded by the outer part. A thin ITO line of 0.5 mm width leads the inner part to an outside contact for voltage application. A homogeneously aligned LC (E44 from Merck) layer of 75 µm thickness is contained in the cell. As discussed previously, for the circular hole of D=15 mm diameter in the patterned electrode, usually a distance of d=6.0 mm between the hole-patterned electrode and the LC layer is needed for lens operation. In the present cell, d is only (300+100+75) µm=475 µm. Liquid glycerin with high electrical resistivity (approximately 10⁴ Ωm) is injected into the chamber, and its effect is observed experimentally.

 

Fig. 2. (a) Interference pattern when the chamber is filled with air, and voltages of amplitudes V ₁=15 V_rms and V ₂=4 V_rms, and of frequency f=1 kHz are applied. (b) Photo of the cell captured by the interferometer when liquid glycerin is partly injected into the chamber and no voltages are applied. (c) Interference pattern when the chamber is partly filled with glycerin and voltages of amplitudes V ₁=15 V_rms and V ₂=4 V_rms, and of frequency f=1 kHz are applied.

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The properties of the lens are examined by an interference method. The LC cell is placed between two crossed polarizers, with the rubbing direction of the cell making an angle of 45° with each polarizer. A laser beam of 405 nm wavelength is incident on the LC cell. It is divided by the first polarizer into ordinary and extraordinary waves. The ordinary wave experiences a spatially uniform phase shift, while the extraordinary wave experiences a spatially varying phase shift. The second polarizer recombines the two waves, and the interference between them takes place. The interference fringe patterns give the information of the phase shift experienced by the extraordinary wave [11]; the phase difference between adjacent fringes is 2π. Figure 2(a) shows the interference pattern at V ₁=15 V_rms, V ₂=4 V_rms, and f=1 kHz before the glycerin is injected into the chamber. Since d is too short for a hole as large as D=15 mm diameter, the gradient electric field is confined near the boundary of the hole area and so is the gradient refractive index. Thus, there are interference fringes only near the boundary of the hole area. Then glycerin is partly injected so that part of the chamber [lower part in Fig. 2(b)] is filled with glycerin, and the upper part is still filled with air. When the same voltages V ₁=15 and V ₂=4 V_rms of 1 kHz frequency are applied, interference fringes appear, as shown in Fig. 2(c). As discussed previously, the charge redistribution in the cell expands the gradient electric field to a wider area; it smoothes the spatially abrupt field in the LC layer. While the electric field in the LC layer is still confined near the boundary in the upper part of the cell, it expands to the whole area where there is glycerin. A gradient distribution of the refractive index then appears in the lower part of the cell, and one can see a lot of interference fringes there when V ₁=15 V_rms and V ₂=4 V_rms of 1 kHz frequency are applied.

 

Fig. 3. Interference patterns changing with the amplitude of V ₂ when the chamber is completely filled with glycerin and voltages of amplitude V ₁=11 V_rms and of frequency f=400 Hz are applied.

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After the chamber is completely filled with glycerin, a gradient electric field spreads over the hole area, and a gradient distribution of refractive index is then formed. By adjusting the amplitudes and frequency of the voltages, one can get a lens-like distribution of refractive index. The experiment shows that at V ₁=11 V_rms, f=400 Hz, the LC cell has lens-like phase transformations and becomes an LC lens, the properties of which change with V ₂. Figure 3 shows the interference fringes at various values of V ₂. The dashed circles represent the position of the circular hole in the patterned electrode. The interference patterns are composed of almost circular fringes. So the properties of the LC lens are nearly axially symmetrical. The number of the interference fringes decreases with V ₂, meaning that the gradient of the phase profile of the extraordinary wave decreases with increasing V ₂.

 

Fig. 4. Phase retardation at various values of V ₂.

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Figure 4 shows the phase retardations of the extraordinary wave at various values of V ₂ derived from the interference patterns. The symbols are the measurements, and the curves represent the regression results using quadratic equations. It can be seen that the phase retardation is tunable by V ₂, the LC lens shows high optical quality, and the quality is preserved over the whole range of V ₂.

 

Fig. 5. Lens power at various values of V ₂.

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Figure 5 shows the lens power changing with V ₂. Similar to the LC lenses driven by two voltages reported previously [11], V ₂ flattens out the spatially varying electric field and hence the refractive index in the LC layer. As a result, the lens power decreases monotonically with the increasing V ₂.

It is convenient for us to examine the mechanism for the reformation of the electric field by a layer of conductive material in an LC cell using liquid glycerin that is viscous and does not volatilize appreciably. However, the properties of liquids are usually variable; the conductivity of the liquid glycerin slightly changes with time. As a result, the performance of an LC lens containing liquid glycerin is unstable. Instead of a liquid film, an LC lens fabricated using a solid film with weak conductivity may have similar but much more stable properties.

5. Conclusion

The realization of an LC lens of large aperture but low driving voltages introducing a thin layer of weakly conductive material is reported. The redistribution of the charges in the weakly conductive material smoothes the spatially varying electric field, and even if the ratio of the diameter of the hole in a patterned electrode to the distance between the hole-patterned electrode and the LC layer is too large compared to the standard value found previously, the formation of a desired spatial slowly varying electric field in the LC layer, and hence lens-like distributions of refractive index, becomes possible. The effect of the weakly conductive layer is demonstrated. An LC lens is realized having a diameter as large as 15 mm and with driving voltages as low as 11 V_rms. The properties of the lens are electrically tunable, and over the entire voltage range high optical quality is preserved. The lens power decreases monotonically with the controlling voltage.