Liquid crystal (LC) lenses with a circularly hole-patterned electrode possess excellent characteristics in optical performance, especially for the capability of tunable focal lengths. But, non-uniformly symmetrical electric fields in LC lenses usually induce disclination lines when operating. In general, the occurrence of disclination lines not only degrades their optical capability such as imaging performance, but also spends more time for tuning focal lengths. In this paper, we use a way of polymer stabilization to successfully prevent the disclination lines in LC lenses. Even arbitrarily adjusting the applied voltages in LC lenses, it seems no occurrence of disclination lines again. In addition, we compare the basic optical performance for LC lenses with or without polymer stabilization. From experimental results, it shows that they almost have the same optical performance.
© 2011 OSA
On the basis of unique electro-optical characteristics, the material of liquid crystals (LCs) is usually used to study and fabricate some optical devices for applications. Recently, studies of LC lenses have become a popular topic because its capabilities are obviously different from the conventional glass lenses. Until now, numerous types of LC lenses have been proposed such as spherical-shaped LC lens [1,2], LC lens with inhomogeneous polymer network  and hole-patterned liquid crystal lens  etc. In addition, polymer stabilization is a usual and useful process for fabricating some special liquid crystal displays (LCDs) such as multi-domain vertical alignment (MVA)  and patterned vertical alignment (PVA)  etc. Using ultraviolet (UV) light exposure in the LC cells doped with a little amount of reactive mesogen (RM), a great improvement of display performance can be achieved including high contrast ratio and fast response time. Moreover, the study of polarization independent LC micro-lens array has been demonstrated by means of the surface-controlling technique on the alignment layer with mixed RM material .
Among most of LC lenses, the typical one with a circularly hole-patterned electrode possesses some characteristics including easy fabrication, excellent capabilities of tunable focal lengths and large effective apertures etc. However, this kind of LC lenses also has a serious drawback, that is, occurrence of disclination lines when operating. Disclination lines not only degrade optical performance of the LC lenses, but also spend more time to tune focal lengths. Many researches had pointed out the cause of disclination lines [8,9] and proposed some methods to resolve this problem such as controlling LC lenses with two individually applied voltages , symmetrical structure of electrodes  and adding an extra in-plane electric field in LC lenses [11,12]. Generally speaking, using an extra electric field not only efficiently prevent the disclination lines, but also provide more flexibility to achieve better optical performance in LC lenses. Certainly, more fabricating processes or complicated controlling circuits are necessary.
In this work, we demonstrate that a way of polymer stabilization is successfully used in LC lenses with a circularly hole-patterned electrode of 7 mm in diameter to prevent the occurrence of disclination lines when operating. We also compare the optical performance of LC lenses with or without polymer stabilization. From experimental results, it shows that the major characteristics of LC lenses are very consistent for LC lenses with or without polymer stabilization.
2. The structure of PSLC lens with a circularly hole-patterned electrode
Figure 1 shows the cross-section of a conventional LC lens with a circularly hole-patterned electrode. Here, we briefly illustrate the PSLC (polymer stabilized liquid crystal) lens. It is the same structure as well as conventional LC lenses, except the injected material in the cells. The injected material in conventional LC lenses is just only LCs. But, the injected material in PSLC lenses is a mixture of LCs, RM and photo initiator, which will be treated with an extra process of UV exposure. The PSLC lens has a sandwich structure composed of two glass substrates. The thicker one is as the upper substrate with a circularly hole-patterned ITO (indium tin oxide) electrode. The other thinner one is as the under substrate with a whole ITO conductive film. Both substrates are coated with polyimide (PI) and mechanically rubbed for homogeneous LC alignment. Two stripes of Mylar spacer are placed along the opposite sides of cell boundaries for controlling cell gap. Finally, the completed empty cell is injected with the mixture by means of capillarity. In our previous work, we demonstrated an annoying phenomenon of linkage between the migrating zigzag line and the disclination line, which could be permanently stayed in LC lenses to degrade optical performance when operating LC lenses for a long time . It should be noticed to fabricate this kind of LC lens. A few crucial specification of PSLC lens are described as follows. The circularly hole-patterned ITO electrode is 7 mm in diameter; thickness of LC layer is 125 μm; the upper glass substrate is 1.4 mm thickness and the under glass substrate is 0.7 mm thickness, respectively. The LC lenses are homogeneous LC cells.
Although the LC lens with a circularly hole-patterned electrode is easily fabricated and has good optical performance, disclination lines usually occur to affect its optical functions when operating. The major cause of disclination line comes from the interaction between the electric fields and LC directors in cells. In general, hole-patterned electrode provides a non-uniformly axially-symmetrical electric field so that LC molecules near the surface of upper substrate will be reorientation with reverse directions when applying voltages as shown in Fig. 2 . A simple way of applying voltages with a slowly increasing rate is efficient to prevent disclination lines, but it will spend more time when operating, especially for the LC lenses with large apertures.
3. Processes of polymer stabilization in the PSLC lens
Polymer stabilization is usually used to improve the performance of LC optical devices. Here, we try to use it to prevent disclination lines in LC lenses. The preparation of PSLC lenses is described as follows: We made one material mixed with reactive mesogen (RM257, purchased from Merck), photo initiator (Iragcure 651 purchased from Chiba) and LCs (E7 purchased form Merck) with a weight ratio of 1.40: 0.14: 98.46. The completely mixed material was injected with capillarity into the empty cells on the 100°C hot plate. The completely injected LC lenses were applied voltages with a slowly increasing rate from 0 Vrms to 140 Vrms in order to prevent occurrence of disclination lines. The applied voltage in the LC lenses was a square waveform with frequency of 1 kHz. And then, the injected LC lenses were exposed with ultraviolet light (7 mW/cm2) for 4 minutes when applying voltages of 140 Vrms. After UV exposure, there were some polymer structures formed near the surfaces of glass substrates, which was as well as most illustration shown in papers [6,14]. The formed polymer structures affected LC molecules near the surface of glass substrates. But, they did not affect other LCs away from surfaces of glass substrates in the cells, which could be illustrated with the proof of no interference patterns in the PSLC lens without applied voltage. Figure 3 shows the processes of polymer stabilization with UV exposure in a PSLC lens with applied voltages. The polymer structures are generated from the injected mixture after UV exposure. When removing the applied voltages, the LC directors near the glass surface are stabilized in the directions as same as the reoriented LC directors by electrical fields.
4. Measurement and optical performance of PSLC lenses
We adopt the popular way to evaluate optical performance of LC lenses, which is observation of interference patterns in LC lenses with respect to variously applied voltages. In Fig. 4(a) , it shows an experimental setup for observing interference patterns in LC lenses. A spatially filtered and collimated He-Ne laser (wavelength of 632.8 nm) is normal incident to the LC lens, which expanded beam size is 4 cm in diameter. A pair of crossed polarizers is placed in front and behind of LC lens, respectively, which directions of polarization are ± 45° with respect to the rubbing direction of the LC lens. Finally, a CCD camera is used to record the interference patterns. The observed interference patterns of LC lenses are shown in Fig. 4(b) and 4(c). In Fig. 4(b), it shows the interference patterns of the LC lens without RM dopant and UV exposure. When directly adjusting the applied voltages from 0 Vrms to 180 Vrms in this lens, the disclination line appears in the cell. Eventually, the disclination line still exists when applying a lower voltage of 60 Vrms directly adjusted from 180 Vrms. On the contrary, in Fig. 4(c), it shows the interference patterns of the LC lens with RM dopant and UV exposure. The polymer structures stabilize the LC directors near the glass surfaces of PSLC lens. Therefore, the reorientation of LCs will have the same directions to avoid occurrence of disclination lines when directly applying voltages form 0 Vrms to 180 Vrms. Simultaneously, a lower applied voltage of 60 Vrms also occurs no disclination lines. When turning off the applied voltage, no interference pattern exists in the cell. The PSLC lens shows the similar characteristics as well as the LC lens without RM dopant and UV exposure. Obviously, the polymer structures have not completely stabilized all LC directors in the cell.
Using polymer stabilization, we have successfully prevented the occurrence of disclination lines in LC lenses. But, does the polymer stabilization affect no disadvantage for optical performance in LC lenses? In order to verify it, we did the following experiments. We compared the characteristics of focal lengths versus applied voltages for two LC lens possessing the same cell conditions, except with or without RM dopant and UV exposure. Figure 5(a) shows the comparisons of focal lengths with respect to applied voltages between two LC lenses. Obviously, both of them have almost same characteristics of tunable focal lengths from ∞ to 26 cm. Simultaneously, we also compared their interference patterns extracted in the radial direction from center to edge of circular hole-pattern in LC lenses with the CCD camera. Figure 5(b) and 5(c) shows the individual interference patterns with applied voltages of 180 Vrms in LC lenses, which have the same rings each other. The same rings in interference patterns mean the same optical performance of LC lenses.
Using the CCD camera, we also observed the intensity distribution of a passing laser beam through the PSLC lens in focused and unfocused statuses, respectively. The experimental results are shown in Fig. 6(a) and 6(b). In general, the numbers of rings appearing in the interference patterns of LC lenses provide the information of total phase retardation from center to edge of effective apertures. If the rings in interference patterns are numbers N, the total phase retardation will be 2πN. A popular equation is used to roughly calculate focal lengths of LC lenses by means of numbers N in interference patterns as shown in Eq. (1) .
In Eq. (1), r is the effective radius of LC lenses in which of circular area the interference patterns exist; the λ is the wavelength of incident laser beam; the N is the number of rings in interference patterns; the Δδ is the total phase retardation from center to edge in the cells. When the PSLC lens with applied voltages of 60 Vrms, we got the 31 rings in interference patterns with the CCD camera, which was inputted in Eq. (1) to get a focal length of 31.2 cm for the incident He-Ne laser. In the same status of PSLC lens, the focal length was 30 cm by means of measurement of focused light spots. In Fig. 6(c), it shows the comparisons of tunable focal lengths of a PSLC lens from rings N in interference patterns and experimental measurement, respectively. Obviously, they are very consistent each other except for the regions with higher and lower applied voltages. We think that the inconsistency of focal lengths is caused from different distribution of LC directors in the cells. In general, a well-behaved LC lens possesses an ideal distribution of LC directors to achieve a profile of quadratic refractive indices in radial direction. When applying lower voltages, LC directors have not completely reoriented in central area so that there is no distribution of gradient refractive indices here. Moreover, when applying higher voltages, the rings in larger radial positions disappear so that its optical intensity becomes more uniform in this area. This phenomenon is shown in Fig. 4. It is also no distribution of gradient refractive indices here. Therefore, an optimal applied voltage about 60 Vrms induces an ideal distribution of LC directors to achieve a profile of quadratic refractive indices in radial direction for this PSLC lens.
The imaging performance of PSLC lenses was also observed. Figure 7(a) shows the setup for observing imaging performance of the PSLC lens. A polarizer with its polarization parallel to the rubbing direction of PSLC lens was placed in front of the CCD camera. The target was placed in front of 23 cm away from the PSLC lens. In Fig. 7(b) and 7(c), they show the target was taken photos by the CCD camera when the PSLC lens with applied voltages 0 and 60 Vrms, respectively. A clearer photo was achieved when tuning focal lengths of the PSLC lens with applied voltages.
Using polymer stabilization to prevent disclination lines, it must be noticed that the optical characteristics of PSLC lenses are very sensitive to the amounts of RM dopant. Comparing with the previous work by T. Nose et al. , both studies have similar conclusions. But, larger dimensions of LC lenses such as apertures and cell gaps are significantly different each other. Now, we have demonstrated that polymer stabilization does work to prevent disclination lines even in LC lenses with larger dimensions. The polymer structures can fix LC directors in the cells when using concentration of RM dopant higher than 1.4 wt.% (1.5 wt.%, 2 wt.% and 2.5 wt.% of RM dopant concentration were used in this study), so that the interference patterns permanently exist even no applied voltage. Figure 8 shows the results of a PSLC lens with 1.5 wt.% RM dopant after UV exposure with applied voltages of 44 Vrms. In Fig. 8(a), it shows the obvious interference patterns in the cell without applied voltage, which means that this cell has an intrinsic focal length. When tuning focal lengths with applied voltages, it needs higher voltages than the cells with lower concentration of RM dopant. Simultaneously, the interference patterns become cloudier when directly applying voltages from low to high, which is shown in Fig. 8(b). It also induces cloudy interference patterns for cells with higher concentration of RM dopant when UV exposure for longer time. This cloudy interference patterns are induced by more complicated polymer structures.
For another case, the PSLC lens with 1.3 wt.% (or lower concentration than 1.3 wt.%) RM dopant was still observed occurrence of disclination lines even if it was processed with UV exposure for longer time (about half or two hours) as shown in Fig. 9 . Figure 9(a) shows there is no interference pattern in the cell without applied voltage after polymer stabilization. In Fig. 9(b), when directly applying a voltage of 50 Vrms, the disclinations line occurs in the cell as similar as the LC lenses without RM dopant.
We have demonstrated a way of polymer stabilization to prevent occurrence of disclination lines in LC lenses, so that their optical characteristics can be maintained as well as the LC lenses without polymer stabilization. Both of RM dopant and UV exposure are very sensitive to final optical performance in the PSLC lenses. We have successfully achieved the operated PSLC lenses without disclination lines when using 1.4 wt.% RM dopant and UV exposure (7 mW/cm2) for 4 minutes in the cells.
References and links
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