CHAPTER 3. MULTI-ELECTRODE DRIVEN LC LENS
3.5 C ONCLUSION
Figure 3-8 MeDLC lens with different width of electrodes to further finely control the LC orientations.
3.5 Conclusion
Multi-electrically Driven Liquid Crystal Lens (MeDLC Lens) was proposed to realize a highly tunable LC lens with wide range of superior focusing. Through high freedom of multi-electrically control, the phase retardation of LC layer was significantly optimized for different focal length. In the comparison, two of general homogeneous LC lenses with external and internal electrodes were investigated. The results showed conventional LC lenses with small number of driving electrodes limit the focusing range, and only can be apply to particular focal length for acceptable focusing performance. For cylindrical MeDCL Lens with 60um LC cell gap and 1.5mm aperture size, the focusing was tunable from 3.5cm to infinity. Furthermore, corresponding FWHM of focusing profile was maintained narrower.
These results indicated MeDLC Lens increase the feasibility for tunable lenses. A smooth variance in focal length and stable focusing performance in wide range were also achieved.
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Chapter 4.
Gradient Driven Liquid Crystal Lens Exhibiting Ultra-low Operating Voltages
So far, although we applied the structure of MeDLC lens to improve the optical properties for each focal length, we can find the driving voltage of MeDLC lens is still high (~30Vrms).
Obviously, it is not only means the results are still unfeasible for general applications but also indicate the structures of LC lenses should be intrinsically innovated. In this chapter, a novel structure named Gradient Driven LC lens (GD-LC lens) was proposed. This structure intrinsically reduced the requirement for driving voltage down to few voltages. Combining with the concept of multi-control of MeDLC lens, GD-LC lens not only can be driven by operating voltage but also the driving frequency.
4.1 Introduction
Before getting into GD-LC lens, we have to discuss why the conventional structures of LC lenses usually require high driving voltage and long focusing time. Figure 4-1 (a-d) shows four kinds of homogeneous LC lenses including internal and external electrodes with single control and multi-control. Each of them was simulated the distribution of electric field inside the LC cells, as the green line shows the equal potentials. For the first structure, two internal electrodes (Figure 4-1 (a)), as the driving voltage was applied, we can find the gradient variation of electric field was yielded. This kind of electric field can be used to generate a lens profiled of phase retardation in the aperture of the electrodes. However, ratio of the potential really applied to the LC cell to generate the LC effect was low (around 10% as indicated in the figure), which means as we applied 30Vrms to the electrodes, only around 3Vrms was used.
In fact, the most of the electric field leaked outside of the LC cell. On the other hand, the structure with external electrodes, as shown in Figure 4-1 (b), although the insertion of high K
material (i.e. the glass) can smooth electric field communicated to the LC layer, the ratio of the potential really applied to the LC cell was low as well. Besides, the potential difference between the border and center was small. For the structure of MeDLC lens (Figure 4-1(c)), as discussed in Chapter 3, we can notice MeDLC lens has higher ability to control the electric field communicated to the LC layer than that of structure with only two electrodes, but it still had the drawback of low efficiency. Only around 10% voltage difference was really applied to the LC cell. Therefore, the driving voltage was required very high. The last structure, internal multi-electrode, as shown in Figure 4-1 (d), simulated discrete electric field in the LC cell due to the non-uniform arrangement of electrodes. This kind of electric field cannot generate lens profile which requires a smooth variation in the orientation of LC directors. Nevertheless, the potential applied to the LC cell can be totally fed to deform the LC molecules.
To summarize the above discussion, our previous simulation work indicated the configuration with internal continuous-distributed electrode has the ability to achieve gradient electrical field and maintain the energy inside the LC layer. These two features not only yielded the gradient phase retardation, but also sufficiently employed the applied energy.
Figure 4-2 shows a structure for achieving these. Inside the LC layer, the applied energy is conserved by the covered continuous-distributed electrode, as the equal-potential lines show, which is distinguished from the conventional structures leaking out the electrical field. The generated gradient electrical field, as well, yielded gradient distribution of LC molecule to form lens-like phase retardation. Thus, the applying voltage can be reduced which also implied the focusing time can be improved.
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(a)
(b)
(c)
(d)
Figure 4-1 The simulations of electric field for four kinds of homogeneous LC lenses including (a) internal single control, (b) external signal control, (c) external multi-control, and (d) internal multi-controls.
Figure 4-2 The structure of internal continuous electrode performs a smooth gradient electrical field and can conserve the electrical energy inside the LC layer.
4.2 Gradient Driven Liquid Crystal Lens (GD-LC Lens)
4.2.1 Concept
To achieve the configuration as shown in Figure 4-2, Gradient Driven Liquid Crystal Lens (GD-LC Lens) was proposed to intrinsically solve the issue of high driving voltage and slow focusing. GD-LC Lens utilized a high resistance layer (high R layer) to be the internal continuous-distributed electrode to achieve low operating voltage and improve the focusing time simultaneously. Experiments for testing the properties of the high R layer were investigated. The high R layer, which was spin coated on a substrate to connect two controlling electrodes. This structure generated gradient electrical distribution when applied two different operating voltages on each controlling electrode. Clevious P (sheet resistance~1MΩ/□) from Baytron was chosen to be the high R layer. A 60μm cell gap of LC molecule, E7 (Δn=0.2) from Merck, was anti-parallel directed to controlling electrodes. Two of the controlling electrodes were separated by 2mm, as Figure 4-3 shows. In the investigation of spatial phase retardation, different operating voltages driven at 1 kHz were applied to the right side of controlling electrode. The left side electrode was grounded to yield an initial potential difference (ΔV) between two electrodes. Different interference pattern were
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by symmetrically combining two identical structures with the same operating voltage. On the other hand, at V=5Vrms, the interference pattern was denser on the right side, as shown in Figure 4-4 (c). A concave lens also can be realized by the driving. Figure 4-4 (b) shows linear phase retardation between two electrodes which is unsuitable for lens applications.
Figure 4-3 The testing device of LC cell with high resistance layer connected by two controlling electrodes.
(a) (b) (c)
Figure 4-4 The results of interference pattern of the testing device driven by different operating voltages, (a)ΔV=3 Vrms, (b)ΔV=3.6 Vrms, and (c) ΔV=5Vrms. The LC cell was design by 60μm cell gap driven by the two controlling electrodes with 2mm separation.
4.2.2 Structure and Principles
According to the testing results, the structure of GD-LC Lens was constructed by combining triple internal electrodes with the high resistance layer. Three controlling electrodes included two marginal controlling electrodes and a central controlling electrode. By applying the
volta
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∙ (4-2)
indicates the basic parameters of transmission lines. The resistance R in Equation (4-2) is calculated as following
∙ (4-3)
where is the conductivity of the high R layer. and are the cross section and length of the resistance. is equation (4-3) is the sheet resistance. The schematic is shown in Figure 4-6.
Figure 4-6 The schematic of resistance of the controlled high R layer.
To calculate the capacitance C in Equation (4-2), the structure was firstly considered to be controlled under uniform electrode field. The induced dipole moments of two directions parallel and perpendicular to LC direction, as shown in Figure 2-4, were used. The equivalent polarization is
∥ ∥
⇒ ∥ (4-4)
The schematic is shown in Figure 4-7. The electric field was along the z direction which induced the polarization, ∥ and . The equivalent capacitance, C, could be calculated by
as
1 (4-5)
where d and A were the thickness and area of the meshed element respectivly. The conductance, G, and inductance L, in Equation (4-2) were ignored for the calculations.
Figure 4-7 The schematic of induced polarizations by z direction electric field.
The LC direction, angle , of LC molecule over the cell gap derived by Euler-Lagrange method can be described by splay geometry driven by uniform electric field, E,
1 ⁄ /
(4-6) where K11, and K33represent the splay and bend of Frank elastic constants respectively. is the maximum angle in the middle plane of LC layer which can be numerically calculated by replacing z by half thickness of the LC layer, h/2. The threshold field Ec is
∆ (4-7)
which indicates there is a minimum voltage to distort the LC directions. By interacted calculations, Figure 4-8 shows the simulation result, which the solid line and dotted line means the voltage distribution and the corresponding phase retardation, respectively.
Although the gradient voltage distribution was simulated, the phase retardation was unpredicted in the low voltage region from the model only considering the configuration as transmission line and driven by uniform electric. The complete electrical field should be considered in simulations.
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Figure 4-8 The simulated voltage distribution and corresponding phase retardations, the region which applying voltage under threshold value cannot distorted the LC directions.
In other words, the model only considering the configuration as transmission line and driven by uniform electric may miss the accuracy of complete electrical field simulations.
Although the simulation work cannot obtain information for analyzing of GD-LC lens, an R-C circuit can be used to model this structure, as show in Figure 4-9. From the circuit, following principles could be observed.
GD-LC lens can be voltage and frequency driving.
The resistance of the high R layer should be control in a proper range. If the resistance is chosen too low. The resistance from the hetero junction will occupied large ratio of applied voltage. On the other hand, as the resistance of the high R layer is too large, only a small ratio of current can achieve the center area if V1 is higher than V0. These two situations all result in no phase retardation in the central area.
Extremely high frequency operation will result in smaller capacitance impedance. As a result, there is also small ratio of current pass through the high R layer to yield phase retardation.
Figure 4-9 The R-C circuit utilized to model GD-LC lens.
4.3 Experimental Results
For investigation of focusing profile of GD-LC Lens in convex mode, the device with 2mm lens aperture was setup in front of GENTEC Beamage Series CCD sensor at a distance of corresponding focal length. The incident light source was 632.8nm polarized Hi-Ne LASER.
The marginal controlling electrodes were driven at 2.4 kHz, and the central electrode was grounded and connected to the ground electrode. As the operating voltage was at V=0, the incident light passed through the device directly without focusing, as Figure 4-10 (a) shows.
The top and bottom figures of Figure 4-10 indicate the top-view and cross-section of the measured beam profile. At V=2.35Vrms, which the phase retardation was driven in the convex mode, the incident light was converged, and showed a focusing result, as Figure 4-10 (b) illustrated. The results showed the structure of GD-LC Lens is feasible for lens applications. Although the 60um thickness of LC layer is tested, the operating voltage was low as 2.35Vrms for 5cm focal length.
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Figure 4-10 The focusing profile of GD-LC Lens drivenat (a) V=0, and (b) V=2.35Vrms@2.4kHz for 5cm focal length.
The focal length of GD-LC Lens is voltage and frequency dependent. As operating voltage and frequency increased, the focal length became gradually shorter. Figure 4-11 shows the relationship between focal length to operating voltage and frequency. In this study, the LC cell gap was designed as 60μm and the operating voltage was generally lower than 3Vrms.The shortest focal length was 2.5cm which was not be further estimated due to the limitation of the experimental setup and the CCD sensor’s structure. As Figure 4-11 shows, the range of driving voltage was from 1.9Vrms to 2.7Vrms to yield the focal length from 2.5cm to 10cm. By controlling the driving frequency, the focusing profile can be further modified, as shown in Figure 4-12. Through the result, the focusing profiles could be superior by the two control freedom, voltage and frequency. Although the profiles at the shortest and longest focal length cannot be as well as that of the middle range, these voltage-frequency control can yield wilder range of focusing than that of external and internal structure in Figure 3-6. To achieve higher control freedom, the multi-electrode concept should be combined with GD-LC lens.
Figure 4-11 The relationship of focal length to operating voltage and frequency of GD-LC Lens.
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Figure 4-12 The focusing profiles of GD-LC lens at different focal length from 2.5cm to 10cm controlled by voltage and frequency.
4.4 Phase Retardation of Convex and Concave Modes
The interference pattern is one of the mostly used methods to measure the phase retardation of LC cells. To evaluate the optical properties of GD-LC Lens, we investigated the phase retardation by observing the interference pattern between the ordinary and extraordinary rays passed through the lens cell under crossed polarizers. The rubbing direction of the lens cell is oriented at 45° with respect to the fast axis of the linear polarizer. Two images of GD-LC Lens driven in convex and concave modes are shown in Figure 4-13 (a) and (b) respectively.
In convex mode, as shown in Figure 4-13 (a), GD-LC Lens yielded a phase retardation
approximating to that of ideal lens with 1.6mm effective lens aperture. This result was coherent to that as shown in Figure 4-13, according to the following relation:
≅ ∙
2∆ ∙ (4-8)
where r, and f donate the aperture radius, and focal length respectively. The central grounded electrode with two marginal controlling voltages drives GD-LC Lens in concave mode. The results presented the phase retardation is much closer to that of an effective ideal lens, as Figure 4-13 (b) illustrated.
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(a)
(b)
Figure 4-13 The phase retardation of GD-LC Lens operated in (a) convex, and (b) concave modes. By the different operating arrangement, both convex and concave lenses were achieved.
Table 5 shows the summary of comparison between GD-LC Lens and conventional LC lens with internal electrodes. Through the result, GD-LC Lens dramatically improved 86.0 % operating voltage and can be only driven by less than 5Vrms which has been within the range of normal driver IC.
Table 5 The comparison of focusing time and corresponding operating voltage. The result shows GD-LC Lens significantly improved driving voltage and only can be only driven by less than 5Vrms.
Comparison LC cell Gap Operating Voltage
GD-LC Lens 60 μm (E7) 2.35 Vrms
Conventional LC Lens with
Internal Electrodes 60 μm (E7) ~25Vrms
4.5 Conclusion
GD-LC Lens was proposed exhibiting ultra-low operating voltage for the structure with 60um LC cell gap and 2mm lens aperture. The focal length was voltage and frequency tunable driven by less than 5Vrms. Compare to the conventional result, which usually requires extremely high driving voltages, GD-LC Lens brought the applications utilizing LC lenses to be feasible and practical. Furthermore, both convex and concave effective lenses were achieved by the structure of GD-LC Lens with different operating voltage. Therefore, not only the structure of GD-LC Lens intrinsically solved the issue of high driving voltage in the applications of LC lenses but also the concept of gradient driven would be potentially used for future form of LC lenses.
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Chapter 5.
Over-drive Method for Fast Focusing Liquid Crystal Lens
5.1 Introduction
As mentioned in previous sections, Liquid crystal (LC) is wildly used in many optical applications because of the properties of high sensitivity to electric field and easy control. For lens applications, LC lens owns a very unique property that the focal length is electrically tunable without mechanical moving and shape changing. This advantage made applications for focal length tunable and switchable system slimmer and more compact. However, for lens application, optical power of LC lenses is relatively smaller than that of conventional lenses.
Thus, thickness of the LC layer is usually required few tens or over hundreds of micrometers to generate high optical power rather than that of few micrometers in LCDs. The large thickness results in slow focusing time. For example, as the relation of optical power, P, shows
2∆ (5-1)
P is dependent on the difference of reflective index between that at border and center, ∆ , cell gap, d, and radius of aperture radius, r. The optical power is difficult to achieve 25m-1, as the LC lens has 1mm aperture radius and 60um LC cell gap (Merck nematic E7), whose F/# is large as 20. As ∆ is constrained by the index of material and only has a small region of variation due to structures of LC lenses, the cell gap is usually designed much thicker.
According to rising time, of LC devices, larger cell gap results in slow focusing time which is proportional to d from relaxing state to focusing state, as Equation (5-2) shows.
/
/ 1 (5-2)
where is the function of cell gap d, rotational viscosity , elastic constant K, threshold voltage , and applied voltage V. The slow focusing time makes applications unfeasible and unpractical, such as lens head in mobile devices which is requesting very fast auto-focusing or zoom functions, and 3D switchable displays having large numbers of viewing zones. To overcome slow response of LC cells, over-drive is employed for accelerating the response times in LCD industry. By optimized the over driving voltages and switching to target operation, the LC response time can be much reduced.
5.2 Over-drive Method for LC Lens
In this chapter, we propose Over-drive (OD) method for reducing the focusing time of LC lenses. Different from that for LCDs, the OD method investigated focusing behavior of LC lenses to determine the timing for switching. The appropriate operation can significantly reduce the focusing time.
For a test sample, we prepared a homogeneous LC lens structure with external driving electrodes which were patterned upon the glass, as shown in Figure 5-1(a). The electrodes were driven by OD voltage (~65Vrms) which was higher than that for particular focal length (~45Vrms for 5cm). The variation of normalized focusing intensity with time which was used to indicate the variation of focusing performance, as illustrated in Figure 5-1 (b), was measured by GENTEC Beamage Series CCD sensor placed at the focal length of the LC lens illuminated by a laser source (λ = 632.8nm). The initial focusing shows the OD voltage generated an instantaneous but unstable focus. The following focus ability was immediately decay and went to a stable state. This phenomenon was investigated by Fluorescence Confocal Polarizing Microscopy (FCPM) method [67] to analyze the exact director of LC molecules rotated with time, whose details investigations of FCPM for LC lens will be discussed in following section. The analysis showed gradient electric field by the OD voltage
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molecules rapidly and continually rotated to form another phase retardation that generated the focus in the stable state which had similar focusing intensity with the initial focusing, although the two forms of LC directors were totally different.
(a)
(b)
Figure 5-1 (a) General structure of homogeneous LC Lens driven by marginal over-drive voltages, and (b) The curve of focusing response time to normalized intensity on CCD sensor for a particular focal length. The over-drive voltages yielded a initial
Figure 5-1 (a) General structure of homogeneous LC Lens driven by marginal over-drive voltages, and (b) The curve of focusing response time to normalized intensity on CCD sensor for a particular focal length. The over-drive voltages yielded a initial