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.