## 3 PVC Gel Lens
### Lenticular Microlens Array  
According to the operation mechanism, a PVC gel is particularly attractive for making microlens. One method is to use an interdigitated electrode to actuate the PVC gel ([PERSON] et al., 2018; [PERSON] et al., 2018). Figure 9 illustrates the device structure of the lens and the driving method. The cross-sectional structure of the device is depicted in Figure 9a. It consists of a glass substrate, an electrode, and PVC/DBP gel. The PVC gel cast on the substrate forms a flat membrane. Figure 8: Device structure of a circular PVC lens: (**a**) structure of the electrode and (**b**) the operation mechanisms. The electrode on the glass substrate has an interdigitated pattern, as given in Figure 9b. By applying a DC voltage, the charged plasticizer molecules shift toward the anode electrode. Due to the electrostatic repulsive force, the surface of the PVC membrane is undulated with a wavy configuration (Figure 9c). Due to the surface tension, the membrane is smoothly curved. Therefore, the membrane functions as a lenticular microlens array (LMA). When the incident light passes through the LMA, it can be converged by the convex surface. If the polarity of the voltage is inverted, then the charged molecules shift to the new anode electrode, causing the trough of the waves to be the crest (Figure 9d). When the voltage is removed, the membrane can be restored to its flat shape. For a prepared MLA, the aperture of each lenticular lens in the array is 40 \(\upmu\)m, and the thickness of the PVC/DBP membrane is \(\sim\)25 \(\upmu\)m in the null voltage state. The refractive index of the PVC/DBP (1:9 by weight) gel was measured to be n \(\sim\)1.49. By increasing the voltage from 30 V to 50 V, the focal length of the MLA changes from infinity to \(\sim\)88 \(\upmu\)m. The response time is in the range from several seconds to tens of seconds, depending on the operating DC voltage. The response time includes the rise time (\(\tau_{\text{r}}\)) and fall time (\(\tau_{\text{f}}\)), which is defined as the transmittance change between 10% and 90%. The response time can be measured using a pulse voltage to impact the PVC membrane, as shown in Figure 10. By applying a +40 V pulse voltage with 172-s duration to the PVC membrane (Figure 10a), the light transmittance goes through three stages: rise, saturation, and fall. In the rising stage, the surface of the PVC membrane is undulated with a wavy shape. In the saturation stage, the wavy shape is stable. In the restoring stage, the undulated PVC membrane slowly returns to being flat. The rise time depends on the applied voltage, but the decay time is a natural process, so the total response time (\(\tau_{\text{r}}+\tau_{\text{f}}\)) is 102 s + 118 s. To improve \(\tau_{\text{f}}\), we could apply a polarity-inverted voltage to the undulated PVC membrane, as shown in Figure 10b. When V = \(-\)40 V is continuously applied to the electrode, \(\tau_{\text{f}}\) is reduced to \(\sim\)30 s. In this period, the PVC membrane returns to its flat shape. Afterwards, the PVC membrane is undulated again by the +40 V pulse. This process has been explained in Figure 9.  
Figure 9: Device structure and driving method of the lenticular microlens array: (**a**) cross-sectional structure, (**b**) interdigitated electrode, (**c**) PVC membrane with undulated surface, and (**d**) shifting the surface profile using polarity inverted voltage. According to the results shown in Figure 10, the polarity-inverted voltage can largely decrease \(\tau_{\mathrm{f}}\), so that \(\tau_{\mathrm{f}}<<\tau_{\mathrm{r}}\). This is because \(\tau_{\mathrm{r}}\) and \(\tau_{\mathrm{f}}\) correspond to the shape constructing and shape collapsing, respectively. During the shape constructing, the generated electrostatic force needs to overcome the surface tension of the PVC membrane. Therefore, the effective force used to deform the PVC membrane is reduced.