Open Access
Add to BibSonomy
Abstract
In this paper, we demonstrate a variable aperture with graded attenuation combined with adjustable focal length lens actuated by hydraulic control. Two cylindrical chambers and a middle substrate are stacked to form the device body. An elastic film is fabricated in the middle substrate like a sandwich. In the initial state, the dyed liquid is fully covered on the elastic film. The variable aperture shows the state of the maximum optical attenuation. When the bottom chamber is injected with liquid, the elastic film can form a convex surface. The dyed liquid will be pushed to the side wall of the chamber by the raised elastic film and the optical attenuation can be varied by changing the volume of the injected liquid. The proposed device can achieve both the variable attenuator function and the variable-focus lens function. The experiments show that the variable aperture can obtain dynamic attenuation ranges from 33.01 dB to 0.71 dB, and the zoom liquid lens can reach 2.9☓magnifying power. The device can be applied in imaging systems and fiber-optic communications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Variable optical attenuators (VOAs) are widely used in the applications such as fiber-optic communications, sensing and imaging. Various VOA schemes have been proposed, among them micro-electro-mechanical system (MEMS) VOAs are the most well-known designs due to the advantages of fast response, high-integration, and accurate control [1–5]. In 2012, a hybrid electromagnetic and electrothermal actuation for 3D MEMS VOA was studied. Dynamic attenuation ranges of 40 dB was achieved at the voltage of 4 VDC. In 2018, researchers employed a MEMS torsion mirror to reduce the wavelength dependent loss (<0.4 dB). However, these devices may have reliability issues associated with the usage of moving micro-mechanical components like mirrors and shutters.
Recently, optofluidics technologies which combine micro-photonics/optics with microfluidics on a common platform have been widely applied to the miniaturized optical devices due to the merits of low consumption, broadband, and high transmittance. Liquid crystal (LC) VOAs and liquid VOAs are the most common designs. Polymer-network liquid crystal (PNLC)-based VOAs have a fast response time within 20 ms. However, the high operating voltage and light scattering cannot be ignored [6–8]. Moreover, nematic LC grating VOAs have been proposed with the diffraction efficiency of 30%. Although the polymer-stabilized blue phase LC has a high diffraction efficiency (~40%), the driving voltage can reach 160V [9,10]. Liquid VOAs actuated by electrowetting control [11–15], dielectrophoresis control [16–18], electric force control [19,20], and hydraulic control [21–23] have been studied intensively. Most of the electrowetting VOAs and dielectrophoresis VOAs only work in the visible spectral region, which will limit the real applications like fiber communications. In 2011, an integrated optofluidic attenuator was proposed by the researchers. The measured dynamic range of optical transmission is up to 47 dB, and the response time is below 100 ms for a 2 mm input beam. However, the relative high driving voltage (130V, 200Hz) will shorten the lifetime of the device. Recent years, scholars have developed several kinds of optofluidic irises and attenuators based on hydraulic control due to remarkable advantages, including low cost, ease of miniaturization, high fabrication yield, reconfigurability, and adaptability. Hence, the hydraulic control method is regarded as the promising way to achieve the optofluidic VOAs.
Most of the optofluidic VOAs are achieved by absorbing the light beam with dyed liquid. The dyed liquid is controlled to shrink or expand within the chambers based on electrical or mechanical control. The drawbacks of these methods are that they cannot guarantee the regular shape of the dyed liquid which will reduce the repeatability of the device [11,12]. Researchers have developed an optical attenuator using a deformable liquid droplet [17,18]. In these designs, the dyed droplet must be driven to touch the upper substrate in order to form a light channel with a high driving voltage. Thus, the dyed droplet will partially stick on the upper substrate which would affect the property of the optical attenuation. Some of other designs utilize a stretchable droplet or tunable liquid lens to deflect the incident beam [13,24]. The advantages of these designs are the simple fabrication and easy operation. While even at the maximum deflection state, partial light beam can still pass through the device. Therefore, the optical intensity attenuation is limited. Compared with our previous works [25–27] and the reported works, in this paper, we demonstrate a variable aperture with graded attenuation combined with adjustable focal length lens. The proposed device can achieve two functions simultaneously: one is to variably control the aperture, and the other is to achieve an adjustable focal length lens. For details, the shape of the dyed liquid can be tuned by changing the liquid-liquid interface. Thus, the attenuation process of the light intensity can be controlled well in a gradient change. When the device is applied in an optical system, the device can change the light intensity and aperture size to control the spherical aberration and depth of field. Besides, the focal length of the adjustable lens can be tuned so that the imaging magnification can be adjusted without mechanically moving any component and optical power can be enhanced in the system. In this way, the adaptive zoom function and dynamic control of light can be realized in the optical system.
2. Structure and operating principle
2.1 Structure and mechanism of the device
Figure 1 shows the structure and mechanism of the proposed device. An elastic film is fabricated between two annular sheets to form the middle substrate. Two cylindrical chambers and the middle substrate are stacked to form the whole structure of the device. Chamber-1 is filled with the dyed liquid and anther immiscible transparent liquid. Chamber-2 is filled with the transparent liquid. The two chambers are connected with pumping syringes through the channels for pulling in/out the liquids. In the initial state, the dyed liquid is fully covered on the middle substrate. The device shows the state of maximum optical attenuation, as shown in Fig. 1(a). Figure 1(b) is the optical image of the proposed device. When chamber-2 is injected with the liquid-2, the elastic film will form a convex surface. Liquid-3 will be pushed to the side wall of the chamber by the raised elastic film. That is to say, liquid-3 cannot stay in the center of the elastic film and forms an annular type from the top view, as shown in Fig. 1(c). When chamber-2 is further injected with liquid, the curvature of the elastic film can be increased continuously, as shown in Fig. 1(d). Thereby, the optical attenuation can be varied by changing the liquid volume. As for the curvature of liquid-liquid interface can be tuned, the zoom liquid lens function can be also realized, as shown in Figs. 1(c)-1(d). as shown in Fig. 1, the change of the checkerboard patterns just illuminates that the change of the lens focal length and magnifying power can be realized based on the proposed device schematically.
Fig. 1 Structure and mechanism of the device. (a) Cross-section of the proposed device. (b) Optical image of the proposed device. (c) State of injecting the liquid. (d) State of further changing the liquid volume.
2.2 Theory of the proposed device and the fabrication
According to Fig. 1, when liquid-2 is injected into the channels, the shape of the elastic film changes to a convex profile. To obtain the relationship between the volume change ΔV and the focal length (F), we consider a general case wherein the interface curvature can be convexity during the actuating process. Assuming that the liquid-liquid interface is spherical, and the volume change is the volume of the spherical cap of the interface approximately. When the pumping syringe works, the volume change (ΔV) through the channels will force the elastic film to bulge outward or shrink inward. The radius of the curvature (R) and ΔV have the following relationship:
where r0 is the inside diameter of the annular sheet. For a lens, the focal length can be expressed as follows:where n1 and n2 are the refractive indexes of liquid-1 and liquid-2 in the chambers respectively. Hence by substituting Eq. (2) into Eq. (1), the relationship between ΔV and F can be calculated.The fabrication is described as follows. To form the middle substrate, a polydimethylsiloxane (PDMS) film and two polymethylmethacrylate (PMMA) sheets are fabricated by employing the high temperature bonding machine. The thickness of the elastic film is 100 μm (@ Boer Materials co., LTD, China, the type of BD-film KYQ-100; the tensile strength is 5.0 Mpa, the tearing strength is 10.0 KN/m, and the elasticity modulus is 2.3 Mpa). The height, inside diameter and the outside diameter of the sheets are 0.5 mm, 20 mm and 15 mm, respectively. The cylindrical PMMA cubes with channels are designed as the chambers. The height and diameter of the chambers are 5 mm and 20 mm, respectively. The diameters of the two channels are both 0.5 mm. Then the two chambers, the middle substrate and two substrates are stacked together by glue UV-331. The total height of the device is 13 mm. The silicon oil (the density is 0.98 g/cm3, the viscosity is 10 mpa∙s, and the refractive index is 1.38) is used as liquid-1. The phenylmethyl silicone oil (the density is 1.08 g/cm3, the viscosity is 150 mpa∙s, and the refractive index is 1.49) is used as liquid-2. The water mixed with ink is used as liquid-3 (the density is 1.08 g/cm3, the viscosity is 1.5 mpa∙s) [28–31]. In our experiment, the volume ratio of liquid-1 and liquid-3 is ~1:2. If liquid-3 is less than a third of the total volume of chamber-1, the light will pass though the device in the initial state. If the volume of liquid-3 is greater than 1/2 of the total volume, the aperture size changes will be limited. Besides, liquid-3 needs to have a higher density because of the basic mechanism of gravity.
3. Experiments, results and discussion
3.1 Experiment and optical property of the proposed device
In the first experiment, we use a LED light to illuminate the device. In our experiments, we used a LED area light with tunable light power to illuminate the device, and the CCD camera (From YVSion, type of YS-HU800C, China; 2/3” COMS) is placed 30 mm away from the top substrate. In the initial state, the dyed liquid fully spreads to the surface of the elastic film. The light intensity attenuation reaches maximum, as shown in Fig. 2(a). When the liquid volume changes from 0 μl to 270 μl, the elastic film forms a convex surface leading to the dyed liquid pushed to the side wall of the cavity, as shown in Figs. 2(b)-2(i). Hence, the light intensity attenuation can be variably controlled. In this experiment, the largest liquid volume change is ~270 μl. If chamber-2 is further injected with liquid-2, the elastic film will be destroyed and it is hard to recover to the original shape.
Fig. 2 Results of the aperture size changes under different volumes. (a) ΔV1 = 0 μl. (b) ΔV2 = 40 μl. (c) ΔV3 = 90 μl. (d) ΔV4 = 130 μl. (e) ΔV5 = 170 μl. (f) ΔV6 = 210 μl. (g) ΔV7 = 240 μl. (h) ΔV8 = 260 μl. (i) ΔV9 = 270 μl.
As shown in Fig. 2, the clear apertures are not uniform in transmittance. That is because when the curvature of elastic film increases gradually, the dyed liquid rushes to the side wall of the chamber slowly and part of the dyed liquid will still cling to the elastic film leading to decreasing the transmittance of the aperture, as shown in Figs. 2(b)-2(g). While, when we further increase the curvature of elastic film, the dyed liquid will be completely pushed to the sidewall of the chamber. In this state, the transmittance is uniform, as shown in Figs. 2(h)-2(i) [32]. That is also why the proposed device is called variable aperture with graded attenuation.
In our experiment, the “transmittance” means “normal transmittance” because the transmittance is achieved by scattering the light through the maximum aperture, as shown in Fig. 2(i). The transmittance at the maximum aperture [Fig. 2(i)] is measured. The transmittance can achieve to be above 82% at the wavelength of 400 nm-750 nm, as depicted in Fig. 3.
When a LED light (λ = 632.8 nm) illuminates the device, the attenuation can be calculated by the following equation:
where A represents the light attenuation, Pi is the input light power, and P0 is the output light power. In our experiments, we used a LED area light with tunable light power to illuminate the device, and the CCD camera (From YVSion Technology Inc, type of YS-HU800C, China; 2/3” COMS) is placed 30 mm away from the top substrate. To measure the light power, we used an optical power meter (From Daheng New Epoch Technology Inc, type of LP100, China, detector size ~20 mm). The light attenuation is not that straight forward. We used a black cap with a 15 mm light hole to cover the whole device, and the detector is placed tightly to the light hole. In the initial state, the light power of the incident light is 200 μw, and the measured output light power is ~0.1μw. Hence, the attention first reaches a maximum value of ~33.01 dB. As the injected liquid volume increases, the attenuation gradually decreases. When the volume change reaches to 270 μl, the light power of the incident light is ~170 μw. So, the insert loss is ~0.71 dB. However, when the liquid volume is further increased, the attenuation cannot be further decreased as the elastic film has already reached its maximum elongation. Specifically, as shown in Fig. 2, the apertures size changes under different volumes. The apertures size determines the optical attenuation. For detail, in the initial state, the aperture size is ~0 mm, as shown in Fig. 2(a), and there is no light passing through to device. The optical attenuation reaches to maximum value ~33.01dB. Similarly, when the aperture size is increased by liquid pressure, as shown in Figs. 2(b)-2(i), part of the light can pass through the device. The optical attenuation begins to be decreased. When the volume change increases to 270 μl, the aperture size reaches to the maximum, and the amount of light has reached its maximum. In this state, the optical attenuation reaches to the minimum value ~0.71dB. Moreover, the normalized light intensity of the aperture under the volume changes of 0 μl, 130 μl, and 270 μl, are also depicted in Fig. 4.Fig. 4 Measured light attenuation and normalized light intensity of the aperture under different volume changes.
The relationship between the switch time and the repeatability are another key parameter to measure the performance of the device. The silicon photodetector linked with an oscilloscope is used to measure the switch time. To measure the switch time of the liquid device, the actuating (relaxing) time is defined when the light intensity attenuation changes from 33.01 dB (0.71 dB) to 0.71 dB (33.01 dB). The results are shown in Fig. 5. The measured average actuating time and relaxing time are ~3.6 s and ~2.5 s, respectively. From the repeated experiments, it can be proved that the proposed device has a relatively good repeatability.
The proposed device can also achieve the function of variable focus. To evaluate the performance of the liquid lens during actuation process, a CCD is used to record the image changes. The printed letter is placed 5 mm away below the device. When liquid-2 is pulled in chanmber-2 through channel-2, the images under different liquid volumes are shown in Fig. 6. When the injected liquid is less than 130 μl, the light aperture is limited and the light intensity attenuation is large. Hence, the device can only function as a liquid zoom lens only if the liquid volume change exceeds to ΔL2 > 130 μl. When the injected liquid is increased from ~130 μl to ~270 μl, the curvature of the liquid-liquid interface is always convexity and the sizes of the images are magnified accordingly, as shown in Figs. 6(b)-6(h). The measured magnifying power can reach 2.9☓.When the volume change ΔL6 > 270 μl, the magnification cannot be increased anymore because the elastic film has reached its tensile limit. The liquid lens with an aperture can be achieved in this state, thus it can also control off-axis aberration to some extent. In our device, chamber-1 is filled with water/ink mixture and the traditional methyl silicone oil. When we calculate the optical power of the device, liquid-3 has already been pushed to the side wall of the chamber by the raised elastic film and there is little liquid-3 staying to in the center of the elastic film. Thus, liquid-1 and liquid-3 will not form a liquid-liquid interface when we calculate the optical power.
Fig. 6 Results of the variable focus liquid lens with tunable apertures. (a) ΔL1 = 0 μl. (b) ΔL2 = 130 μl. (c) ΔL3 = 180 μl. (d) ΔL4 = 220 μl. (e) ΔL5 = 250 μl. (f) ΔL6 = 270 μl.
The imaging quality is an important criterion to evaluate a liquid lens. In the second experiment, a USAF-1951 resolution target is placed 5 mm behind the liquid lens. When the liquid lens is imaged in a CCD, the horizontal lines in group 3, number 3 is resolvable. That is to say, the liquid lens has a resolution of 10.08 lp/mm. The liquid lens is also simulated in Zemax-EE. Figure 7 shows the simulated modulation transfer function (MTF) and the imaging experiment of the liquid lens. In the simulation, the resolution is ~16.10 lp/mm when the MTF >0.1. The difference between the experiment and simulation may be the light absorption of the liquids. Besides, the elastic film has not been considered in the simulation.
We also measured the aperture size changes and the focal length changes of the liquid lens. As shown in Fig. 8, the aperture size can be varied from ~6.1 mm to ~10.4 mm and the focal lengths can be varied from ~63.1 cm to ~12.1 cm, when the liquid volume changes from 130 μl to 270 μl.
3.2 Discussion
The key novelty of the proposed device is that it can be used as both an optical intensity attenuator and a zoom liquid lens with an easy fabrication and simple structure. Therefore, the device can be applied to the zoom optical system with controlling the light intensity adaptively. However, some optical properties of the device can also be improved. In our device, the density of liquid-1 is 0.98 g/cm3 and the density of liquid-3 is 1.08 g/cm3. The densities of the two liquids are not matched. Thus, when we rotate the device 90 degrees, the liquid-liquid interface in chamber-1 will become an inclined plane and cannot work as an optical attenuator [33, 34]. While, as for the lower chamber, the densities of liquid-2 and liquid-3 are the same. Thus, liquid-2 in the lower chamber will still keep a good surface. Based on our previous work [35], if the two liquids are density-matches and placed in the horizontal position. The device can keep a good shape of liquid-liquid interface by applying 200 rpm vibration. However, we can still find three density-matched liquids with different refractive index as the filled liquids. Then, the device can have a reasonable stability and achieve the variable aperture with graded attenuation and variable focus. Besides, the refractive index difference between liquid-1 and liquid-2 is not large enough, which will have a limitation on the optical power. In the next work, we will search two suitable filled liquids with conditions of density-matched, and higher refractive index difference. From Fig. 5 we can see that the average actuation time is relatively slow (~3.6 s). That all depends on the injection speed of pump. The highest injection speed of our pump can reach 882.5 μl/ms. However, the fast injection speed may cause a vibration in the device which has a negative influence on the mechanical stability. So, we should take a tradeoff between the fast speed and mechanical stability [36,37].
4. Conclusion
In this paper, a variable aperture with graded attenuation combined with adjustable focal length lens is proposed. The device can be used as both optical attenuator and adaptive liquid lens and provide competitive features such as simple fabrication, low insertion loss (~0.71 dB), large dynamic range to ~33.01 dB. And the measured magnifying power can reach 2.9☓. The device has the promising applications for optical fiber communications and imaging systems. In the further work, we will focus on improving the resolution of the zoom liquid lens and search a method to enhance mechanical stability of the device when it is placed vertically.
Funding
National Natural Science Foundation of China under Grant No. 61805169, 61805130, and 61535007.
References
1. J. C. Chiou and W. T. Lin, “Variable optical attenuator using a thermal actuator array with dual shutters,” Opt. Commun. 237(4-6), 341–350 (2004). [CrossRef]
2. C. Lee, “Variable optical attenuator using planar light attenuation scheme based on rotational and translational misalignment,” Microsyst. Technol. 13(1), 41–48 (2006). [CrossRef]
3. K. H. Koh, Y. Qian, and C. Lee, “Design and characterization of a 3D MEMS VOA driven by hybrid electromagnetic and electrothermal actuation mechanisms,” J. Micromech. Microeng. 22(10), 105031 (2012). [CrossRef]
4. R. R. A. Syms, H. Zou, J. Stagg, and H. Veladi, “Sliding-blade MEMS iris and variable optical attenuator,” J. Micromech. Microeng. 14(12), 1700–1710 (2004). [CrossRef]
5. H. Sun, W. Zhou, Z. Zhang, and Z. Wan, “A MEMS variable optical attenuator with ultra-low wavelength-dependent loss and polarization-dependent loss,” Micromachines (Basel) 9(12), 632 (2018). [CrossRef] [PubMed]
6. K. M. Chen, H. Ren, and S. T. Wu, “PDLC-based VOA with a small polarization dependent loss,” Opt. Commun. 282(22), 4374–4377 (2009). [CrossRef]
7. W. Hu, A. Srivastava, F. Xu, J. T. Sun, X. W. Lin, H. Q. Cui, V. Chigrinov, and Y. Q. Lu, “Liquid crystal gratings based on alternate TN and PA photoalignment,” Opt. Express 20(5), 5384–5391 (2012). [CrossRef] [PubMed]
8. M. W. Geis, P. J. Bos, V. Liberman, and M. Rothschild, “Broadband optical switch based on liquid crystal dynamic scattering,” Opt. Express 24(13), 13812–13823 (2016). [CrossRef] [PubMed]
9. W. Hu, A. Kumar Srivastava, X.-W. Lin, X. Liang, Z.-J. Wu, J.-T. Sun, G. Zhu, V. Chigrinov, and Y.-Q. Lu, “Polarization independent liquid crystal gratings based on orthogonal photoalignments,” Appl. Phys. Lett. 100(11), 111116 (2012). [CrossRef]
10. J. Yan, Y. Li, and S. T. Wu, “High-efficiency and fast-response tunable phase grating using a blue phase liquid crystal,” Opt. Lett. 36(8), 1404–1406 (2011). [CrossRef] [PubMed]
11. P. Müller, A. Kloss, P. Liebetraut, W. Mönch, and H. Zappe, “A fully integrated optofluidic attenuator,” J. Micromech. Microeng. 21(12), 125027 (2011). [CrossRef]
12. P. Müller, R. Feuerstein, and H. Zappe, “Integrated optofluidic iris,” J. Micromech. Microeng. 21(5), 1156–1164 (2012). [CrossRef]
13. S. A. Reza and N. A. Riza, “A liquid lens-based broadband variable fiber optical attenuator,” Opt. Commun. 282(7), 1298–1303 (2009). [CrossRef]
14. R.-Y. Yuan, L. Luo, J.-H. Wang, L. Li, and Q.-H. Wang, “1×2 optofluidic switch for optical beam routing and variable power distribution,” IEEE Photonic Tech L. 30(18), 1629–1632 (2018). [CrossRef]
15. C. U. Murade, J. M. Oh, D. van den Ende, and F. Mugele, “Electrowetting driven optical switch and tunable aperture,” Opt. Express 19(16), 15525–15531 (2011). [CrossRef] [PubMed]
16. C. G. Tsai and J. A. Yeh, “Circular dielectric liquid iris,” Opt. Lett. 35(14), 2484–2486 (2010). [CrossRef] [PubMed]
17. H. Ren, S. Xu, and S. T. Wu, “Deformable liquid droplets for optical beam control,” Opt. Express 18(11), 11904–11910 (2010). [CrossRef] [PubMed]
18. H. Ren, S. Xu, D. Ren, and S. T. Wu, “Novel optical switch with a reconfigurable dielectric liquid droplet,” Opt. Express 19(3), 1985–1990 (2011). [CrossRef] [PubMed]
19. J. H. Chang, K. D. Jung, E. Lee, M. Choi, S. Lee, and W. Kim, “Variable aperture controlled by microelectrofluidic iris,” Opt. Lett. 38(15), 2919–2922 (2013). [CrossRef] [PubMed]
20. J. Wan, F. Xue, C. Liu, S. Huang, S. Fan, and F. Hu, “Optofluidic variable optical attenuator controlled by electricity,” Appl. Opt. 57(28), 8114–8118 (2018). [CrossRef] [PubMed]
21. Y. Hongbin, Z. Guangya, C. F. Siong, and L. Feiwen, “Optofluidic variable aperture,” Opt. Lett. 33(6), 548–550 (2008). [CrossRef] [PubMed]
22. P. Müller, N. Spengler, H. Zappe, and W. Mönch, “An optofluidic concept for a tunable micro-iris,” J. Micromech. Microeng. 19(6), 1477–1484 (2010). [CrossRef]
23. W. Song and D. Psaltis, “Pneumatically tunable optofluidic 2 × 2 switch for reconfigurable optical circuit,” Lab Chip 11(14), 2397–2402 (2011). [CrossRef] [PubMed]
24. S. Xu, H. Ren, J. Sun, and S. T. Wu, “Polarization independent VOA based on dielectrically stretched liquid crystal droplet,” Opt. Express 20(15), 17059–17064 (2012). [CrossRef]
25. C. Liu and D. Wang, “Light intensity and FOV-controlled adaptive fluidic iris,” Appl. Opt. 57(18), D27–D31 (2018). [CrossRef] [PubMed]
26. C. Liu, L. Li, D. Wang, L. X. Yao, and Q. H. Wang, “Liquid optical switch based on total internal reflection,” IEEE Photonic Tech L. 27(19), 2091–2094 (2015). [CrossRef]
27. L. Li, C. Liu, H. Ren, and Q. H. Wang, “Fluidic optical switch by pneumatic actuation,” IEEE Photonic Tech L. 4(25), 338–340 (2013). [CrossRef]
28. S. Xu, Y. Liu, H. Ren, and S. T. Wu, “A novel adaptive mechanical-wetting lens for visible and near infrared imaging,” Opt. Express 18(12), 12430–12435 (2010). [CrossRef] [PubMed]
29. F. Mugele and J. C. Baret, “Electrowetting: from basics to applications,” J. Phys. Condens. Matter 17(28), R705–R774 (2005). [CrossRef]
30. Z. W. Li and J. L. Xiao, “Strain tunable optics of elastomeric microlens array,” Extreme Mech. Lett. 4, 118–123 (2015). [CrossRef]
31. Z. Li and J. Xiao, “Mechanics and optics of stretchable elastomeric microlens array for artificial compound eye camera,” J. Appl. Phys. 117(1), 014904 (2015). [CrossRef]
32. Z. Li, Y. Zhai, Y. Wang, G. M. Wendland, X. Yin, and J. Xiao, “Harnessing surface wrinkling-cracking patterns for tunable optical transmittance,” Adv. Opt. Mater. 5(19), 1700425 (2017). [CrossRef]
33. H. Ren and S. T. Wu, “Variable-focus liquid lens,” Opt. Express 15(10), 5931–5936 (2007). [CrossRef] [PubMed]
34. A. Mikš and F. Šmejkal, “Dependence of the imaging properties of the liquid lens with variable focal length on membrane thickness,” Appl. Opt. 57(22), 6439–6445 (2018). [CrossRef] [PubMed]
35. C. Liu, D. Wang, L. X. Yao, L. Li, and Q. H. Wang, “Electrowetting-actuated optical switch based on total internal reflection,” Appl. Opt. 54(10), 2672–2676 (2015). [CrossRef] [PubMed]
36. Z. Li, Y. Wang, and J. Xiao, “Mechanics of curvilinear electronics and optoelectronics,” Curr. Opin. Solid St. M 19(3), 171–189 (2015). [CrossRef]
37. Z. Li, Y. Wang, and J. Xiao, “Mechanics of bioinspired imaging systems,” Theore. Appl. Mech. Lett. 6(1), 11–20 (2016). [CrossRef]
