1. Introduction

Lens devices are indispensable in optical systems. In recent years, the miniaturization of mobile cameras and the development of 2D/3D displays require lenses with a light weight and an adjustable focal length without mechanically moving parts [1–6]. Consequently, liquid crystal (LC) lenses have become important optical components because of their slimness and electrically tunable focus length. The function of LC lenses is essentially determined by the quadratic distribution of the refractive index that converges or diverges the incident light. Over the past 20 years, LC lenses in variable sizes have been presented. Several methods have been proposed to demonstrate large aperture LC (LALC) lenses, such as the combination of the solid lens and the LC layer [7–9], the dielectric dividing principle [10, 11], polymer/LC composition film [12, 13], concentric multi-ring electrode [14, 15] and hole-patterned electrode [16–18]. However, LALC lenses that comprise a solid lens and an LC layer exhibit insufficient focus change and a large volume. Building an LALC lens based on the dielectric dividing principle requires materials with different permittivity but similar optical refractive indices. However, appropriate materials are difficult to obtain. An LALC cell made of polymer/LC composition film typically has an unsmooth polymeric film that scatters incident light. The curved polymeric film strongly anchors LCs in an essential focus, and thus, narrows down the tunable focus range. An LALC lens that uses concentric multi-ring electrodes has a complicated electrode structure and requires multiple addressing voltages. Furthermore, the discrete phase distribution that results from neighboring discrete electrodes has to be smoothened by the introduced floating electrodes [15]. Among the aforementioned options, the hole-patterned LALC lens has a convenient fabrication process, a simple addressing scheme, and widely tunable focal range [16]. Nonetheless, a thick dielectric layer (TDL) has to be inserted between the hole-patterned electrode and the LC layer to distribute the fringing electric field throughout the center of the aperture hole (AH). However, the inserted TDL significantly increases the operation voltage of the lens. It also decreases lens power (defined as the reciprocal of the focal length) of the lens [19], because TDL increases vertical component of the electric field in the AH center, therefore results in the smaller voltage difference and as a consequence the smaller phase difference between the periphery and center of AH in the LC layer. The drawbacks of high operation voltage and low lens power can be improved by replacing the TDL with a thin high-resistance film [20–22]. However, such film is difficult to lay out uniformly on the substrate surface, which distorts the wavefront of the incident light [23].

The optimum ratio of the AH diameter to the dielectric layer thickness is approximately 3: 1 in a conventional hole-patterned LALC lens [22, 24]. For a hole-patterned LALC lens with 6 mm-diameter AH, the required dielectric layer is approximately 2.2 mm thick, which requires an extremely high operation voltage that is unfavorable for practical applications [22]. In the present study, a floating ring electrode is embedded between the dielectric layer and the LC layer of the hole-patterned LALC lens with 6 mm AH. The floating ring electrode prevents the gathering of the fringing electric field around the periphery, but distributes the fringing electric field throughout the entire AH of the LALC lens. The thickness of the dielectric layer and the operation voltage of the hole-patterned LALC lens can be effectively decreased using this novel design. Compared with the conventional TDL LALC lens, the proposed LALC lens features high lens power because of the weak vertical component of the fringing electric field in the AH center. Consequently, a large voltage difference also occurs, which results in the large phase difference between the periphery and center of the AH in the LC layer [19]. The proposed hole-patterned LALC lens reaches a minimum focal length of 17 cm at 40 V and has a low wavefront error of approximately 0.07 λ, which is comparable with that of the commercially available solid glass lens. The experimental preparations, floating ring electrode design, and electro-optical measurements and results are presented in this study.

2. Experimental preparations

Figure 1(a) depicts the structure of the proposed floating ring electrode-embedded (FREE) LALC lens, which comprises three indium–tin–oxide (ITO) glass substrates (Chipset technology Co., Ltd, Taiwan) that are 0.55 mm thick. The AH diameter on the top electrode is 6 mm. The middle electrode consists of a ring electrode with the inner and outer diameters of 1.95 mm and 2 mm, respectively. The dielectric layer (dielectric constant ~7.6) inserted between the top and middle electrodes measures 0.55 mm. The bottom electrode is a planar electrode. The inner surfaces of the middle and bottom substrates were coated with homogeneous polyimide (PI) AL-58 (Daily Polymer, Taiwan) and were rubbed antiparallel to each other. The cell gap was determined using 125 μm-thick Mylar spacers. Nematic E7 (from Daily Polymer, Taiwan) was then injected into the empty cell via capillary action. E7 had the birefringence of 0.22, dielectric anisotropy of 14.5, average elastic constant of ~13 pN, and viscosity of 232.6 mPa•s at room temperature. To analyze the influence of the floating ring electrode, a ring electrode-free (REF) LALC lens and a conventional hole-patterned LALC lens with TDL (referred to as TDL LALC lens hereafter) were constructed. As shown in Fig. 1(b), the dielectric layer thickness of the REF LALC lens is the same as that of the FREE LALC lens (0.55 mm). As shown in Fig. 1(c), the structure of the TDL LALC lens is similar to that of the REF LALC lens. However, the TDL LALC lens has the 1.25 mm-thick dielectric layer, which has been adopted to reduce the gathering of the fringing electric field around the periphery, and instead, distribute it throughout the AH center [25]. In the present experiment, considering the available glass specification in our laboratory, the adopted TDL in the TDL LALC lens is 1.25 mm thick, which is less than the 2.2 mm thick TDL suggested in [22]. A 1 kHz square-wave AC voltage was supplied to the LALC lenses on the top hole-patterned electrode and the bottom planar ITO electrode. The middle ring electrode was always kept at a floating potential.

 

Fig. 1 Schematic diagram of structures of the (a) FREE LALC lens, (b) REF LALC lens, and (c) TDL LALC lens.

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3. Electro-optical measurements and discussions

Figure 2 shows the optical interference fringes of the REF, FREE, and TDL LALC lenses under various voltages. The interference fringes were determined using the method described as follows [16]: A He–Ne laser with a wavelength of 632.8 nm was normally incident on the lens cell located between a pair of crossed polarizers. The transmission axes of the polarizers had an angle of 45° with respect to the rubbed direction of the lens cell. The transmitted interference fringe images were recorded using a CCD camera located behind the second polarizer. As shown in Figs. 2(a)–2(d), the REF LALC lens obtains the maximum number of fringes at 40 V; however, those fringes are gathered in the AH periphery. Therefore, the fringing electric field cannot be distributed throughout the entire AH in the REF LALC lens. At 80 V, the fringe numbers decrease because the LCs in the AH periphery become vertically aligned. Meanwhile, the FREE LALC lens also produces the maximum number of fringes at 40 V. These fringes cover the entire AH, which indicates that the fringing electric field is effectively distributed throughout the entire AH with the assistance of the floating ring electrode, as shown in Figs. 2(e)–2(h). Notably, to distribute the fringing electric field throughout the AH center, a TDL has to be used in a conventional TDL LALC lens, as shown in Figs. 2(i)–2(l). However, the TDL used significantly increases the operation voltage of the LC lens. As shown in Fig. 2(k), the TDL LALC lens obtains the maximum number of fringes at 75 V, but the number of fringes is less than those in the FREE and REF LALC lenses. The result indicates that the TDL reduces voltage difference and the associated phase difference between the periphery and the center of the AH.

 

Fig. 2 Interference fringes of the REF LALC lens at voltages of (a) 0, (b) 20, (c) 40, and (d) 80 V; interference fringes of the FREE LALC lens at voltages of (e) 0, (f) 20, (g) 40, and (h) 80 V; interference fringes of the TDL LALC lens at voltages of (i) 0, (j) 20, (k) 75, and (l) 100 V.

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The focal length of the LC lens is related to the number of interference fringes with appropriate spatial distribution according to Eq. (1) [26]:

The obtained interference fringes shown in Fig. 2 were used to depict the phase distributions of the LALC lenses by the similar method used in [2, 27–29]. As shown in Fig. 2, in the AH center, the phase profile is flat, because the LCs in this region are almost homogeneously aligned. The area of the flat phase profile is increased with the decreasing voltage, because the fringing electric field is hard to distribute into the AH center when the applied voltage is low. The flat phase profile doesn’t contribute to the image function of the LC lens. Figure 3(a) shows the phase distributions of the FREE and REF LALC lenses at 40 V. Both LALC lenses generate the same phase shift of 70 π between the periphery and the center of the AH. The phase change of the REF LALC lens is concentrated only within the periphery of the AH. By contrast, that of the FREE LALC lens covers the entire AH because the embedded floating ring electrode assists in tilting the LCs in the AH center. Figure 3(b) shows the phase distributions of the FREE LALC lens at various voltages. The lens-like phase profile appears when the voltage is supplied to the LC lens because the LCs in the periphery of the AH gradually are aligned vertically. When the applied voltage exceeds 40 V, the phase profile gradually flattens because the LCs in the AH center are gradually aligned vertically. The wavefront error of the measured data from the ideal quadratic curve is evaluated to examine the extent of the wavefront aberration of the LALC lens [2]. The wavefront error is defined as the difference between the root mean squares (RMS) of the measured data and the fitted quadratic curve. The calculated wavefront error is represented with the unit λ. A low error indicates good lens quality. The wavefront error of 0.07 λ is the common standard for lens quality of the conventional solid lens [30]. The estimated wavefront errors of the FREE LALC lens at 20, 40, and 80 V are 0.14, ~0.07, and 0.18 λ, respectively. Figure 3(c) depicts the voltage-dependent wavefront errors of the FREE LALC lens with AH diameters of 6 and 5.2 mm. As the AH diameter is 6 mm, the wavefront error of the FREE LALC lens increases rapidly with the decreasing voltages when the supplied voltage is less than 20 V, because of the flat phase distribution in the AH center. When the applied voltage exceeds 30 V, the lens-like phase distribution covers the entire AH, and can be well fitted with quadratic curve. Notably, at the voltages between 30 to 40 V, the RMS errors are below 0.07 λ that is comparable with that of the commercially available solid glass lens. When the applied voltage exceeds 40 V, the wavefront error exceeds 0.07 λ and gradually increases with voltage. As shown in Fig. 3(b), when the supplied voltage exceeds 20 V, the wavefront error is mainly caused by the phase deviation generated within the periphery of the AH. If only the AH width between −2.6 mm and 2.6 mm (AH diameter is 5.2 mm) is considered, the wavefront error of the FREE LALC at 40 V approaches 0.04 λ, i.e., nearly perfect lens function. This is because that the wavefront errors generated in the periphery of AH is disregarded. Consequently, an RMS dip is observed around 40 V in Fig. 3(c). The phase distributions of the FREE LALC lens at 40 V and the TDL LALC lens at 75 V are depicted in Fig. 3(d). The evaluated wavefront error and the maximum phase shift of the TDL LALC lens are 0.1 λ and 36 π, respectively, which are worse than those of the FREE LALC lens at 40 V. Consequently, the FREE LALC lens has better lens quality, lower operation voltage, and larger tunable focal range than the conventional TDL LALC lens. As expected, the phase difference between the periphery and the center of the AH in the TDL LALC lens decreases with increasing the thickness of TDL [19]. Therefore, if the thickness of the TDL is 2.2 mm as suggested in [22], then the maximum phase shift of the LALC lens will be considerably below 36 π.

 

Fig. 3 Phase distributions: (a) FREE and REF LALC lenses with AH diameter of 6 mm at 40 V; (b) FREE LALC lens with AH diameter of 6 mm at 20, 40, and 80 V; (c) voltage-dependent wavefront errors of the FREE LALC lens with AH diameters of 6 and 5.2 mm; (d) FREE and TDL LALC lenses with AH diameter of 6 mm at 40 V and 75 V. The symbols and solid lines indicate the measured data and the fitted curves, respectively. In (c), the red dashed line represents the common standard, and the black dashed line represents upper limit of the acceptable lens quality of the solid glass lens, respectively.

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Figure 4 shows the measured focal lengths of the FREE and TDL LALC lenses as a function of applied voltage. The He–Ne laser beam was normally incident on and focused by the LALC lens, which was placed behind a polarizer whose transmission axis was parallel to the rubbing direction of lens cell. The distance between the LC lens and the focused point was defined as the focal length. As shown in Fig. 4, when the supplied voltage is changed from 40 to 60 V, the FREE LALC with AH diameter of 5.2 mm can be electrically tuned from 17 to 18.5 cm with wavefront error less than 0.1 λ, which is upper limit of the acceptable lens quality of the solid glass lens [2]. Without considering the extent of wavefront error, the focal length of the FREE LALC lens can be tunable from 17 to 28.5 cm at voltages from 40 to 140 V. On the contrast, the TDL LALC lens requires a high voltage of 75 V to achieve the minimum focal length of 27.8 cm. Therefore, the FREE LALC lens develops a relatively low operation voltage and large lens power.

 

Fig. 4 Voltage-dependent focal lengths of the FREE and TDL LALC lenses. The solid line indicates the fitted curve with spline interpolation function of MATLAB.

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Theoretically, the focal length of a gradient refractive index (GRIN) lens can be estimated as [31]:

The interference fringe observation system was adopted to observe the dynamic response of the LALC lens, whereas the CCD camera was replaced with a power meter [32], which recorded the transmittance of the LALC lens. The rise (fall) time was defined as the required time during which the transmittance of the LALC lens became stable when the supplied voltage was suddenly turned on (off). To achieve the minimum focal length, the rise time of the FREE LALC lens is 18 s (from 0 to 40 V), whereas that of the TDL LALC lens is 31 s (from 0 to 75 V), as shown in Fig. 5(a). The rise time of the FREE LALC lens is faster than that of the TDL LALC lens. By contrast, to relax from the minimum focal length, the fall time of the FREE LALC lens is 115 s (from 40 to 0 V), whereas that of the TDL LALC lens is 78 s (from 75 to 0 V), as shown in Fig. 5(b). The response time of the FREE LALC lens can be improved via polymer stabilization [33], the use of dual-frequency LC materials [34], or the doubling of the thin LC layer structure [27]. Among these methods, the FREE LALC lens that adopts the double thin LC layer structure is expected to remarkably decrease the response time and to generate lens power that is approximately twofold larger than that using the single LC layer.

 

Fig. 5 Rise times (a) and fall times (b) of the FREE and TDL LALC lenses.

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The mechanism that distributes the fringing electric field throughout the entire AH of the LALC lens with the embedded floating ring electrode can be explained as follows. As depicted in Fig. 6(a), the REF LALC lens only has a thin dielectric layer between the hole-patterned electrode and the LC layer, and thus, the fringing electric field is concentrated in the AH periphery. By contrast, adding a floating ring electrode at the interface between the thin dielectric layer and LC layer focuses the electric field lines and increases the electric field strength around the floating metal ring electrode [35]. The increased electric field strength assists in tilting the LCs near the floating ring electrode located near the AH center, as shown in Fig. 6(b). Accordingly, the fringing electric field distribution and the phase difference of the LC lens cover the entire AH in the FREE LALC lens. Notably, the operation principle of the floating ring electrode in this study is entirely different from that of the floating electrode demonstrated in the concentric multi-ring electrode LC lens in [15]. In their design, a thin layer of SiO2 (approximately 30 nm) is deposited to separate the multi-ring electrode and the floating electrode. The floating electrode is placed in the gap area of the adjacent multi-ring electrode and is overlapped with the small parts of the neighboring multi-ring electrodes on both sides. The potential on the floating electrode becomes the intermediate value of that on both neighboring multi-ring electrodes via dielectric coupling and capacitive voltage division. Consequently, the voltage profile between the neighboring multi-ring electrodes can be effectively smoothened. By contrast, the floating ring electrode in our experiment is not overlapped with the hole-patterned electrodes, and the glass layer that separates the hole-patterned electrode and the floating ring electrode is thick. This setup indicates that dielectric coupling and capacitive voltage division effects can be disregarded. Furthermore, as mentioned in [35], doped metal nanoparticles trap ion impurities and therefore decrease the amount of ion impurities adsorbed onto the surface alignment layers. This effect increases van der Waals dispersion interactions between the LCs and the alignment layers. Consequently, the pretilt angle and the recovery time of the LC cell decrease with increasing metal nanoparticle concentrations. In Fig. 5, the recovery time of the FREE LALC lens is slower than that of the conventional TDL LALC lens. The slow recovery time of the FREE LALC lens is particularly observed in the floating ring electrode area, and its mechanism is similar to that of the metal nanoparticles: the floating ring electrode can be considered a small metal material that attracts ion impurities to adsorb onto the alignment layer next to the floating ring electrode. The ion impurities absorbed onto the alignment layers near the floating ring electrodes increase the pretilt angle of the LCs, which increases the recovery time of the LC lens when the applied voltage suddenly declines. The floating ring electrode can also generate capacitances on the glass layer and the LC layer during voltage supply. The slow relaxation of the capacitances increases the recovery time of the FREE LALC lens when the supplied voltage suddenly declines.

 

Fig. 6 Schematic diagrams of the electric field distributions of the REF and FREE LALC lenses with a dielectric layer of the same thickness: (a) REF type and (b) FREE type. The red solid lines represent the electric field lines in the cells.

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The image performance of the FREE LALC lens was observed using the setup described as follows. A printed paper was placed in front of the FREE LALC lens as the object. A CCD camera with lens module was placed behind and close to the LALC lens to capture the formed images of the object. A polarizer with a transmission axis parallel to the rubbed direction of the LALC cell was attached to the CCD camera. The height of the letter “U” in the object was 0.2 mm. The distance between the object and FREE LALC lens was 12 cm. With an incident light of 632.8 nm, the measured transmittance of a handmade 6-μm-thick LC cell was ~85%, whereas that of the demonstrated 125-μm-thick FREE LALC lens cell was only ~72%, owing to scattering of the thick LC layer. A pinhole with diameter of 5.2 mm was used to decide the clear aperture of the FREE LALC lens. At 0 V [Fig. 7(a)], the obtained image was blurred. When the FREE LALC lens was addressed at 40 V [Fig. 7(b)], the image became clear. The image performance of the FREE LALC lens at low voltage was also demonstrated. A printed paper was placed at a distance of 21 cm away from the FREE LALC lens. At 0 V [Fig. 7(c)], the blurred image was built. When the addressed voltage was switched to 10 V [Fig. 7(d)], the clear image was observed, indicating that the FREE LALC lens at low voltage still preserved lens quality. The obtained image also confirmed that the major image function of the LC lens at low voltage was mainly attributed to the lens-like phase profile in the AH periphery. Notably, the image quality is affected by many conditions, such as scattering of the cell, color dispersion of the LC material, ambient light, the positions of the object, and quality of the used CCD camera.

 

Fig. 7 Image performance through the FREE LALC lens with supplied voltages of (a) 0, and (b) 40 V, the distance between the LALC lens and object is 12 cm. Image performance through the FREE LALC lens with supplied voltages of (c) 0, and (d) 10 V, the distance between the LALC lens and object is 21 cm.

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4. Conclusions

A new hole-patterned LALC lens with an embedded floating ring electrode is demonstrated in the study. The embedded floating ring electrode increases the electric field strength and then assists in tilting the LCs in the AH center of the lens. The dielectric layer used to distribute the fringing electric field into the AH center in the conventional hole-patterned LC lens can be effectively decreased with the assistance of the embedded floating ring electrode. The decreased thickness of the dielectric layer provides the FREE LALC lens with the advantages of lower operation voltage and larger tunable focal range compared with the conventional TDL LALC lens. When a voltage of 40 V is applied, the introduced floating ring electrode modulates the phase retardation of the LALC lens in a nearly perfect quadratic form with wavefront error approaching 0.04 λ within 5.2 mm-diameter AH. Studies to improve the performance of the FREE LALC lens, such as those that address response time, operation voltage, and polarizer-free lens, are underway.