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Abstract
A novel approach for fabricating liquid crystal (LC) lenses is presented. The approach involves the use of a photocurable prepolymer dispersed in a cell fabricated with vertically aligned substrates. A radial gradient UV irradiation intensity distribution is produced using a radial variable neutral density filter. Under UV irradiation, the prepolymer diffuses and is then polymerized on the substrate surfaces owing to vertical phase separation. After polymerization, the diameter of the self-assembled polymer gravel on the substrates has a radial gradient distribution, causing a radial gradient pretilt angle (RGPA) distribution on the substrates and producing LC lenses. By numerical simulation, RGPA LC lens has significantly lower supplied voltage than conventionally hole-patterned electrode (HPE) LC lens, and higher lens power. In the experiment, the fabricated RGPA LC lens with aperture size of 5 mm possesses a simple planar electrode structure, low operation voltage (< 4 V), small root mean square wavefront error (< 0.08 λ), and acceptable focusing quality. By the overdriving scheme, the switched-off time of the fabricated RGPA LC lens reaches 0.27 s. With the novel approach, low-voltage LC lenses with different optical aperture sizes can be easily fabricated.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Compared with a conventional mechanical lens system, which consisted of lenses with focal lengths that can be adjusted through the mechanical changing of relative distances among lenses, liquid crystal (LC) lenses have low weights and costs and electrically tunable focusing capability. Since the first introduction of these lenses approximately 40 years ago [1], different LC lens designs capable of focusing light have been developed. Focal length-switchable LC lenses [2,3] and lens arrays [4,5] have attracted interest because of their potential applications in mobile cameras [6,7], two-/three-dimensional (2D/3D) autostereoscopy [8,9], light field displays for 3D capturing and imaging [10,11], and wavefront correctors [12,13]. LC lens fabrication methods, such as spherical electrode [14], polymer networks [15], hole-patterned electrode (HPE) [16], dielectric dividing principle [17], and multiple ring electrode [18], are known. However, spherical electrode LC lenses consist of solid lens and LC layers that require large volume. Polymer network LC lenses require high-addressing voltages because of the strong anchoring of polymer networks. In an HPE LC lens, a thick dielectric layer is embedded between an active electrode and LC layer to produce quadratic phase distribution. Thus, a high voltage is required to extend fringing electric field into the center of the lens. Building an LC lens according to the dielectric dividing principle requires materials with different permittivities but similar refractive indices. However, appropriate materials are difficult to obtain. LC lenses with multiple ring electrodes have complicated electrode structures and addressing schemes. The electrode structure of an LC lens can be simplified, and its operation voltage can be significantly reduced by creating a radial gradient pretilt angle (RGPA) distribution on the substrate surface of the cell. In recent years, the photosensitive polymer has been widely used to produce the specific LC alignment in the fabrication of LC devices [19]. Pretilt angle of LCs can be controlled from 0° to 90° by the surface localized polymer alignment (SLPA) [20–24]. A SLPA cylindrical LC lens has been fabricated using a movable narrow slit and varying voltages to produce the RGPA distribution during UV irradiation [25]. Precisely controlling the position of the slit and curve voltage requires a complicated process. The SLPA cylindrical LC lens has a switched-off voltage of ∼ 9 V. Bezruchenko et al. developed hybrid-aligned (HA) LC lens based on photo-responsive alignment polymer for RGPA distribution [26,27]. The alignment polymer layer on the bottom substrate was subjected to UV irradiation through a 1.5 mm-diameter hole-patterned photomask, and thus the light intensity distribution induced an RGPA distribution required for LC lens. The fabrication of the HA LC lens required complicated treatments and the phase profile of the resulting LC lens was significantly deviated from the parabolic curve. Tseng et al. controlled the ratio between horizontal and vertical alignment domain sizes to induce spatially variable pretilt angle distribution [28]. The RGPA was affected by the concentration of the horizontal alignment polymer ROP-103 and a UV laser with a Gaussian intensity profile. The diameter of the resulted HA LC lens was less than 1 mm. The stacked alignment layer required a complicated fabrication process. Even with the HA structure, the two aforementioned RGPA HA LC lenses still had a switched-off voltage of 10 V. The HA structure also indicated that the birefringence of the LC material cannot be utilized effectively. Further, their methods were not suitable for the fabrication of large aperture LC lenses (aperture diameter of > 4 mm) or LC lens of various aperture sizes because of the small diameters of the employed gradient UV sources. Different from conventional LC lenses, Pancharatnam-Berry (PB) LC lenses aligned the LC molecules with a continuously varying azimuthal angle distribution. A photo-alignment material had to be coated on the substrate of PB LC lens cell. After interference exposure, the azimuthal angle of LCs induced a PB phase distribution. The circularly polarized light converged or diverged after passed through the PB LC lens [29,30]. PB LC lenses possessed large aperture size, high optical power, and fast response time due to a thin LC layer used. Recently, the ferroelectric PB LC lens had been demonstrated [29–31], yielding the diffraction efficiency up to 87% and response time of 300 µs with a low operation voltage. PB LC lenses had been used to overcome the issues of accommodation-convergence in head-mounted display devices [32,33] and generation of spatially separated focuses [34]. However, the focal length of PB LC lenses was not switchable continuously due to diffractive lens function.
We proposed a new method for controlling the pretilt angles of an LC, using photocurable prepolymer in an LC cell fabricated with vertically aligned substrates [35]. Under UV exposure, the prepolymer approached and polymerized on the substrate surfaces because of vertical phase separation induced by differences among the surface tensions of the employed materials. After UV curing, the self-assembled polymer gravels on the substrates altered surface polarity and changed the pretilt angle of the LC in the cell. Evidently, the formed polymer gravels were oriented along the rubbing direction of the substrates, and the amplitude and pitch of the self-assembled gravels could be controlled by regulating UV curing intensity and supplied voltage during curing [36].
In this study, the homogeneously-aligned LC lens with an aperture size of 5 mm was constructed using the photocurable prepolymer NOA65 and vertically aligned substrates. After UV irradiation through a radial variable neutral density (RVND) filter, the self-assembled polymer gravel on the substrates of the cell had a radial gradient amplitude distribution, which induced RGPA distribution and enabled the lens function in the LC cell. In comparison with the conventional HPE LC lens, the fabricated RGPA LC lens required a low voltage and has a high lens power, which was confirmed by the calculated voltage drops in the LC layer and the interference fringes of the lens cell. In the experimental part, polymer morphology on the polymerized substrate was observed by scanning electronic microscopy (SEM). The optical interference fringes of the fabricated LC lens were recorded and used in determining operation voltage, depicting phase profiles, and estimating wavefront error. The switched-off voltage of the fabricated RGPA LC lens was only 4 V, far lower than that (10 V) in the HA LC lenses presented in [26,28] and that (9 V) in the SLPA LC lens presented in [25]. Diffraction-limited value was calculated and used in examining the focusing qualities of the LC lens. The transient transmissions, transmission spectrum and imaging performance of the LC lens cell were investigated in the content.
2. Motivation
The motivation of this experiment was explained by the numerical calculation with the finite element software Comsol Multiphysics (Comsol Inc.). In the calculation, the free energy density f of LCs can be described by the director $\hat{n}$ and the director ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over E} }$ as:
The LC director $\hat{n}$ can be obtained by the following equations:
The interference fringe pattern of the LC lens can be obtained by calculating the transmission T of the LC lens under crossed polarizers using the following equations [37],
where $\varGamma $ is the phase retardation of LCs, $\lambda $ is the wavelength of incident light, d is the LC cell thickness, neff and no are the effective refraction index along rubbing direction and the ordinary index of LCs, respectively. Figures 1(a) and 1(b) show the structures of the HPE and RGPA LC lenses, respectively, both of which have the same cell thickness of 13 µm and optical aperture (OA) of 5 mm. The thickness and dielectric constant of the glass dielectric layer in the HPE LC lens were 1.1 mm and 6.7, respectively. The glass dielectric layer was used to extend the fringing electric field into the OA center of HPE LC lens and create a quadratic phase curve [38]. The nematic parameters used for calculation were E7 (Δn = 0.22, $\Delta \varepsilon$= +14.07, k11 = 11.1 pN, k22 = 5.9 pN, k33 = 17.1 pN, and ${\gamma _1}$ = 233 mPa·s at 20 °C, obtained from Daily Polymer, Taiwan) [39]. The pretilt angle of the LCs in the HPE LC lens was set to 2°, and voltage was supplied across the top hole-patterned and bottom planar electrodes. The pretilt angle distribution of the RGPA LC lens was assumed to be in a cosine function, with 88° in the OA periphery and 2° in the OA center, as shown in the inset of Fig. 1(b). Notably, the actual pretilt angle distribution of the fabricated RGPA LC lens was not measured in this experiment, since the non-homogeneous alignment of LCs in the lens cell. From the calculated voltage drops in the LC layer [Figs. 1(c) and 1(d)], with the maximum voltage drop of 1.5 V in the LC layer, the conventional HPE LC lens requires a high voltage of 200 V because of the effects of fringing electric field and thick glass dielectric layer. By contrast, the RGPA LC lens only requires a low voltage (1.5 V) owing to the free of the glass dielectric layer and the utilization of planar electrode structure, which easily extends the voltage into the OA center. Furthermore, the calculated interference fringes [Figs. 1(e) and 1(f)] reveal that the RGPA LC lens provides larger phase retardation than the conventional HPE LC lens.
Fig. 1. Structure scheme of (a) conventional HPE and (b) RGPA LC lenses. Inset indicates the pretilt angle distribution of RGPA LC lens defined in the calculation; calculated voltage drops in the LC layer for the (c) conventional HPE LC lens at 200 V and (d) RGPA LC lens at 1.5 V; calculated interference fringes of the (e) conventional HPE LC lens at 200 V and the (f) RGPA LC lens at 1.5 V.
3. Experimental preparations
An empty cell was assembled with two indium–tin–oxide glass substrates coated with vertical polyimide AL-8088C (Daily Polymer, Taiwan) and were rubbed antiparallel. The thickness of the empty cell was controlled with a 12 µm Mylar spacer. The LC mixture consisted of nematic E7 and a small amount of the photocurable prepolymer NOA65 (Norland Optical Adhesive, USA). The NOA65 concentration was set to 2.5 wt%. The LC mixture was then injected into the empty cell by capillary action. Initially, the LC molecules were aligned homeotropically, and NOA65 prepolymers were homogeneously dispersed in the cell, as shown in Fig. 2(a). A uniform UV light source passing through a RVND filter with 5 mm diameter was used to cure the cell. The RVND filter had maximum transmission approach 100% at center and minimum transmission approach 0% at periphery. Under UV irradiation, the prepolymer diffused and was polymerized on the substrates through vertical phase separation [35]. Afterward, the polymer gravels with radial gradient amplitude distribution were generated on the substrates, inducing RGPA distribution on the substrates of the cell and enabling RGPA lens, as shown in Fig. 2(b). UV intensity and irradiation time were set at 5 mW/cm2 and 3.5 min, respectively. Polymer morphology on the substrate surfaces was observed after the fabricated LC cell was peeled off, and the substrates were dipped in cyclohexane solution for 3 h for the removal of residual LCs on the substrate surfaces. After the LCs were washed off completely, the substrates were coated with a thin gold film measuring ∼ 5 nm and observed through a SEM.
4. Results and discussion
Figure 3 shows the SEM images of the self-assembled polymer gravel on the substrates of the fabricated RGPA LC lens. The amplitude of the self-assembled polymer gravel was related with the transmission of the used RVND filter. The polymer gravels at point B had the larger amplitude than those at point A because the prepolymers had sufficient time to coalesce into large droplets under weak UV irradiation [36]. Accordingly, the amplitude of polymer gravels between points A and B gradually changed due to the used RVND filter with gradient transmission distribution. Thus, the RGPA on the substrate surface of the cell was induced.
Figure 4 depicts the optical interference fringes of the fabricated RGPA LC lenses at various voltages. The LC lens cell was placed between a pair of crossed polarizers with a transmission axis of 45° with respect to the rubbing direction of the lens cell. An expanded He–Ne laser with a wavelength of 632.8 nm was incident normally through the polarizers and lens cell. The interference fringes were recorded using a high-resolution charge-coupled device (CCD) camera located behind the analyzer. The focal length (f) of the LC lens correlated with the number (N) of interference fringes with an appropriately spatial distribution, which can be represented by the following formula: [40]
where r is the radius of OA, and λ denotes the wavelength of incident light. Figures 4(a)–4(e) show that the number of interference fringes decreased as voltage increased. The focal length of the fabricated RGPA LC lens increased with voltage because of the increased LC tilt angle in the OA center relative to the substrate surface. The increase resulted in a small phase difference from the OA center to the OA periphery. Without supplied voltage, the LC lens had the most number of interference fringe and thus the largest lens power. As the voltage reached 4 V, the LCs in the entire OA were almost aligned in the same high-tilt angle and the phase difference from the OA center to the OA periphery disappeared, indicating that lens function was switched off. Notably, the fabricated RGPA LC lens had a low operation voltage (4 V). The optical interference fringes of the LC lens at various voltages were further calculated. The results are shown in Figs. 4(f)–4(j). Obviously, at increased voltages, the changes in fringe numbers in the calculated results were similar to those in the measured results. Notably, in the fabricated cell, the pretilt angle in the entire OA was not distributed in a cosine function. Moreover, the generated polymer gravels decrease the surface anchoring energy of substrates [35]. Consequently, fringe distributions in the measured images were slightly different from those in the calculated images. In Figs. 4(a)–4(c), the slight deformation in the fringes may be caused by the alignment defects from polyimide and the inhomogeneity of handmade RVND filter, which can be avoided via improvements in the alignment process and photomask fabrication. After a few weeks or cycles of heat treatment, the deterioration in the fringes of fabricated RGPA LC lens has been observed, possibly attributed to the weak anchoring from polymer surface and the residual prepolymer in the bulk. Optimizations in the prepolymer material and UV irradiation dosage can improve the stability of RGPA alignment.Fig. 4. Measured interference fringes of the fabricated RGPA LC lens at (a) 0, (b) 1, (c) 2, (d) 3, and (e) 4 V; calculated interference fringes of the fabricated RGPA LC lens at (f) 0, (g) 1, (h) 2, (i) 3, and (j) 4 V.
An He–Ne laser was used in obtaining the voltage-dependent transmission (V–T) curves of the LC lens cell. The supplied voltage was 1 kHz square wave. The LC lens cell was positioned between a pair of crossed polarizers, and the rubbing direction of the LC lens cell had an angle of 45° with respect to the transmission axis of the polarizer. The V–T curves in the OA center and OA periphery are presented in Fig. 5. Notably, the oscillating peak number of the V–T curve in the OA center was larger than that of the V–T curve in the OA periphery, confirming that the LC pretilt angle in the OA center was lower than that in the OA periphery. Furthermore, the amplitudes of the polymer gravels in the OA periphery were relatively large and nonuniform (Fig. 3), which scattered the incident light, disrupted the reorientation of the LCs, and reduced the maximum transmission of the V–T curve in the OA periphery.
Figure 6 shows the measured focal lengths of the fabricated RGPA LC lens as a function of supplied voltage. An expanded He–Ne laser beam was incident normally into the LC lens cell. The LC lens cell was placed behind a polarizer with a transmission axis parallel to the rubbing direction of the lens cell. The focal length was defined as the distance between the LC lens cell and focused laser spot. The focal length of the fabricated RGPA LC lens changed from ∼125 to 400 cm at a voltage range of 0–3 V. When the voltage exceeded 3 V, the focal length considerably lengthened because the pretilt angles at the OA center and OA periphery were almost similar and the interference fringes nearly disappeared. The focal lengths can be further reduced using the LC material with high birefringence.
Figure 7(a) plots the phase retardation profiles of the fabricated RGPA LC lens at various voltages, and the phase retardation was calculated from the obtained optical interference fringes in Fig. 4. The symbols indicate the positions of dark fringes, and the solid lines indicate the quadratic fitting curves. The wavefront error of the experimental data was then calculated from the ideal quadratic curve and used in examining the extent of the wavefront aberration of the LC lens. The wavefront error was defined as the root mean square (RMS) of the difference between the experimental data and the fitted quadratic curve. The calculated RMS error was characterized with the unit of λ. A low RMS error implied superior lens quality. The RMS error of 0.07 λ was defined as the common standard for the conventional solid lens [18,41]. For ophthalmic application, an RMS error of less than λ/4 was considered acceptable [42]. As shown in Fig. 7(b), the RMS error of the fabricated RGPA LC lens was 0.077 λ at 0 V, which decreased with increased voltage. When the voltage reached 3 V, the interference fringe number of the LC lens was less than 3 (Fig. 4). Thus, the calculated RMS error approached 0. Consequently, the fabricated RGPA LC lens with OA of 5 mm diameter has prospective ophthalmic application because of its low RMS error (< 0.08 λ).
Fig. 7. (a) Phase retardations and (b) RMS errors of the fabricated RGPA LC lens at various supplied voltages.
The full width at half maximum (FWHM) of the focusing spot of the fabricated RGPA LC lens operated at 0 V was used in the analysis of focusing quality of LC lens. The FWHM value of the diffraction-limited spot (Airy disk) can be calculated using the following well-known formulas: [43,44]
where NA is the numerical aperture; r denotes the OA radius of the LC lens; dFWHM refers to the FWHM of the Airy disk. As shown in Fig. 6, the measured focal length (125 cm) of the RGPA LC lens at 0 V was substituted into Eqs. (9) and (10) for the calculation of NA and dFWHM. The calculated dFWHM was 165 µm. The FWHM value of the measured focusing spot was 178 µm, which was less than 1.38x dFWHM, indicating that the fabricated RGPA LC lens provided an acceptable focusing quality [43,44].The interference fringe observation system was adopted and used in observing the dynamic response of the fabricated RGPA LC lens, whereas the CCD camera was replaced with a photodetector connected to an oscilloscope [41]. The addressing (recovery) time was defined as the required time during which the transmission of the LC lens reached stable when the supplied voltage was turned on (off). As shown in Table 1, the addressing time of the LC lens decreased with increased voltage because the addressing time was mainly dominated by the supplied voltage. Addressing time was also determined by adopting the overdriving scheme, in which a pulse voltage of 5 V was first supplied to the LC lens cell for 200 µs, followed by the desired voltage. Obviously, the addressing time was significantly decreased to the order of sub-second by the overdriving scheme. As seen in Fig. 4(e), when the fabricated RGPA LC lens was supplied with a voltage of 4 V, the interference fringe disappeared. Thus, the lens function was switched off. According to Table 1, the switched-off time of the fabricated RGPA LC lens reached 0.27 s under the overdriving scheme. In general, the recovery time increased with supplied voltage because of the increased rotation angle, which required the longer time to rewind back to the zero voltage state. The average recovery time is ∼1.49 s, which is mainly decided by the LC layer thickness. The calculated recovery time of the conventional HPE and RGPA LC lenses is similar of ∼ 0.8 s. The measured recovery time was larger than the calculated one because the formed polymer gravels decreased the surface anchoring energy of the substrate and increased the recovery time [35].
Table 1. Dynamic response of the RGPA LC lens.
The transmission spectra of the fabricated RGPA LC lens cell and traditional homogeneous LC cell in the visible wavelengths were also measured. As shown in Fig. 8(a), the transmission of the RGPA LC lens cell was ∼10% lower than that of the homogeneous LC cell because of light scattering from the polymer gravels and refraction index mismatch among the surfaces. Imaging performance was recorded with the following setup. A CCD camera with lens module was placed in front of the LC lens cell. A polarizer with a transmission axis parallel to the rubbing direction of the LC lens cell was placed between the CCD camera and LC lens cell. An object of doll was placed in the rear of the LC lens. The distance between the CCD camera and LC lens was 1 cm, and the distance between the LC lens and doll was 39 cm. First, the blur doll image [Fig. 8(b)] was obtained when the LC lens was removed. As the LC lens was re-inserted and supplied with 0 V, the doll image [Fig. 8(c)] became clear. Subsequently, another clear doll image [Fig. 8(d)] was obtained when the distance between the LC lens and doll was 45 cm and the LC lens was supplied with 1 V. Notably, light scattering from the LC lens cell caused the images in Figs. 8(c)–8(d) to be slightly darker than that in Fig. 8(b). Light scattering loss is caused from the polymer gravels and refraction index mismatch among the surfaces. Reference [36] demonstrated the stronger UV irradiation intensity induced smaller self-assembled gravel. Accordingly, enhancing the high UV irradiation intensity to decrease the amplitude of self-assembled gravel was possible to decrease the light scattering loss.
Fig. 8. (a) Transmission spectra of the fabricated RGPA LC lens cell and conventional homogeneous LC cell. Imaging performances (b) without RGPA LC lens, and with the fabricated RGPA LC lens at (c) 0 V and (d)1 V.
5. Conclusions
A low-voltage RGPA LC lens with simple planar electrodes was fabricated using self-assembled polymer gravel with a radial gradient amplitude distribution on the substrate. In numerical simulations, if the maximum voltage dropped in the LC layer is fixed at 1.5 V, the supplied voltages of conventional HPE and RGPA LC lenses are 200 and 1.5 V, respectively. This result reveals that RGPA LC lens requires a small supplied voltage. Moreover, RGPA LC lenses provide large lens power. In the experimental parts, the morphology of polymer gravel formed on the substrate of fabricated RGPA LC lens is verified with SEM images. The fabricated RGPA LC lens provides tunable focal lengths of 125–400 cm at low operation voltages (0–3 V) and exhibits a low switched-off voltage (4 V) and fast switched-off time (0.27 s). Moreover, it has an RMS error of below 0.08 λ within the operation voltage range. The fabricated LC lens is then used in a practical imaging system. In general, an LC lens with an aperture size near 4 mm can be used in the fabrication of contact lenses for the presbyopia correction [45]. As aperture size reaches the order of centimeter, LC lenses can be further applied to adaptive eyeglasses [46]. Therefore, the proposed approach shows promise in ophthalmic applications because it can be used in preparing low-voltage LC lenses with optical apertures of various sizes. Furthermore, the fabricated RGPA LC lens can efficiently utilize the birefringence of LC materials and yield large lens power.
Funding
Ministry of Science and Technology, Taiwan (107-2112-M-018-003-MY3, 108-2811-M-018-502).
Acknowledgments
The authors would like to thank Mr. Ting-Yu Wang for contribution during preliminary investigations.
Disclosures
The authors declare no conflicts of interest.
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