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Abstract
In this study, a large-aperture hole-patterned liquid crystal (LHLC) lens was prepared from a mixture of nematic liquid crystal (NLC, E7) and organic material (N-benzyl-2-methyl-4-nitroaniline, BNA). The electro-optic properties of doped and undoped samples were measured, compared, and analyzed. The doped sample exhibited a response time that was ∼6 times faster than that of the undoped sample because BNA doping decreased the rotational viscosity of the NLC. BNA dopant effectively suppressed the RMS error of LHLC lens addressed at the high voltage. Furthermore, the BNA dopant revealed a considerable absorbance for short wavelengths (< 450 nm), automatically providing the LHLC lens with a blue light filtering function for ophthalmic applications.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent decades, liquid crystals (LCs) have been used in numerous tunable photonic devices, such as optical phased arrays for laser beam steering [1], tunable focus lenses for camera zoom lenses [2], variable optical attenuators for telecommunications [3], LC-infiltrated photonic crystal fiber [4,5], two-/three-dimensional (2D/3D) displays [6], endoscopes [7], and laser-pumped dye-doped LC laser [8]. LC lenses have attracted great attention from photonic researchers because of their electrically tunable focal length, compact size, light weight, and low power consumption [9,10]. Several approaches have been proposed to construct large-aperture LC lenses, such as the combination of a glass lens and an LC layer [11], the dielectric dividing principle [12], the polymer/LC structure [13], cholesteric LC lens [14], smectic LC lens [15], multi-ring electrode [16], hole-patterned electrode [17], and Pancharatnam–Berry lens [18,19]. Among these approaches, the LC lens that uses a hole-patterned electrode has the advantages of easy construction, simple cell structure, and extensively tunable focal range. This kind of LC lens has an LC layer that is sandwiched between hole-patterned and planar electrodes. When voltage is supplied to the lens cell, the hole-patterned electrode provides an axially-symmetric nonuniform electric field, which causes the LC to create a refractive index gradient along the radial distribution. After passing through the lens cell, the incident light converges. However, the dynamic response of hole-patterned LC lenses with a large aperture size (> 4 mm) is usually in the order of several or several 10 s due to the effect of the fringing electric field and the intrinsic rotational viscosity of the LC. For example, the turn-on time of the 7 mm aperture hole-patterned LC lens is ∼50 s, which is further reduced to ∼20 s by applying an extra horizontal field [20]. The turn-on time of a 6 mm aperture hole-patterned LC lens operating with two driving voltages is ∼1.8 s [21,22]. The turn-off time of a 4 mm aperture hole-patterned LC lens introduced with a pair of ring and pie electrodes is ∼12 s, which is further shortened to ∼5 s by the dual-frequency driving scheme [23]. Previously, we have also fabricated the 6 mm aperture hole-patterned LC lens with an ultra-thin indium–tin–oxide (ITO) film as the weakly conductive layer, whose turn-off time is ∼ 7.5 s [24]. Moreover, 6 mm aperture hole-patterned LC lenses with a floating ring electrode inserted require a slow turn-off time of more than 100 s [25,26]. Table 1 summarizes the response times of the large-aperture hole-patterned LC (LHLC) lenses. Their response times are not fast enough for practical applications.
Table 1. Response times of the LHLC lenses.
Synthesizing a nematic LC with low viscosity is a straightforward approach to improve the response time of LC devices. A high-birefringence and low-viscosity LC material with negative dielectric anisotropy (Δɛ) was synthesized to reduce the image blur in LC display TVs [27]. Moreover, an ultralow-viscosity nematic LC mixture with a low activation energy was also proposed to suppress significantly the rising rate of viscosity at low temperatures [28]. However, an LC material with negative Δɛ is unsuitable for achieving a hole-patterned LC lens with a positive tunable focal length; hole-patterned LC lenses filled with an ultralow-viscosity nematic LC mixture require a thick cell gap to preserve the lens power because the birefringence of the LC mixture is only ∼ 0.1, which is unfavorable for decreasing the response time of the lens cell. Other approaches have also been presented to accelerate the dynamic response of LC devices. For example, dual frequency LCs (DFLCs), which exhibit positive Δɛ at low frequencies and negative Δɛ at high frequencies, have been used to decrease the rise time and fall time of LC devices by controlling the voltage frequency [23]; polymer-stabilized LC (PSLC) microlens has achieved a fast response time of less than 20 ms due to the anchoring effect provided by the formed polymer networks [29]; and nanoparticle dispersion has been reported to improve the dynamic response of LC devices [30]. Nevertheless, DFLCs require a relatively complicated driving scheme, and the dielectric heating possibly shifts the crossover frequency, leading to performance instability during high-frequency operation. PSLC devices require a high voltage to address the reorientation of the LCs restricted by the polymer network; moreover, the improvement in the response time of LC devices with nanoparticle dispersions is insignificant, and nanoparticle aggregation causes light scatterings. In view of the above, different ways of decreasing the response time of hole-patterned LC lenses must be sought.
Organic N-benzyl-2-methyl-4-nitroaniline (BNA) was first developed by Hashimoto et al. [31]. BNA exhibits a ∼300 times higher second harmonic generation efficiency compared with that of the standard urea and is phase matchable [31,32]. BNA is favorable to the realization of devices because of its THz, nonlinear optic, linear electro-optic, and possibly piezoelectric properties. However, LC devices fabricated with BNA dispersion have yet to be reported. In the current study, the doping of organic BNA is done during the fabrication of hole-patterned LC lenses with an optical aperture diameter of 4 mm. The optical interference fringes and focal lengths of undoped and doped lens cells are measured to compare the lens powers and the tunable focusing capabilities. To examine the lens and focusing qualities, their wavefront errors and the full widths at half maximum (FWHM) of focusing spots are evaluated. Meanwhile, their dynamic responses are obtained by measuring the transient transmissions. In addition, the transmission spectra of these lens cells are obtained to confirm the absorbance of the BNA dopant, and their imaging performance are practically demonstrated. In the experiment, the turn-off time of the conventional hole-patterned LC lens is ∼ 6 s, and that of the BNA-doped hole-patterned LC lens is 0.9 s. The remarkable improvement in turn-off time provides a promising way of overcoming the slow response drawback of LHLC lenses.
2. Experimental preparations
As shown in Fig. 1(a), the lens cell was composed of 1.1 and 0.55 mm-thick ITO glass substrates (Chipset Technology Co., Ltd, Taiwan). The ITO surface of the top substrate was etched with a 4 mm diameter hole pattern. The inner surfaces of the top and bottom substrates were coated with homogeneous polyimide AL-1426CA (Daily Polymer Corp., Taiwan) and then rubbed in the antiparallel direction. The cell gap was determined with 25 µm-thick Mylar spacers. Organic material BNA was purchased from Seedchem Company Pty. Ltd, Australia, and its molecular structure was shown in Fig. 1(b). The mixture of nematic LC (NLC, E7) (Daily Polymer, Taiwan) and BNA was prepared with a concentration ratio of 97:3. The LC mixture was then filled into the empty lens cell through capillary action above the isotropic temperature of the NLC. NLC E7 had a rotational viscosity (γ) of 232.6 mPa·s; dielectric anisotropy Δɛ of 14.5; birefringence Δn of 0.22; and elastic constants k11, k22, and k33 of 11.1, 5.9, and 17.1 pN at 20°C, respectively. The LHLC lens filled with pristine NLC E7 was also fabricated to confirm the effects of BNA in the LHLC lens. The LHLC lenses filled with the mixture and pure NLC are respectively referred to as BNA-doped and pure LHLC lenses hereafter. The actual photo of the pure LHLC lens was shown in Fig. 1(c). The photo of the BNA-doped LHLC lens was almost the same as that of the pure LHLC lens. A 1 kHz square-wave AC voltage was supplied to the LHLC lenses across the top hole-patterned and bottom planar ITO electrodes. The 5 µm-thick homogeneous BNA-doped LC cells with antiparallel rubbing treatment were also fabricated to understand the effects of BNA doping. Their voltage-dependent transmissions were used to estimate Δn of NLC [33]. Moreover, the phase transition temperatures Tni (or clearing temperatures) was observed using a polarizing optical microscope, in which LC cell was heated up from nematic to isotropic phase at a rate of 0.25 °C/min with a temperature controller (T95-PE, Linkam, UK). Figure 1(d) reveals Δn and Tni decrease with the increased BNA concentration. At BNA concentration of 3 wt%, Δn is saturated. Notably, BNA doping decreases Tni and hence the order parameter S and Δn. It also decreases γ due to the decreased S, according to the following equations [34,35].
where T is the ambient temperature; Δn0 is the birefringence of NLC at 0 K; b is a proportionality constant related to the molecule shape, dimension and moment of inertia; E is the activation energy of molecule rotation; Kb is the Boltzmann constant; β is a material parameter. Notably, excessive BNA may disturb the LC alignment and hence degrade the turn-off time of LC cell. Once BNA concentration exceeds 5 wt%, the LC mixture becomes jelly form. One month later, the electro-optical performances of BNA-doped LHLC lens still remain similar. Therefore, the BNA concentration of 3 wt% was used to fabricate the BNA-doped LHLC lens cell in this paper.
Fig. 1. (a) Structure scheme of LHLC lens cell; (b) molecular structure of BNA; (c) actual photo of pure LHLC lens cell; (d) measured birefringence of NLC and phase transition temperatures in the homogeneous BNA-doped LC cells.
3. Results and discussion
The interference fringes were determined with the typical implement [36]. 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 captured with a charge-coupled device (CCD) camera located behind the second polarizer. The neighboring dark (bright) fringes indicate the 2π phase difference. As shown in Fig. 2, the fringe number increased with the voltage due to the NLC reorientation in the aperture hole (AH) periphery to increase the phase difference between the AH center and periphery. Furthermore, the fringes gradually spread over the AH center with the voltage. When the supplied voltage reached 80 V, the fringes of these LHLC lenses distributed throughout the entire AH, indicating that these LHLC lenses can be regarded as optical lenses. The pure and BNA-doped LHLC lenses had the most fringe numbers (or maximum lens power, MaxP) at 90 and 100 V, respectively. The fringe number with appropriate spatial distribution is related to the focal length f of the LHLC lens, as expressed by Eq. (4): [37]
where r is the AH radius, N denotes the fringe number of the LHLC lens, and λ represents the wavelength of the incident light. When the voltage was increased further, the fringe number decreased because the NLCs in the AH center were also tilted, decreasing the phase difference between the AH center and periphery. Notably, the fringe number of the BNA-doped LHLC lens was less than that of the pure LHLC lens because the BNA dopant decreased the birefringence of NLC.Fig. 2. Interference fringes of the pure LHLC lens cell with a supplied voltage of (a) 40, (b) 80, (c) 90, and (d) 140 V; and those of the BNA-doped LHLC lens cell with a supplied voltage of (e) 40, (f) 80, (g) 100 and (h) 140 V. Red dashed lines indicate the AH region.
The focal lengths of the LHLC lens as a function of supplied voltage were experimentally measured, as shown in Fig. 3. The measurement implementation is described as follows. The A He–Ne laser with a beam diameter of 2 cm was normally incident on and focused by the LHLC lens, which was placed behind a polarizer with a transmission axis parallel to the rubbing direction of the lens cell. The distance between the LHLC lens and the focus point was defined as the focal length. Figure 3 shows that the minimum focal length of the pure and BNA-doped LHLC lenses are ∼ 45 and 55 cm at 90 and 100 V, respectively. The difference in focal lengths could be attributed to the decrease in NLC birefringence by BNA doping. If considered as an optical lens, the pure and BNA-doped LHLC lenses have tunable focal lengths of 45–50 cm and 55–70 cm, respectively, at 80–140 V. Consequently, the BNA-doped LHLC lens had a wider tunable focal length range compared with the pure LHLC lens within the same voltage range. Improvement in the high operation voltage of LHLC lenses had been presented by insertion of modally addressed scheme [2,24,38,39].
The obtained interference fringes shown in Figs. 2(b)–2(d) and 2(f)–2(h) were used to depict the phase distributions of the BNA-doped and pure LHLC lenses at various voltages by using the same method used in [40,41], as shown in Figs. 4(a) and 4(b). The symbols and the solid line indicate the measured data and the quadratic fitting curve, respectively. The wavefront error of the measured data from the ideal quadratic curve was then evaluated to examine the extent of the wavefront aberration of the LC lens [40], as shown in Fig. 4(c). The RMS error of 1/4 λ was adopted as the usual reference for ophthalmic applications [42]. Figure 4(c) shows that the RMS errors of the pure LHLC lens increased with the voltage, and those of the BNA-doped LHLC lens almost kept near 0.05 λ. That indicated BNA doping effectively suppressed the RMS error of LHLC lens addressed at the high voltage, possibly because BNA doping changed the Δɛ of NLC and hence the spatial electric field and the associated phase retardation distributions. The RMS errors of both LHLC lenses were lower than 1/4 λ at a voltage range of 80–140 V, where they can be regarded as optical lenses, indicating that the BNA doping in the LC lens preserved the remarkable lens quality.
Fig. 4. Phase retardations of (a) pure and (b) BNA-doped LHLC lenses at various voltages and (c) their evaluated RMS errors.
Figure 5 shows the focusing spot profiles of the LHLC lenses addressed at MaxP. The FWHM of the focusing spot could be used to analyze the focusing quality of the LC lens. In optics, the best focusing spot is described by an Airy disk that a perfect lens with a circular aperture could generate, which is limited by light diffraction [43]. The FWHM value of the diffraction-limited spot (Airy disk) can be calculated using the following well-known formulas: [1,44]
where NA is the numerical aperture, r denotes the AH radius of the LC lens, and dFWHM refers to the FWHM of the Airy disk. The focal lengths (Fig. 3) of the pure and BNA-doped LHLC lenses with MaxP were substituted into Eqs. (5) and (6) to calculate the dFWHM. If the obtained FWHM value of the focusing spot is less than 1.38x dFWHM, then the LHLC lens can be considered to possess a good focusing quality. The calculated dFWHM of the pure and BNA-doped LHLC lenses were 74.8 and 91.4 µm, respectively. As shown in Fig. 5, the measured FWHM values of both LHLC lenses were located between the dFWHM and the 1.38x dFWHM, indicating that they possess good focusing qualities because of their small RMS errors.Focal length measurement was adopted to observe the dynamic response of the LHLC lens with MaxP. A photodetector connected with an oscilloscope was placed at the focal length of the LHLC lens to record its transient transmission. The turn-on (-off) time is defined as the required time during which the transmission of the LHLC lens increases (decreases) and then reaches a stable state when the supplied voltage is suddenly turned on (off). Figure 6(a) shows that the turn-on times of the pure and BNA-doped LHLC lenses were 15 and 5 s, respectively. The turn-on time of the BNA-doped LHLC lens was smaller than that of the pure LHLC lens due to the higher supplied voltage. The turn-on times of these LHLC lenses could be improved further by adopting the overdriving scheme in which a high pulse voltage of 160 V was first supplied to the LC lens cell for 200 ms and then switched to the desired voltage. As shown in Fig. 6(c), the turn-on times of the pure and BNA-doped LHLC lenses decreased to ∼ 5 and 0.9 s, respectively. The turn-on time of the BNA-doped LHLC lens was reduced to below 1 s by the overdriving scheme. Moreover, BNA doping decreased the rotational viscosity of the NLCs and hence the associated turn-on time. As presented in [21,22], the turn-on time of our LHLC lenses could be further decreased drastically with the two-driving-voltage scheme, which requires an extra ITO planar electrode outside the hole-patterned electrode. Figure 6(b) shows that the turn-off times of the pure and BNA-doped LHLC lenses are 6 and 0.9 s, respectively. Notably, the turn-off time of the BNA-doped LHLC lens is ∼ 6 times smaller than that of the pure LHLC lens because BNA doping remarkably decreased the rotational viscosity of the NLCs. Table 2 summaries the response times of pure and LHLC lenses. The response times of the 5 µm-thick homogeneous BNA-doped LC cells were measured. The obtained results also showed that the BNA doping markedly decreased the response time of LC cell. However, the accurate rotational viscosities of the BNA-LC mixtures were not determined in this paper, since the possible flow effects of BNA-LC mixture in the cell. The study of the detailed mechanism responsible for the BNA doping decreases rotational viscosity of the NLCs is still in progress. Notably, LHLC lenses with subsecond level of turn-off time could be achieved with BNA doping. The turn-off time could be further decreased with the stacked LC layers [45].
Fig. 6. Dynamic responses of pure and BNA-doped LHLC lenses with MaxP when the voltage is (a) turned on, (b) turned off, and (c) turned on by overdriving scheme.
Table 2. Response times of pure and BNA-doped LHLC lenses.
The imaging performances of the pure and BNA-doped LHLC lenses were observed using the following setup. A doll was placed in front of the LHLC lens cell. A CCD camera with a lens module was placed behind and near the LHLC lens cell to capture the formed image of the doll. A polarizer with a transmission axis parallel to the rubbed direction of the LHLC cell was attached to the CCD camera. The doll was 3 cm high. The distance between the CCD camera and the LHLC lens cell was set to 1 cm. The distance between the pure LHLC lens cell and the doll was 24 cm, and that between the BNA-doped LHLC lens cell and the doll was 26 cm. During capture, the LHLC lenses were addressed at MaxP. The doll’s image was fuzzy without the LHLC lens (Fig. 7(a)). When the LHLC lenses were inserted and addressed at MaxP, clear doll images were obtained (Figs. 7(b) and 7(c)). The captured images revealed that the pure and BNA-doped LHLC lenses provided a similar imaging performance because of their similar lens quality. In the visible wavelengths of 450–700 nm, the measured transmissions of the pure and BNA-doped LHLC lens cells were similar. However, the BNA dopant had an intrinsic absorbance in wavelengths less than 450 nm, as shown in Fig. 7(d). This result indicated that BNA doping automatically provided the LHLC lens with a blue light filtering function for ophthalmic applications. The color coordinates of the pure and BNA-doped LC cells are similar. Consequently, the BNA doped-LC lens is suitable to adopt on the display panel or OLED light source, filtering the blue light without degrading the color performance of the image.
Fig. 7. Imaging (a) without LHLC lens and with (b) pure and (c) BNA-doped LHLC lenses addressed at MaxP. (d) Transmission spectra of pure and BNA-doped LHLC lenses.
4. Summary
In this study, the electro-optical properties of BNA-doped and pure LHLC lenses are demonstrated. BNA doping broadens the tunable focal length range of the LHLC lens and remarkably decreases the rotational viscosity of the NLC and hence the response time of the LHLC lens. It also effectively suppresses the RMS error of LHLC lens addressed at the high voltage. The turn-off time of the BNA-doped LHLC lens is 6 times smaller than that of the pure LHLC lens. By using the overdriving scheme, the turn-on time of the BNA-doped LHLC lens also reaches the subsecond level. The imaging performance of the BNA-doped LHLC lens is similar to that of pure LHLC lens because of their similar lens and focusing qualities. Furthermore, the transmission spectrum indicates that the BNA dopant has a drastic absorbance at wavelengths less than 450 nm, automatically providing the LHLC lens with a blue light filtering function for ophthalmic and display applications.
Funding
Ministry of Science and Technology, Taiwan (107-2112-M-018-003-MY3, 108-2811-M-018-502).
Disclosures
The authors declare no conflicts of interest.
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