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Abstract
A 4 mm-aperture hole-patterned liquid crystal (LC) lens has been fabricated using a LC mixture, which consisted of rutile titanium dioxide (TiO2) nanoparticles (NPs) and nematic LC E7, for the first time. The TiO2 NP dopant improves the addressing and operation voltages of the LC lens significantly because it strengthens the electric field surrounding the TiO2 NP and increases the capacitance of lens cell. Unlike the doping of common colloidal NPs, that of rutile TiO2 NPs increases the phase transition temperature and birefringence of the LC mixture, thereby helping enhance the lens power of LC lens. In comparison with a pure LC lens, the TiO2 NP-doped one has approximately 50% lower operation voltage because of the strengthened electric field around the NPs and has roughly 2.8 times faster response time because of the decreased rotational viscosity of the LC mixture and the increased interaction between the LC molecules by the NP dopants. Notably, the doping of rutile TiO2 NPs improves the operation voltage, tunable focusing capability, and response time of LC lens simultaneously. Meanwhile, this method does not degrade the focusing and lens qualities. The imaging performances of TiO2 NP-doped LC lens at various voltages are demonstrated practically by tunable focusing on three objectives at different positions. These results introduce NP in the application of LC lenses.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Liquid crystalline materials have been imposed to the study and fabrications of some optical devices because of their unique electro-optical properties. Specifically, liquid crystal (LC) lens is an active area of research because of its suitability for several emerging applications, such as 2D/3D switchable displays, augmented reality, and eye glasses [1–4]. Generally, LC lens requires electrical control to generate a gradient LC orientation that results in a parabolic refractive index distribution that converges or diverges the incident light. In the last two decades, various types of LC lenses, such as the combination of the solid lens and LC layer [5–7], polymer gravel lens [8,9], concentric multi-ring electrode [10,11], and circular hole-patterned electrode [12,13], have been proposed. Among these lenses, the hole-patterned LC lens is an attractive option because it realizes any sizes of optical aperture easily, possesses excellent tunable focal length capability, and only requires simple fabrication and addressing scheme. However, several drawbacks also exist. For example, the effect of the fringing electric field produced by the hole-patterned electrode and the intrinsic rotational viscosity of the nematic LCs result in the slow dynamic response of LC lens; and the utilization of a thick dielectric layer causes high operation voltage [14–19]. Various tactics, such as polymer stabilization [20], two-driving-voltage scheme [21,22], and additional weakly conductive layer [23,24], have been used to prevent these issues. Moreover, the electro-optical properties of SiO2 nanoparticle (NP) doped in polymer-dispersed LC lens have been reported [25]. The modification of the physical properties of LCs through NP doping according to the enhancement in the performance of LC devices has attracted considerable attention. The effects of NP doping are usually investigated in the traditional homogenously-aligned (HA) or vertically-aligned (VA) LC cells. For example, MgO NPs decrease the threshold voltage of LC cell [26]; silica NPs suspended in LCs exhibit bi-stable characteristics [27]; ferroelectric NPs increase dielectric anisotropy and rotational viscosity but decrease the elastic constants of LCs [28]; ZrO2 NPs suppress the screening effect [29], and carbon nanotube-doped LCs exhibit rapid response time [30]; and quantum dots are used to improve the properties of LC devices, such as pronounced memory effect and enhanced luminescence [31,32]. Each type of NP exhibits distinct influences on LC properties [33]. However, discussions about the effects of NP doping in LC lens, especially for the titanium dioxide (TiO2) NPs, are scarce. Recently, we utilize the doping of organic BNA material to fabricate the LC lens [34]. BNA dopant can produce a considerable decrement in the turn-off time of LC lens but without any improvement in the operation voltage and lens power of the LC lens.
The insulating TiO2 has attracted considerable attention for device applications because of its high permittivity, high refractive index, low cost, chemical inertness, non-toxicity, and photocatalytic activity. TiO2 exists in the structures of rutile, anatase, and brookite [35]. Anatase and rutile possess tetragonal structures, whereas brookite displays an orthorhombic structure. Rutile and anatase are the most common phases, whereas brookite is the less common one. The anatase phase is chemically and optically active. Therefore, it is widely used as a dopant material in LC investigations. Compared with anatase TiO2, rutile TiO2 possesses better stability and higher refractive index. Furthermore, the dielectric constant of rutile TiO2 is remarkably higher than that of anatase TiO2, indicating that the rutile and anatase TiO2 doping may obtain different electro-optical properties.
In the current paper, the doping of rutile TiO2 NPs is imposed to fabricate 4 mm-aperture hole-patterned LC lens for the first time. The optical interference fringes and focal lengths of undoped and doped lens cells are measured to compare the addressing and operation voltages and the tunable focusing capability. To examine the lens and focusing qualities, their wavefront errors and the full width at half maximum (FWHM) of focusing spots are evaluated. Meanwhile, their response times are obtained by measuring the focused and defocused transient transmissions. In addition, their imaging performances are demonstrated practically. The results show that the TiO2 NP-doped LC lens provides wider tunable focal length range within lower operation voltages and approximately 2.8 times faster response time than the pure one. If used as an optical lens, then TiO2 NP-doped LC lens has relatively stable RMS error values within operation voltages. TiO2 NP dopant preserves the imaging quality of LC lens. The improvement mechanisms of the electro-optical properties of LC lens with doping of the rutile TiO2 NPs have been discussed in this study.
2. Experimental preparations
Figure 1 illustrates the structure of the hole-patterned LC lens with aperture hole (AH) of 4 mm. It consisted of two indium tin oxide (ITO) glass substrates (Chipset Technology, Miaoli, Taiwan). The top and bottom glass substrates were 1.1 mm and 0.55 mm thick, respectively. The ITO surface of the top glass substrate was etched with a hole diameter of 4 mm via photolithographic process. The inner surfaces of both substrates were coated with a homogeneous polyimide AL 1426 CA (Daily Polymer Kaohsiung, Taiwan) and rubbed antiparallelly. The cell gap was controlled by using a 25 µm-thick Mylar spacer. The LC mixture consisted of nematic LC E7 (Daily Polymer Kaohsiung, Taiwan) used as a host material and TiO2 NPs (Sky Spring Nanomaterials, Inc., USA) used as a guest material. The LC E7 had a nematic–isotropic temperature of 59 °C, dielectric anisotropy Δɛ of 14.1 at room temperature (RT), 1 kHz frequency, and birefringence Δn of 0.216 (n0=1.522 and ne=1.738) at the wavelength λ = 589 nm, respectively. The silane-coated rutile TiO2 NPs with a diameter of 20 nm were dissolved in 1-propylalcohol solution to disperse well in LCs. The TiO2 NP-doped concentration was fixed to 0.5 wt%. The LC mixture was initially heated up to the isotropic phase and then filled in the empty lens cell through the capillary action. After filling, the LC mixture was cooled down to the nematic phase. The LC lens filled with pure LC E7 was also fabricated to compare the electro-optical properties of doped and undoped LC lenses. The LC lenses filled with the LC mixture and pure LC E7 had the same cell structure and were defined as the TiO2 NP-doped and pure LC lenses hereafter. In this experiment, an AC voltage with frequency of 1 kHz was subjected to lens cell across the top hole-patterned and bottom planar electrodes. The capacitance of the lens cell was measured using a LCR meter (Hioki 3532-50, Nagano Prefecture, Japan), where the applied AC field across the cell was 0.1 V/µm, and the frequency was changed from 42 Hz to 5.5 MHz. Furthermore, the 5 µm-thick pure E7 and 0.5 wt% TiO2 NP-doped HA LC cells with antiparallel rubbing treatment were fabricated to understand the effects of rutile TiO2 NP doping. Their voltage-dependent transmissions were used to estimate the Δn of the LC mixture [36]. Their phase transition temperatures TNI (or clearing temperatures) were observed using a polarizing optical microscope, in which LC cells were heated up from nematic to isotropic phases at a rate of 0.25 °C/min using a temperature controller (T95-PE, Linkam, UK).
3. Results and discussion
Figure 2 depicts the optical interference fringes of the fabricated pure and TiO2 NP-doped 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 neighboring bright (dark) fringes indicated a 2π phase difference. The focal length (f) of the LC lens correlated with the number (N) of interference fringes with an appropriate spatial distribution, which can be represented by the following formula [37]:
where r is the AH radius, and λ denotes the wavelength of the incident light. 1/f is defined as lens power. At 0 V (Figs. 2(a) and 2(f)), the dark stripes are caused by the nonuniform cell gap of handmade cells. As the voltage increases, the fringe numbers of these LC lenses gradually rise because of the increment in the LC tilt angle in the AH periphery measured from the substrate surface, resulting in the large phase difference from the AH center to the AH periphery. At low voltages (Figs. 2(b) and 2(g)), the fringes of the TiO2 NP-doped LC lens distributes closer to the AH center than the pure one. The fringes of pure and TiO2 NP-doped LC lenses distribute throughout the entire AH at 90 V and 50 V (Figs. 2(c) and 2(h)), respectively, where the applied voltages are defined as the addressing voltages (Vadd) because they can be used as optical lenses (i.e., the interference fringes fill almost the entire optical aperture of the LC lens). TiO2 NP-doped LC lens has relatively low Vadd. Under the applied field, the insulating TiO2 NP is considered a high dielectric sphere that strengthens the electric field surrounding the dielectric sphere along the direction of the applied field, thereby consequently decreasing Vadd of the LC lens [38]. Moreover, Fig. 2(k) shows the frequency-dependent capacitances of pure and TiO2 NP-doped homogenous LC lens cells, showing that TiO2 NP doping increases the capacitance of the cell. Increased capacitance indicates that the potential near the AH center strengthens and assists in the reorientation of LCs in the AH center, thereby reducing Vadd of the LC lens [39]. The pure and TiO2 NP-doped LC lenses produce most fringe number (or maximum lens power, MaxP) at 100 V and 80 V (Figs. 2(d) and 2(i)), respectively. When the voltage is increased further, the LC tilt angle in the AH periphery saturates, and LCs in the AH center begin to tilt, thereby reducing the phase difference from the AH center to the AH periphery and the associated fringe number of these LC lenses. TiO2 NP-doped LC lens has more fringes than pure one because the TiO2 NP dopants increase Δn of the LC mixture and the phase difference from the AH center to the AH periphery. Table 1 shows the observed TNI and calculated Δn of the pure E7 and 0.5 wt% TiO2 NP-doped HA LC cells. The rutile TiO2 NP dopants increase TNI, Δn, and associated order parameter S of the LC mixture. Some reports have demonstrated that TiO2 NP doping increases the order parameter S of LC mixture. For example, the anatase TiO2 NP dopants induce the strong intermolecular forces and hence increase S of the LC mixture because the alkyl isothiocyanatotolanes and alkylphenyl isothiocyanatotolanes of LC molecules absorbed strongly on the polar surfaces of the NPs [40]. The dispersion of copper-incorporated TiO2 NPs provided the strong Coulomb interaction between the induced partial negative charge at nitrile groups in LCs and the large positive charge at the Cu atom ions in the NPs and increased the S of the LC mixture [41]. For our TiO2 NP-LC composite, the increased S and Δn may be attributed to the enhanced the interaction between the LC molecules through rutile TiO2 NP dopants. The detailed mechanism for the mutual interactions between the NPs and LCs will be investigated underway.
Fig. 2. Interference patterns of the pure LC lens at (a) 0 V, (b) 30 V, (c) 90 V, (d) 100 V, (e) 140 V; interference patterns of the TiO2 NP-doped LC lens at (f) 0 V, (g) 30 V, (h) 50 V, (i) 80 V, (j) 140 V. The yellow dashlines indicate the AH area of LC lens. (k) frequency-dependent capacitances of the pure and TiO2 NP-doped LC lenses.
The electrically tunable focal lengths of these LC lenses with various voltages are demonstrated in Fig. 3, in which the experimental setup is described as follows: an expanded He–Ne laser with the wavelength of 632.8 nm was normally incident on the LC lens. The LC lens was mounted behind a polarizer with a transmission axis parallel to the rubbing direction of the lens cell. The distance between the LC lens and focusing point was defined as focal length. The measured focal length has an error value within ± 1 cm. The measured focal lengths initially decrease and then increase with voltage. The minimum focal lengths of pure and TiO2 NP-doped LC lenses are 30.2 cm at 100 V and 26.5 cm at 80 V, respectively. When the voltage is below 130 V, the focal lengths of TiO2 NP-doped LC lens are slightly smaller than those of the pure one because the TiO2 NP dopants increase the Δn of the LC mixture and hence the phase difference between the AH center to the AH periphery. If the voltage exceeds 130 V, then their focal lengths become similar because the LC tilt angles in the AH center and periphery saturate. If used as an optical lens, then the tunable focal length ranges of the pure and TiO2 NP-doped LC lenses are 30.2–35.5 cm at 100–140 V and 26.5–39.2 cm at 50–80 V, respectively. The strengthend electric filed around the NPs reduces the operation voltage of LC lens by approximately 50%. Noticeably, the TiO2 NP doping markedly broadens the tunable focal length range and reduces the operation voltage of the LC lens.
Table 1. TNI and Δn of the homogeneous pure E7 and 0.5 wt% TiO2 NP-doped LC cells.
Figure 4 presents the calculated focusing spot sizes of these LC lenses operated with 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 was described by an Airy disk that a perfect lens with a circular aperture could generate, limited by light diffraction [42]. The FWHM value of the diffraction-limited spot (Airy disk) can be calculated by using the following formulas [43,44]:
where NA is the numerical aperture, and dFWHM refers to the FWHM of the Airy disk. In Fig. 3, (f) of these LC lenses with MaxPs were substituted into Eqs. (2) and (3) to calculate dFWHM. If the measured FWHM value of the focusing spot is less than 1.38× dFWHM, then the LC lens is considered to possess an acceptable focusing quality. The calculated dFWHM of pure and TiO2 NP-doped LC lenses are 49.68 µm and 43.60 µm, respectively. Figure 4 shows that the measured FWHM values of the focusing spot of both LC lenses are less than 1.38× dFWHM, indicating that the TiO2 NP dopants preserve the acceptable focusing quality. TiO2 NP-doped LC lens has larger lens power and hence smaller FWHM focusing spot value than the pure one.Fig. 4. Measured FWHM of the focusing spots and calculated dFWHM for the pure and TiO2 NP-doped LC lenses addressed with minimum focal length. Insets indicate the measured focusing profiles.
Figure 5 plots the phase retardations of these LC lenses within the operation voltages by using their interference fringe distributions. The symbols and solid lines indicate the measured results and quadratic fitting curves, respectively. The wavefront error of the experimental data was then calculated from the ideal quadratic curve to examine the extent of the wavefront aberration of LC lens [45,46]. The wavefront error was defined as the root mean square (RMS) of the difference between the experimental data and 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 [45,46]. As shown in Table 2, the RMS errors of these LC lenses decrease with the increased voltage, but that of the pure LC lens increases again when the voltage exceeds 130 V. If used as an optical lens, then the TiO2 NP-doped LC lens has relatively stable RMS errors within the operation voltages.
Fig. 5. Phase retardations and RMS errors of the (a) pure and (b) TiO2 NP-doped LC lenses at various voltages. The symbols and solid lines represent the measured data and quadratic-fitting curve, respectively.
Table 2. RMS errors of the pure and TiO2 NP-doped LC lenses at operation voltages.
Figure 6(a) represents the turn-on and -off times of the pure and TiO2 NP-doped LC lenses. The implement to measure the voltage-dependent focal lengths was used to record the transient transmissions of LC lens, where a power meter was placed at the focal length of the LC lens. The turn-on (off) time was defined as the time during which the transient transmission reached saturation when the LC lens was suddenly switched on (off) with a voltage of 100 V. The turn-on times of pure and TiO2 NP-doped LC lenses are 8 s and 2.2 s, respectively. The TiO2 NP-doped LC lens has a relatively rapid turn-on time because of the decreased γ of the LC mixture. The strengthened electric fields surrounding the TiO2 NPs assist in LC reorientation and decrease the turn-on time of the LC lens [38]. On the other hand, the turn-off times of pure and TiO2 NP-doped LC lenses are 8 s and 3.5 s, respectively. The TiO2 NP-doped LC lens has the turn-off time that is approximately 2.3× faster than the pure one because of the decreased γ of the LC mixture and the increased interaction between the LC molecules caused by the NP dopants.
Fig. 6. (a) Turn-on and -off times of the pure and TiO2 NP-doped LC lenses. (b) frequency-dependent dielectric losses of the pure and TiO2 NP-doped VA LC cells.
The frequency-dependent dielectric losses of 5 µm-thick pure and TiO2 NP-doped VA LC cells were measured to explain how TiO2 NP doping decreases γ of the LC mixture. As shown Fig. 6(b), the peak frequency fp of dielectric loss of VA cell shifts towards higher frequency region with TiO2 NP doping. This relaxation mode is related to the LCs reorientation along the short molecular axis. The relaxation time (τ) of the LC mixture can be related to the fp of dielectric loss by the following relation [47]:
TiO2 NP doping significantly increases fp and hence decreases τ of the LC mixture. τ is also related to the potential barrier (η) based on the following equation: where b is the height of the potential barrier around the short molecular axis, R is the gas constant, and T is the temperature. Meier and Saupe proposed that η is proportional to τ [48]. TiO2 NP doping decreases τ and hence b and associated γ of the LC mixture [49], then accelerates the response time of the LC lens.If the TiO2 NP-doped concentration is less than 0.5 wt%, then the electro-optical properties of the TiO2 NP-doped LC lens are similar to those of the pure one. When the TiO2 NP-doped concentration exceeds 0.5 wt%, the response time of the TiO2 NP-doped LC lens can be decreased further, as shown in Table 3. However, the excessive TiO2 NP dopants blur the interference fringes of the LC lens because of the light scattering by the refractive index mismatch of interfaces between the LCs and NPs (Figs. 7(a)–7(c)). The fuzzy fringes degrade the imaging quality of the LC lens. Therefore, the TiO2 NP-doped concentration is fixed to 0.5 wt% in this experiment.
Fig. 7. Interference fringes of (a) 0.5 wt%, (b) 0.7 wt%, and (c) 1 wt% TiO2 NP-doped LC lenses addressed at 80 V.
Table 3. Response times of 0.5 wt%, 0.7 wt%, and 1 wt% TiO2 NP-doped LC lenses.
Figure 8 shows the imaging performances of the pure and TiO2 NP-doped LC lenses, which are recorded on the basis of the following implement. A CCD camera with lens module was placed in front of the LC lens to capture formed objective images. A polarizer was attached on the CCD camera with the transmission axis parallel to the rubbing direction of the LC lens. Three objective dolls were placed at 35, 31, and 27 cm away from the pure LC lens, respectively. At 0 V, the objectives were blur (Fig. 8(a)). When the pure LC lens was addressed at 60 V, the objective at 35 cm could be seen clearly (Fig. 8(b)) because of the focusing capability of the LC lens. As the voltage was changed to 100 V, the objective at 27 cm was clear while the pure LC lens was operated with MaxP (Fig. 8(c)). If the voltage further reached 140 V, then the objective at 31 cm became clear because of the increase in the focal length of the pure LC lens (Fig. 8(d)). Subsequently, pure LC lens was replaced by the TiO2 NP-doped one, and three objective dolls were placed at 36, 31, and 28 cm away from the LC lens, respectively. At 0 V, these objectives were defocused (Fig. 8(e)). At 60 V, the objective at 36 cm was clear (Fig. 8(f)). When the LC lens was addressed with MaxP (80 V), the objective at 28 cm became clear (Fig. 8(g)). As the voltage was changed to 140 V, the objective at 31 cm was clear because of the increased focal length of the LC lens (Fig. 8(h)). As a result, the pure and TiO2 NP-doped LC lenses produce similar imaging performance, indicating that the TiO2 NP dopants do not damage the imaging quality of the LC lens.
Fig. 8. Imaging performances of the pure LC lens at (a) 0 V, (b) 60 V, (c) 100 V, and (d) 140 V; those of the TiO2 NP-doped LC lens at (e) 0 V, (f) 60 V (g) 80 V, and (h) 140 V.
4. Summary
The doping of rutile TiO2 NPs is used to fabricate the hole-patterned LC lens for the first time. TiO2 NP dopants increase TNI and Δn of the LC mixture and the lens power of the LC lens. In comparison with pure LC lens, TiO2 NP-doped lens has approximately 50% lower operation voltage because of the strengthened electric field around the NPs and around 2.8 times faster response time because of the decreased rotational viscosity of the LC mixture and the increased interaction between the LC molecules by the NP dopants. TiO2 NP-doped LC lens has a significantly lower Vadd, wider tunable focal length range within narrower operation voltages, and faster response time than pure one. It also has relatively stable RMS errors within the operation voltages. The TiO2 NP dopants preserve the acceptable focusing quality of LC lens. The pure and TiO2 NP-doped LC lenses demonstrate similar imaging performance. The doping of rutile TiO2 NPs provides a promising option to realize a superior LC lens.
Funding
Ministry of Science and Technology, Taiwan (107-2112-M-018-003-MY3, 108-2811-M-018-502).
Acknowledgments
Author B. P. Singh is sincerely thankful for the Department of Science & Technology (DST), New Delhi [No. DST/ INSPIRE Fellowship/2016/IF160572] for providing financial assistance in the form of INSPIRE Fellowship.
Disclosures
The authors declare no conflicts of interest.
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