1. Introduction

The controllability of liquid crystal (LC) molecules by external stimuli helped this material find vast applications ever since it was discovered [1–3]. The LC based technologies were rapidly integrated into displays [4], and research continues to focus on this application [5,6]. Later, the technology was found significant in non-displays areas too, including smart windows [7], spatial light modulator [8], switches [9] and so on. According to a recent study [10], adaptive liquid crystal lenses (ALCL) accounts for most of the research conducted on non-display applications of the liquid crystal in the past four decades. Different techniques have been proposed and studied for ALCL production, including curved lenses [11–14], patterned electrode [15–18], Fresnel lenses [19–22]. One approach is to use a modal layer with a specific sheet resistance of approximately few MΩ/□ for gradual electric field injection into the center of the cell [23–26]. This arrangement overcomes the ALCL aperture size limitations in most previous methods. Further, the AMLCL’s equivalent circuit can be put together with electronic components such as resistors and capacitors connected in series. In this equivalent circuit, distributions of the liquid crystal dielectric constant define the capacitance, and modal layer sheet resistance defines the resistance. As the capacitor response is a function of both amplitude and frequency of the trigger voltage, the latter significantly affects the distribution of the refractive index. For example, Andrew K. Kirby et al. used ITO with sheet resistance of 10 MΩ/□ and dual frequency LC (LC1001, Niopik, Russia) to study liquid crystal modal lens with different phase shapes at different frequencies [27]. Hsu et al. used a floating ring electrode embedded into the interface between the dielectric layer and the LC layer in their modal lens to decrease the operation voltage [15]. Capacitor-like structure of the AMLCLs ensures that lens needs low electrical power to drive. Besides that, it strongly depends on the LC thickness, LC dielectric, lens aperture, driving frequency and driving voltage. Simpler production compared with previous methods and the higher control over the process make the study of this type of ALCLs more significant.

All AMLCLs use a rubbing layer for the initiation of LC molecular orientation in the defined direction over the entire cell and pretilt of LC molecules. This layer is often made of polyimide (PI) or (PVA) polymer films and bears notches made with a felt cloth. Further, some dye doped polymers have been used for this purpose by surface photoreactions [28,29]. LC molecules are placed in these notches and are hard-anchored to the rubbing-layer polymer [30]. The trigger voltage applied to electrodes creates a non-uniform electric field in the lens cell, consequently changing its refractive index distribution. When a positive-birefringence LC is used, the distribution features a smaller refractive index at the cell edges compared to its center, making it function similar to a lens.

The present study, first, discusses the preparation of the AMLCL. An optimal PEDOT:PSS/PVA/DMSO polymer blend used for the modal layer which also served as the rubbing layer. The cell electrode is divided into four parts. The electro-optical properties of the adaptive lens are investigated in an optical setup. This study investigates the adaptive lens responses up to 1 kHz. It was shown that applying a voltage across different parts of electrodes and removing some of them creates spherical, cylindrical, and prismatic wavefronts. In the following, the lens response time and its power consumption are covered, and at the end AMLCL was studied in terms of the aberration of the transmitted light.

2. Experiment

A high-quality optical glass is cut into the same size as the stencil mask, that is, 17 mm in both length and width. The substrates were then washed with soap water before being rinsed in acetone, isopropanol, and double-distilled water in that order. The substrates were then left in a 120 °C oven for 20 minutes to dry off. A stencil mask with 5 mm circular holes is designed and prepared by laser cutting machine. In the present design, the circle's circumference, as the lens output aperture, is divided into four parts in which gap between the divided electrodes were measured 0.2 mm. The prepared glass substrate was placed on the stencil mask and the conductive silver layer is coated by vapor deposition with thickness of 100 nm. A PEDOT:PSS/PVA/DMSO polymer blend is used at optimal concentration for the modal layer. The blend is 100 µl PEDOT:PSS (Merck), 5 µl DMSO [31–34] and various volume of 3 wt.% water-based PVA solution. In order to obtain a homogeneous film, the mixture was agitated 30 minutes in a magnetic stirrer and 1 hour in an ultrasonic mixer, before being left to rest for 1 hour, letting the air bubbles out. This was facilitated by placing the mixture in a vacuum chamber for 10 minutes. The polymer blend was spin-coated on the glass substrate at 3000 rpm for 20 seconds with a 5 s rise time. The prepared films were annealed in an oven at 120 °C for 1 hour. Thickness of the layer was measured 100 nm by Dektak Profilometer. Sheet resistance of the films was measured using a Keithley four-point probe (Keithley 2400 Sourcemeter) and the results are presented in Table 1.

Table 1. Surface resistance of different concentration of PEDOT:PSS/PVA/DMSO polymer blends

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Since the sheet resistance must remain around a few MΩ/□, the fourth-row mixture was selected for the modal layer [35,36]. The polymer blend was deposited on the conductive electrode by spin-coating at 3000 rpm for 20 s, with a 5 s rise time. The prepared sample was annealed in a 120 °C oven for 1 hour. The modal layer was rubbed with a felt cloth to create grooves in the modal layer for the initial alignment of LC molecules. Silicon spacers were used to prepare LC cells with a 20 µm thickness and was fixed in place using a UV cure adhesive. The cell was placed on a hot plate and the LC was injected into the cell at 80 °C and then uniformly cooled down to room temperature over 30 minutes. Figure 1(a) shows a schematic of the cell and Fig. 1(b) demonstrates the final cell.

 

Fig. 1. a) Schematic of and b) Fabricated AMLCL: The circumference electrode, is divided into four parts. Both up and bottom substrates are the same expect that rubbing is obtained by unidirectional rubbing of the top substrate in the “+x” direction, while the bottom substrate in the “−x” direction. The substrates are separated by silicon spacer of 20 microns. c) Optical setup to study the wavefront.

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3. Results and discussion

The AMLCL was integrated into an optical setup (Fig. 1(c)) for electro-optical experiments. In this setup, the laser beam passes through a spatial filter. Higher spatial frequencies are filtered out in this optical component. The divergent beam is then converted into a collimated beam wider than the LC lens diameter through a collimator. The beam entered the LC lens after the polarizer. The lens is aligned so that the polarizer axis made a 45° angle with the orientation of LC molecules (i.e. the rubbing direction). After the LC cell, laser beam passed through the second polarizer—the analyzer. The analyzer is placed so that its axis made a 45° angle with the LC molecules’ direction and a 90° angle with the polarizer. In the end, the output beam entered a CCD camera for image processing. AC power supply (Chroma Programmable AC Power Source 61600) is used to apply voltage to the electrodes. The power supply is capable to produce a voltage amplitude of up to 100 V and frequency of up to 1kHz.

4. Adaptive lens

Different trigger voltages, with different amplitudes and frequencies, were applied to the four parts of the electrode (V₁–V₄ in Fig. 1(a)). Applying a voltage across all parts causes the LC refractive index to find an axisymmetric distribution and creates a spherical lens (Fig. 2(a)). The focal length is reduced from infinite (parallel light rays) to its minimum by increasing the voltage amplitude at a fixed frequency. The voltage at minimum focal length defined as V_f. By further increasing voltage, focal length increases. By applying V_f to the electrodes, the LC molecules orientation angle are maximized at the edges of the lens which produce highest possible phase difference between edge and center of the lens. With a further increase in the voltage amplitude beyond V_f, the LC molecules at the center is affected by the electrical field and orientation starts to tilt in the way that edge and center refractive indices difference is decreasing. Accordingly, Focal length bounces back beyond the driving voltage V_f. Based on the birefringence of E7 and the 20 µm thickness of the cell, the maximum phase delay at 632.8 nm is $\Delta \varphi = \frac{{2\mathrm{\pi}}}{\mathrm{\lambda }}\textrm{d}({\Delta \textrm{n}} )\cong 7\; ({2\mathrm{\pi}} )$. Since a maximum of 6 rings appeared and the phase difference between two adjacent rings is 2π, it is safe to conclude that phase delay reached 85% of its theoretical value. This phase loss stems from the fact that the LC starts rotating both at the side and the center when the voltage increases, but it goes faster at the edges compared to the center. Moreover, the lens exit aperture size is 5 mm, and the 6 rings created a focal length of approximately 80 cm ($\textrm{f} = \frac{{{\textrm{r}^2}}}{{2\textrm{N}\mathrm{\lambda }}}$). Figure 2(b) depicts V_f at different frequencies up to 1 kHz. The curve shows that the maximum number of rings appears at a higher voltage amplitude by increasing the frequency.

 

Fig. 2. a) Demonstration of the spherical wavefront by using the CCD fringe images at 1 kHz. b) V_f at different frequencies and showing that it increases with frequency.

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For a cylindrical adaptive lens, the trigger voltage was applied to two opposite parts of the electrode (V₁ & V₃ in Fig. 1(a)) and two other electrodes (V₂ & V₄) were floating. This arrangement produced a cylindrical symmetry in the refractive index distribution of the LC. The linear fringe symmetry is more pronounced in the center of the lens than the edges. The cylindrical adaptive lens reached its peak optical power at 5.2 V trigger voltage in 1 kHz. (Figure 3(a))

 

Fig. 3. a) Demonstration of the cylindrical wavefront by using the CCD fringe images and by applying drive voltage to two opposite parts of the electrode at 1 kHz. b) Demonstration of the prism wavefront by applying drive voltage to only one electrode at 1 kHz.

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The trigger voltage was applied across only one electrode (V₁ in Fig. 1(a)) to obtain an adaptive prism. In this case, the refractive index began to change at the edge of the lens and extended across the cell as the voltage increased. (Fig. 3(b))

As shown in the figure, the linear fringe symmetry is more pronounced in the center of the lens than the edges, as in the edge, electrical field in the cell more manipulated by the other non-biased electrodes. In the center of the lens, linear fringes infer as prism like behavior of the lens.

5. Response time of AMLCL

Response time of the adaptive LC lens is obtained by a photodetector (Thorlabs) using the same optical setup as (Fig. 1(c)) just by replacing the CCD by photodetector as the appropriate location of the wavefront. The active area of the detector (1.0 X 1.0 mm) was set so that changing the trigger voltage from 10 V to 20 V at the frequency of 1kHz affects the detected intensity. The resulting diagram is depicted in Fig. 4(a). The rising part of the diagram is fitted to an exponential function, showing that the diagram progressed by 83% within $9$ ms. Fall time study showed the same behaviour as the rise time. The location of the detector does not affect the detected response time.

 

Fig. 4. a) Response Time of AMLCL by changing the trigger voltage from 10 V to 20 V in adaptive spherical lens. b) 9. Power Consumption of AMLCL at different driving voltages and different frequencies up to 1kHz.

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6. Power consumption of AMLCL

The power consumption of the lens and its electronic performance was studied using the current–voltage (I–V) diagram at different frequencies (Fig. 4(b)). Increasing the voltage in these lenses results in an almost-linear rise in the current and increases the slope of the I–V curve and the power consumption of the lens. The equivalent circuit of the adaptive lens is composed of capacitors and resistors where the capacitor specifications are determined by the electrical properties of the LCs and their alignments. Capacitors are connected by resistors which obtained from the sheet resistance of the modal layer (Fig. 4(b)). Capacitors are in short-circuit mode at high frequencies and pass a larger current. At low frequencies, the capacitor is in open-circuit mode and the current is reduced. The highest electric power consumption is 3 mW and obtained at 1 kHz for a 12 V trigger voltage. The focal length is minimized with 0.5 mW at this frequency which is small compared to other adaptive lenses for adjusting the focal length [37,38]. Low electric power consumption is a strong feature of the AMLCL.

7. AMLCL aberrations

The aberrations of the spherical adaptive lens are obtained by Shack-Hartmann wavefront sensor (SHWS). The collimated polarized laser beam parallel to the rubbing direction (along LC molecules) passed through the AMLCL and enter to the wavefront sensor. This is done by replacing the CCD camera by SHWS and removing polarizer and analyzer in the (Fig. 1(c)). The first 14 orders of the Zernike function including the tip, tilt, spherical aberrations and higher orders were studied at different frequencies. Figure 5 shows an example of Zernike coefficients at 1 kHz for 1–20 V. As evident from the figure, higher-order aberrations are small compared to spherical aberrations. The tip aberration, which has been covered in detail by Louis Begel and Tigran Galstian [34], can be attributed to the pretilt of the LC molecules. The colored column shows the applied voltage. The electrical potential distribution and consequently director angle distribution in the cell leads to phase distribution of the lens and it varies with different voltages and frequencies. Then phase distribution tends to become less aberrated at higher voltages at the frequency of 1 kHz. The frequency behavior of the lens suggests that higher-order aberrations are reduced at higher frequencies.

 

Fig. 5. First 14 Zernike coefficients of wavefront at different driving voltages and at 1 kHz. Color bar corresponds to different driving voltages.

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8. Conclusion

An AMLCL with a PEDOT:PSS/PVA/DMSO polymer modal layer and positive-birefringence liquid crystal (E7) was fabricated. Minimum focal length of the lens was obtained 70 cm at 1 kHz, which is 85% of the theoretical value. Maximum optical power was produced at 1 kHz with electrical consumption power of 3 mW which indicates the low power consumption of the lens. Spherical, cylindrical, and prismatic wavefront were obtained by applying the voltage across different electrodes. This indicates that a compound voltage can be used to obtain a complex wavefront. The small lens thickness and its controllability from the edges, facilitate implementing the concept of combining lenses to achieve more complex wavefront. Using an LC with a larger birefringence enables achieving a higher optical power.