1. INTRODUCTION

Varied-line-spacing (VLS) gratings were introduced at the end of the 19th century and were further developed in the 1950s and 1960s with the appearance of lasers, which enabled researchers to fabricate VLS gratings through holographic lithography [1]. Although the holographic method has the advantage of high fabrication efficiency, it cannot fabricate certain types of gratings with particular line-spacing variation. While interference lithography was proposed to generate plane VLS gratings, the line spacing produced by this method is not continuous. To overcome these shortcomings and obtain continuous and diverse line spacing, researchers combined interference lithography and soft lithography to fabricate plane VLS gratings by employing an elastic medium. This has the advantages of continuous diversity of variation, high fabrication efficiency, and low cost [2]. VLS gratings focus images, eliminate aberration, and reduce stray light in an optical system. They have been widely used to fabricate spherical-grating monochromators for synchrotron radiation [3], operate x-ray spectrometers [4], design optical position sensors [5], etc.

Because of the advantages of the VLS gratings, we propose that a VLS grating with switchable transmission and diffraction states will have wide application in multiview autostereoscopic displays. Therefore, we introduce polymer-dispersed liquid crystal (PDLC) material to record the VLS grating. In recent years, there has been an increased effort to develop characteristics and applications of electrically controlled material, such as holographic polymer-dispersed liquid crystal (H-PDLC), which consists of alternate polymer-rich regions and liquid crystal (LC)-rich regions with periodic distribution of refractive index [6–8]. The pre-exposed PDLC material contains an appropriate proportion of polymer and LC whose ordinary refractive index matches closely with the refractive index of the polymer. Polymerization-induced phase separation (PIPS) within the PDLC occurs under the interference pattern generated by two coherent laser beams with proper wavelength and power. During polymerization, the prepolymer absorbs intense optical energy and polymerizes at the bright region, while the LC molecules are forced to diffuse from the bright region to the dark region. The time required for complete phase separation between the polymer and LC generally depends on the material, laser power, environment temperature, etc. With increased external driving voltage applied to the H-PDLC, the director of the LC molecules gradually rotates and aligns with the direction of the applied voltage. This results in a matching refractive index between the polymer-rich region and the LC-rich region and eliminates the diffraction effect. The main advantages of the H-PDLC are easy fabrication and high diffraction efficiency, and it has many electro-optical applications in optical switches [9,10], electro-optic filters [11,12], distributed feedback lasers [13,14], photonic crystals [15,16], etc.

However, the H-PDLC grating period and diffraction angle are usually fixed owing to the unchangeable spacing between adjacent bright regions and dark regions in the interference pattern. In fact, with the development of optical technology, special types of gratings, such as VLS switchable holographic gratings, have received attention due to demand. Gratings with a nonuniform period are often fabricated by modifying the exposure angle on different locations of the substrate [17]. Therefore, interference between two beams of spherical wave is usually adopted to fabricate variable-period gratings. In addition, a cylindrical lens placed in one optical path or each of the two optical paths can also be used to implement a nonuniform period in holographic gratings [18,19]. However, these works just provided theoretical calculation and simulated interference patterns, and did not put their proposals into practical experiments and H-PDLC gratings.

As the works mentioned thus far report only a holographic and ion beam etching method, switching of the VLS gratings could not be realized. In this paper, we report a method to overcome this fundamental limitation and introduce a new type of VLS switchable holographic grating recorded in the PDLC that meets the demands for both a nonuniform period and electrically controlled characteristics. We placed a cylindrical lens in one interference optical path to interfere with another plane wave, resulting in a different exposure angle on the sample surface. The period produced by this method varies continuously. In addition, for each period volume grating, the diffraction efficiency can be adjusted by changing the applied driving voltage.

2. FABRICATION OF VLS H-PDLC GRATING

Figure 1(a) shows the experimental setup for the VLS H-PDLC grating fabrication. A laser beam with a wavelength of 532 nm was chosen to generate the interference pattern. After the beam expander, the beam was divided into two coherent beams with diameters of 20 mm. We put a cylindrical lens with a focal length of 200 mm into one interference optical path, and one cylindrical wave interfered with another plane wave reflected by the mirror. The period of traditional holographic gratings with constant space frequency can be expressed as

 

Fig. 1. (a) Schematic illustration of the experimental setup for fabricating VLS H-PDLC gratings. (b) Interference pattern showing the varied strip within PDLC. (c) Diagram of varied exposure angles interacting on the sample surface.

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The theoretical varied period was calculated by Chen et al. [18] by using Fourier optics. A plane wave with amplitude $A$ is perpendicularly incident on the plane surface of the cylindrical lens along the $z$ axis. The complex amplitude of the transmission wave is

The PDLC material used for our experiments is a mixture of 44.71 wt. % acrylic monomer, ebecryl 8301 acrylated urethane (EB8301, UCB, Inc.); 34.76 wt. % nematic LC (TEB50, Beijing Tsinghua Yawang Liquid Crystal Material Co., Ltd.); 9.94 wt. % cross-linking monomer, 1-Vinyl-2-pyrrolidinone (NVP, Sigma-Aldrich, Inc.); 0.15 wt. % photoinitiator, Rose Bengal (RB, Sigma-Aldrich, Inc.); 0.4 wt. % coinitiator, N-phenylglycine (NPG, Sigma-Aldrich, Inc.); and 9.94 wt. % surfactant, S-271 (Chem Service, Inc.). 0.05 wt. % Ag nanoparticles (NPs) (Beijing Nachen S&T Ltd.) with a mean size of 50 nm were added to the mixture to improve the diffraction efficiency [20]. The mixture was heated uniformly and stirred in an ultrasonic cleaner in dark conditions. It was then left standing for 24–48 h in order to form a homogeneous mixture. The mixture was enclosed in a cell, which had been formed by two pieces of indium–tin-oxide (ITO)-coated glass, and then was subjected to laser exposure. The cell thickness can be controlled by spacers with diameters of 20 μm between the two pieces of ITO glass.

3. ANALYSIS OF VLS H-PDLC GRATING

We performed experiments to analyze the characteristics of the VLS H-PDLC gratings such as period variation, diffraction efficiency, and electro-optic properties. First, the exposure angle ${\theta }_0$ was set at 17.55° and the distance $D$ was set as 43.5 cm. According to Eq. (2), the theoretical period ranges from 1546 to 2054 nm when the horizontal coordinate $x_i$ ranges from $-10$ to 10 mm, respectively (zero is located in the center of the grating). A laser beam with a wavelength of 532 nm irradiated different locations of the grating, as shown in Fig. 2. The spot size for this 532 nm probing beam was less than 1.2 mm, which is suitable for detecting well-defined diffraction spots within the scope of period change. Larger spot size leads to the cover of different periods, which will expand the diffraction spots. The middle spot is the transmitted light, the left spot is the negative first-order light, and the right one is the positive first-order light. As the continuously moving laser illuminated the surface, the diffraction angle changed accordingly, and the positive and negative first-order diffracted light moved on the observation screen. The period values in the lower right corners of the panels in Fig. 2 were calculated by measuring the diffraction angle obtained from the distance between the grating and observation screen and the distance between the transmitted light and positive first-order diffracted light. In addition, the grating periods were also measured by an atomic force microscope (AFM), as shown in Fig. 3. When we prepared the sample for imaging, we removed the substrate and put the sample in ethanol solution to get rid of the LC. We chose three different points on the upper surface of the grating to verify the variation. The number of fringes within the scope of 10 μm proved the period variation in the grating structure. The grating periods were approximately 1851, 1695, and 1587 nm, which are located just within the scope of the theoretical values.

 

Fig. 2. Diffraction patterns of VLS H-PDLC gratings. We detected the diffraction on different positions of grating with $x_i=6.4$, 4, 2.5, $-0.7$, $-3$, and $-6.1\mathrm{mm}$.

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Fig. 3. AFM images of VLS H-PDLC grating samples: (a) ${\mathrm{\Lambda }}_1=1851\mathrm{nm}$ ($x_i=-3.3\mathrm{mm}$), (b) ${\mathrm{\Lambda }}_2=1695\mathrm{nm}$ ($x_i=3.1\mathrm{mm}$), and (c) ${\mathrm{\Lambda }}_3=1587\mathrm{nm}$ ($x_i=7.7\mathrm{mm}$).

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Second, we fabricated gratings with different exposure angles ${\theta }_0$ and distances $D$ to detect the range and variation of periods. We also calculated the theoretical period values according to Eq. (6) for comparison. Figure 4(a) shows the grating periods for three different exposure angles (15.02°, 17.55°, and 20.71°) while the distance between the cylindrical lens and sample is 43.5 cm. Figure 4(b) represents the grating periods for different distances between the lens and sample (37.2, 43.5, and 49 cm) while the exposure angle is 17.55°. The graphs show good agreement between the experimental and theoretical results. In addition, the central period ${\mathrm{\Lambda }}_0$, as illustrated in Fig. 1(c), depends on the exposure angle and the varied scope ${\mathrm{\Lambda }}_1-{\mathrm{\Lambda }}_2$ depends on the distance of the sample from the cylindrical lens. Therefore, one can change the period of H-PDLC gratings by modifying these two parameters in order to meet practical requirements.

 

Fig. 4. Grating period as a function of the (a) exposure angle and (b) distance between the cylindrical lens and the sample. The lines represent theoretical results and the dots show experimental results.

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Third, because the diffraction efficiency, an important indicator for gratings, depends on the exposure time and recording optical intensity, initial experiments were performed to determine suitable fabrication conditions for this VLS grating. Figures 5(a) and 5(b) show the diffraction efficiency of the gratings for different exposure times and recording intensities, respectively. The gratings were fabricated under experimental conditions of ${\theta }_0=17.55°$ and $D=43.5\mathrm{cm}$. We measured the diffraction efficiency for the different grating positions that correspond to the appropriate periods. The first-order diffraction efficiency is defined as $\eta =I_1/(I_1+I_0)$, where $I_1$ and $I_0$ represent the first-order diffracted and transmitted light intensities, respectively.

 

Fig. 5. Diffraction efficiency of gratings as a function of (a) exposure time and (b) recording optical intensity, as well as average diffraction efficiency values versus (c) exposure times and (d) exposure intensity.

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As shown in Fig. 5(a), when the exposure time was 90 s and the optical power was constant at $22\mathrm{mW}/{\mathrm{cm}}^2$, the phase separation between the polymer and LC was not sufficient, and the diffraction efficiency was very low. The diffraction efficiency gradually increased with increasing exposure time. When the exposure time was 120 s, we obtained the maximum diffraction efficiency. Beyond 120 s, however, the efficiency decreased as exposure time increased due to excessive exposure and increased scattering. In addition, as shown in Fig. 5(b), when the exposure time was fixed at 120 s, the maximum diffraction efficiency was obtained with recording optical intensity of $19.1\mathrm{mW}/{\mathrm{cm}}^2$. Above this, increasing intensity led to undue scattering and loss. The diffraction efficiency drops on the edges, which can be explained by two possible factors. First, diffraction efficiency could depend on the grating period. Second, moving the probing laser beam to target the coarsest period of the grating corresponds to moving it toward the edges, and this might result in just simply not covering the whole beam intersection with the grating lines. Furthermore, we also found the average diffraction efficiency values for any given exposure time and optical intensity as shown in Figs. 5(c) and 5(d), respectively. Even though overall the diffraction efficiencies of gratings were not very balanced, which will be improved in future experiments, the varied trend shows that the highest diffraction efficiency (more than 80%) can be obtained with an exposure time of about 120 s and recording optical intensity of about $19.1\mathrm{mW}/{\mathrm{cm}}^2$.

Fourth, we studied the electro-optic characteristics of these H-PDLC gratings. Figure 6(a) shows the measured diffraction efficiency as a function of biasing voltage, which was achieved by increasing the amplitude at a fixed frequency of 50 Hz. It can be seen that the diffraction efficiency gradually decreased as the external voltage increased. Here, the threshold driving voltage is defined as the voltage value when the diffraction efficiency is equal to 90% of the initial diffraction efficiency value. The threshold driving voltages of the variable-period gratings were about $2.2\mathrm{V}/\mathrm{\mu m}$. The diffraction efficiency cannot decrease to zero because the ordinary refractive index of our LC is not strictly equal to that of the polymer, which leads to a refractive index mismatch in the experiments. In addition, the response times of the H-PDLC gratings, including the rise and fall times, were also measured, and the results are shown in Fig. 6(b). The figure shows the detected positive first-order diffracted optical signal when the grating was modulated at a square waveform, where the yellow line represents the driving voltage signal and the blue line represents the diffracted signal. The rise time is defined as the time required for the diffraction intensity to decrease from 90% to 10%, and the fall time is similarly defined as the time required for the diffraction intensity to increase from 10% to 90% [21]. The measured rise time and fall time shown in the partial enlargement are 300 and 750 μs, respectively, which are less than 1 ms.

 

Fig. 6. Measurements for electro-optic characteristics of VLS H-PDLC gratings: (a) measured diffraction efficiency as a function of bias voltage and (b) measured rise and fall time.

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Thus, evaluation of the threshold driving voltage and response time yields an indication of good electro-optic switching characteristics for these variable-period gratings. Due to the electrically controlled feature of the PDLC, the diffraction and transmittance states of the VLS H-PDLC grating can be switchable through an appropriate driving voltage, which broadens the application of an ordinary VLS grating such as a controllable position sensor. Because the VLS H-PDLC grating has a variable period, it has more advantages than a common H-PDLC grating with a constant period and can be applied to other fields. For example, in three-dimensional autostereoscopic displays, the VLS H-PDLC grating instead of an ordinary grating may solve the problem of observation position movement due to varied diffraction angles.

4. CONCLUSION

In conclusion, we demonstrated electrically controlled H-PDLC gratings with continuous varied periods and diffraction angles. A cylindrical lens was adopted in an interference beam to generate a nonuniform interference pattern with another plane wave. The fabricated gratings have variable periods that are in accordance with the theoretical values. The central period and varied scope can be modified by changing the angle between two interference beams and the distance between the cylindrical lens and sample, respectively. The highest diffraction efficiency, more than 80%, was obtained when the exposure time was approximately 120 s and the recording optical intensity was about $19.1\mathrm{mW}/{\mathrm{cm}}^2$. In addition, we studied the electro-optic characteristics of this variable-period grating, and the experimental results show that the threshold driving voltage was approximately $2.2\mathrm{V}/\mathrm{\mu m}$, and the response time, including rise and fall times, was less than 1 ms. This VLS H-PDLC grating with variable period and electrically controlled features will have great potential for diffraction optics such as optical position sensors, optics modulation, and multiview three-dimensional autostereoscopic displays.