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Abstract
A polarization-insensitive liquid crystal (LC) Fresnel lens is developed with binary LC configurations of 90°-twisted nematic (TN) and vertically-aligned (VA) domains in the adjacent zones. A LC mixture comprised of nematic host, photopolymer and chiral material is initially filled into the VA cell with orthogonal rubbing treatment. After the ultraviolet irradiation on the filled LC cell through a photomask with Fresnel zone plate pattern, the interactions among orthogonal rubbing treatment, self-assembly polymer gravels, and chiral material induce the 90°-TN structure in the odd zones, whereas the initial VA structures are maintained in the even zones. The fabricated LC Fresnel lens with binary configuration emerges a maximum diffraction efficiency of around 35% at a voltage of 2.3 V, close to the theoretical diffraction limit of around 41%. The diffractive focus of the LC Fresnel lens is polarization-insensitive at the voltage above 2 V. When the voltage reaches 10 V, the diffractive focus vanishes. The numerical calculation confirms that the polarization-insensitive property appears in the primary focus of the LC Fresnel lens. This work reports a simple method to develop a highly efficient, polarization-insensitive, and electrically tunable LC Fresnel lens which is favorable for imaging system.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Fresnel lenses are enormously interesting due to their wide applications in photonics, optical imaging, long-distance optical communication, and three-dimensional display systems [1–4]. The traditional Fresnel lenses constructed by electron-beam writing [5] or thin-film deposition [6] have certain shortcomings, which comprise the complex fabrication process and fixed diffraction efficiency. Moreover, the diffraction efficiency at the focus is sacrificed due to the blocked even (or odd) zones. The issues can be overcome by using other optical materials, such as liquid crystals (LCs), to fabricate the binary phase Fresnel zones. LC is a good candidate for electrically tunable devices due to its excellent electro-optical performance and low operating voltage. Various LC Fresnel lenses have been developed for beam steering, optical switching, and wavefront shaping in previous decades [7–10]. In comparison to traditional Fresnel lenses, LC Fresnel lenses possess the advantages of relatively simple fabrication, light weight, and electrically tunable diffraction efficiency. The intrinsic anisotropy of LCs unfortunately leads to most LC Fresnel lenses have the polarization dependence on the incident light [11–13]. Aiming to enhance the light utilization efficiency, some manners have been reported to realize the polarization-insensitive LC Fresnel lenses; for instance, polymer and blue phase LC composite (PBPLC) [14], 90°-twisted nematic (TN) LCs [15], polymer dispersed LCs (PDLCs) [7], dye-doped LCs (DDLCs) [16,17], and orthogonal hybrid alignment [18]. However, the PBPLC Fresnel lens has an extremely high operation voltage of around 200 V, which may cause electrode breakdowns and severe hysteresis effects; the maximum diffraction efficiency of 90°-TN LC Fresnel lens is only 25% with a voltage of 20 V because of disclination defects at the edges of zone and bus line; the practicality of PDLC Fresnel lens is hampered by its high operation voltage of around 12 V/µm; the photo-induced dye-adsorption in the DDLC Fresnel lens requires a high power laser (> 24 mW/cm2) to pump azo-dyes to align LCs. The azo dye photoalignment layer has instability to subsequent exposure to light, and the red tint of azo-dye may cause the color distortion in imaging performance; the orthogonal hybrid alignment in the adjacent zones requires two-step linearly polarized ultraviolet (UV) exposures to make. The hybrid LC alignment leads to the tunable range of phase shift in the LC Fresnel lens is decreased by 2x.
Our previous works utilized the self-assembly polymer gravels to adjust the pretilt angle of LCs moderately from vertical to planar [19,20]. The self-assembly polymer gravels was further used to develop a low-voltage gradient-index (GRIN) LC lens [21]. Aiming to develop an efficient tunable Fresnel lens, the self-assemble polymer gravel technique is used to fabricate a polarization-insensitive diffractive LC Fresnel lens. A LC mixture comprised of nematic host, photopolymer, and chiral material is initially filled into the VA cell with orthogonal rubbing treatment. After ultraviolet irradiation through a photomask with a Fresnel zone plate pattern, the LC Fresnel lens with the configuration of 90°-TN and vertically-aligned (VA) LC alignments in the adjacent zones is established. The mechanism responsible for the formation of LC Fresnel lens has been explained in this paper. The 90°-TN LCs in the odd zones have been confirmed with the voltage-dependent transmissions (V-T). The zone patterns of the LC Fresnel lens were observed through a polarized optical microscope (POM). The voltage-dependent diffraction efficiencies and polarization dependence property were examined using a photodetector placed at the focal plane of the LC Fresnel lens. Results show that the fabricated LC Fresnel lens is polarization-insensitive as the applied voltage exceeds 2 V, and it has maximum diffraction efficiency ∼35%. As shown in the Table. 1, both DDLC and the proposed LC Fresnel lenses in this work have the low addressing voltage, high diffraction efficiency, and fast response time. However, the red tint of azo dyes limits the feasibility of DDLC Fresnel lens in imaging systems. Comparatively, the transparency of proposed LC Fresnel lens is favorable for practical imaging applications.
Table 1. Comparison of polarization-insensitive LC Fresnel lenses
2. Experimental methods
Figure 1(a) shows that a 5 ± 1 µm-thick empty cell was assembled with two 0.55 mm thick indium–tin–oxide glass substrates. The inner surfaces of both substrates were spin-coated with vertical polyimide AL-8088C (Daily Polymer, Taiwan) and rubbed in orthogonal directions. A LC mixture that comprised nematic E7 (Daily Polymer, Taiwan), 1.5 wt% photopolymer NOA65 (Norland Optical Adhesive, USA), and 0.265 wt% chiral material R1011 (Merck) was prepared. Nematic E7 had the birefringence Δn = 0.22, dielectric anisotropy Δε = 14.50, elastic constant K11 = 12.00 pN, K22 = 9.00 pN, K33 = 19.50 pN, clearing temperature TNI = 64 °C, and rotational viscosity γ = 232.60 mPas at room temperature (RT). The helical twist power (HTP) of chiral R1011 in nematic LC E7 was 37.6 µm-1 [22]. The induced helix pitches (P) was around 10 µm for 0.265 wt.% R1011 by
where C is the concentration of chiral dopant. The LC mixture was ultrasonicated for 30 minutes at RT and then filled in the empty cell by capillary action. Figure 1(b) shows that the Fresnel zone plate comprised 70 concentric rings, of which the diameter was 0.8 cm. The odd and even zones were transparent and opaque, respectively. The radius (r1) of the innermost zone was 0.5 mm, and that (rn) of the nth zone was given by where n is the zone number. For a binary phase Fresnel lens, the primary focal length (f) was related to r1 as where λ depicted the wavelength of incident beam (λ = 633 nm). The primary f of the Fresnel lens was 50 cm. Fresnel zone lens typically emerges multiple foci at f, f/3, f/5… etc., because of higher-order Fourier components. Most incident beam diffracts into the primary focus. The diffraction efficiency (ηn) of these foci can be expressed as where n = ±1, ± 3, ± 5, and so on. The theoretical diffraction efficiency of the primary focus is 41% [23].Figure 1(c) shows that the Fresnel zone plate was placed on the top substrate of the LC cell as a photomask. A UV light (λ = 365 nm) was used to irradiate the LC cell through the photomask. The UV intensity and irradiation time were set to 1 mW/cm2 and 2 hrs, respectively. The fabrication of the LC Fresnel lens was accomplished after the irradiation. The initially orthogonal rubbing treatment provided a 90°-TN LC alignment. According to the experimental experience, the doped photopolymer and the polymer gravels formed on the substrates declined the twist rate. The addition of chiral material was to compensate the decrease of twist rate, which preserved the 90°-TN structure in the odd zone of the Fresnel LC lens. An expanded He-Ne laser (λ=632.8 nm) with a diameter of 0.8 cm was used to measure the electro-optical properties of the LC Fresnel lens. The photodetector and CCD camera were set behind the LC Fresnel lens to record the focusing, imaging properties, and diffraction efficiency.
3. Results and discussion
Figures 2(a) and 2(b) show the zone pattern images at the center and border of the fabricated LC Fresnel lens, respectively. The evident zone patterns are observed throughout the entire lens. In the odd zones, the photopolymers NOA65 diffuse toward and polymerize as polymer gravels on the substrates due to vertical phase separation during the UV irradiation [24,25]. The self-assembly polymer gravels change the surface polarity of the substrates and decrease the pretilt angle of LCs. The initial orthogonal rubbing treatment induces a 90°-TN LC alignment. However, the doped photopolymer and the formed self-assembly polymer gravels decline the twist rate, resulting in the twist angle of LCs less than 90°. The addition of chiral material compensates the decrease of twist rate so that maintains the 90°-TN LC alignment. On the other hand, the initial VA LCs are kept in the even zones due to lack of photopolymerization. Consequently, the bright and dark images are observed in the odd and even zones under the cross polarizers, respectively. The bright images in the odd zones are caused by the polarization rotation effect of 90°-TN LCs. The defects in the POM images may originate from the polymer gravels disturb the LC alignment. To examine the 90°-TN LCs in the odd zones, the lens sample was placed between a pair of crossed polarizers and a pair of parallel polarizers to measure the V-T curves for normally white (NW) and normally black (NB) states, respectively. A He–Ne laser with a wavelength of 633 nm was normally incident on the innermost zone (first zone) of the lens sample, where a square-wave voltage at a frequency of 1 kHz was subject to the lens sample. Figure 2(c) shows that the intensity in the NW (NB) V-T curve steeply declines (raises) when the applied voltage (V) exceeds 1.5 V. Moreover, the NW and NB V-T curves of 90°-TN LCs were calculated using commercial software LCDmaster 3D (Shintech Optics). The measured results highly agree with the calculated those, confirming the 90°-TN LCs in the odd zones. Aiming at the significance of chiral addition, a LC Fresnel lens was fabricated using the LC mixture comprised of 1.5 wt% photopolymer NOA65 and nematic E7. With the absence of chiral material, the measured V-T curves of the odd zone deviates from those of 90°-TN LCs, indicating the doped photopolymer and the formed self-assembly polymer gravels decline the twist rate.
Fig. 2. POM textures at the (a) center and (b) border of the lens sample. (c) Measured and calculated V-T curves for the odd zone in the lens sample. AT and AO represent the transparent and opaque zones corresponding to Fresnel zone plate mask; P and A are the directions of transmission axes of the polarizer and analyzer, respectively. Rtop and Rbottom indicate the rubbing directions of top and bottom substrates in the lens sample, respectively.
Figures 3(a) to 3(c) show a portion of zone patterns in the LC Fresnel lens addressed at 0, 2, and 10 V, respectively. At 0 V, the color difference between the adjacent zones is caused by binary configuration of 90° TN and VA LC domains in the odd and even zones. As the V exceeds the threshold voltage, the color change in the odd zone is attributed to the reorientation of LCs in the bulk area by the applied field. When the V reaches 10 V, the optical intensity significantly decreases because the LC directors in the odd zones are almost reoriented normal to the substrates, indicating the phase difference between the adjacent odd and even zones is vanished. The leakage of light at the boundaries of the adjacent zones originates from the high twist angle of LCs. In [15], the disclination lines occurred in the 90°-TN LC Fresnel lens, which caused the serious diffraction loss due to symmetrically fringing electric fields induced by zone electrodes. Comparatively, the proposed LC Fresnel lens with binary configuration adopts the planar electrode structure wherein that prevents the appearance of disclination lines.
Fig. 3. POM textures of the LC Fresnel lens addressed at (a) 0 V, (b) 2 V, and (c) 10 V. P and A are the directions of transmission axes of the polarizer and analyzer, respectively. Rtop and Rbottom indicate the rubbing directions of top and bottom substrates in the lens sample, respectively.
Figure 4(a) depicts the voltage-dependent primary diffraction (or focus) efficiencies of the LC Fresnel lens with various incident linearly polarizations. The diffraction efficiency is defined as the ratio of the intensity of the focus spot to that of the transmitted beam through the lens sample. Initially, the diffraction efficiencies are around 20–25% due to the phase difference between the adjacent odd and even zones is larger than π. As the V increases, the diffraction efficiency firstly decreases and thereafter increases. At V > 2 V in the odd zones, the LC directors in the bulk area are reoriented nearly normal to the substrates. Meanwhile, the LC directors near the top and bottom substrates are aligned planarly along the rubbing direction due to surface anchoring, in which the LC layers near the two substrates become orientated orthogonally to each other. Due to the orthogonal planar orientation of the top and bottom boundary layers in the odd zones and the vertical alignment in the even zones, the polarization state of the output light is always the same as that of the incident light. That indicates the LC Fresnel lens with binary configuration is polarization-insensitive at V > 2 V [15]. As shown in Fig. 4(a), the voltage-dependent diffraction efficiencies at incident polarizations of 0°, 45°, and 90° remain consistent at V > 2 V. The maximum diffraction efficiency reaches of 35.14% at 2.3 V, which is close to the theoretical limit of 41% [23]. At this moment, the phase difference between the adjacent odd and even zones reaches π. The diffraction loss is attributed to that the phase difference between the adjacent odd and even zones decreases with the radial radius. The high LC twists at the boundaries between the adjacent odd and even zones also result in the diffraction loss. As V > 2.3 V, the bulk LC directors in the odd zones are gradually reoriented normal to the substrates. Thus, the diffraction efficiency decreases again. At V = 10 V, almost all LC directors are reoriented vertically and the phase difference between the adjacent odd and even zones approaches zero, so that focus effect of the LC Fresnel lens almost vanishes. The residual diffraction efficiency of 7% is caused by the Fresnel diffraction from the surface structure of self-assembly polymer gravels and the various orientations of LCs near the substrates in the odd and even zones. Figure 4(a) shows that the strong diffraction at V = 2.3 V produces a sharp peak of intensity profile at the focal plane of LC Fresnel lens. If the V is switched to 10 V, the diffraction and associated focus are vanished. To elucidate the polarization-independent property, the diffraction efficiencies of the LC Fresnel lens at various incident polarizations are demonstrated in Fig. 4(b). The LC Fresnel lens realized with 90°-TN and VA LCs in the odd and even zones, respectively, are polarization-insensitive.
Fig. 4. (a) Voltage-dependent diffraction efficiency of the LC Fresnel lens. The inset shows the focus spot profile at 2.3 V and 10 V. (b) Diffraction efficiency as a function of incident polarization at 2.3 V.
The intensity profiles of focus spots and voltage-dependent focus intensities at various incident polarizations were calculated using with finite element method software COMSOL to mimic the measured results. The parameters such as LC layer thickness, innermost odd zone radius, zone number, and incident wavelength were set to 5 µm, 10.46 µm, 8, and 632 nm, respectively. The LC directors in the odd and even zones were set to 90°-TN and VA structures, respectively. The calculated primary f was ∼ 200 µm. Figure 5(a) shows that the results reveal the intensity profiles of focus spots at primary focal plane at 2 V are nearly same with various incident polarizations. The central peak intensity originates from the primary focus (1st order diffraction) of LC Fresnel lens, and the ripples on both sides are caused by the higher order diffractions and the large twist angles at the boundaries between the adjacent zones. With increasing the zone number, the central peak intensity increases and the ripples can be suppressed. As shown in Fig. 5(b), at V∼1.6 V, the LC Fresnel lens has maximum focus intensity. If V > 1.6 V, the focus intensities at various incident polarizations would become similar, indicating that the LC Fresnel lens is polarization-insensitive. At V = 4 V, the focus effect vanishes. The calculation results qualitatively explain the polarization-insensitive diffraction behavior of the demonstrated LC Fresnel lens with binary configuration under suitable voltages. Figure 5(c) clearly indicates that the phase difference between the adjacent odd and even zones decreases with the radial radius, resulting in the diffraction loss of LC Fresnel lens. As shown in Figs. 5 (d), the twist angles larger than 90° at the boundaries between the adjacent odd and even zones also contribute the diffraction loss. Furthermore, the voltage-dependent 3rd order focus intensities were calculated, where f was set to 66 µm, as shown in Fig. 5(e). Notably, the 3rd order focus intensity changes with incident polarizations even at high voltages, indicating that higher order focus is polarization sensitive. The cell parameters and designed focal length used in this calculation differ from those of the fabricated LC Fresnel lens, owing to limitations from the computing capability of the used computer. Consequently, the calculated voltage required for maximum focus intensity is lower than the measured one. In Figs. 5(a), 5(c), and 5(d), the calculated results are circular symmetry because the LC Fresnel lens are fabricated with center-symmetric circular zones.
Fig. 5. Calculated (a) intensity profile of primary focus spot at 2 V, (b) voltage-dependent focus intensities at the primary focal plane, (c) phase retardations as a function of radius at 1.6 V, (d) twist angle distribution of LCs at 2 V, and (e) voltage-dependent focus intensities at the 3rd order focal plane.
The focus patterns of the LC Fresnel lens addressed at 2.3 V were captured from the CCD camera placed at various positions. When the CCD camera was arranged at 50 cm behind the lens cell, a tight focus spot was captured because of the primary focus of the LC Fresnel lens, as shown in Fig. 6(a). As the CCD camera gradually moved far away from the lens cell, the light spot began to be diverged, as shown in Fig. 6(b). To measure the dynamic response of the LC Fresnel lens, a photodetector was set at the primary focal plane and its output monitored on an oscilloscope to record the transient transmissions. The turn-on (off) time was determined as the time taken for that the transmission changed from minimum (maximum) to maximum (minimum) when the V across the lens sample was suddenly switched from 10 (2.3) V to 2.3 (10) V. The turn-on and turn-off time of the LC Fresnel lens is obtained ∼ 10 ms and 14 ms, respectively.
Fig. 6. Focus patterns of the LC Fresnel lens without polarizer. The distances between the lens sample and CCD camera were (a) 50 cm and (b) 60 cm, respectively.
To evaluate the image quality of the LC Fresnel lens, a black piece of cardboard with a transparent letter “L” was located in front of the lens cell addressed with a maximum diffraction efficiency (at 2.3 V). The real size of the letter “L” was 0.5 cm in height. The photos were captured without any polarizers. When the CCD camera was set at a distance of 27 cm behind the LC Fresnel lens, several focus order images were observed at the same time (Fig. 7(a)). The central spot, smaller, bigger, and inverted images represent the higher, + 1st, zeroth, and -1st orders, respectively. The zeroth order image was the normal real image whose size was equal to that of the original letter. As the CCD camera was moved to the primary f (∼50 cm) of the LC Fresnel lens, the majority of transmitted light was diffracted to the focal point. Thus, the zeroth order image and a tight spot were obtained (Fig. 7(b)). If the CCD camera was further far away (76 cm) from the LC Fresnel lens, the +1st order inverted “L” image was captured (Fig. 7(c)). These results indicate that the sample indeed behaves similar to a lens. As shown in Figs. 7(d)–(f), the +1st order images (smaller “L”) are almost similar with various incident polarizations due to polarization insensitive primary focus, where the CCD camera was set at a distance of ∼27 cm behind the LC Fresnel lens. The central spot intensity slightly changes with incident polarizations because the higher order focus is polarization sensitive. The central spot intensity at incident polarizations of 0° is notably lower than those at incident polarizations of 45° and 90°, which agrees with the calculated result in Fig. 5(e).
Fig. 7. Imaging properties of LC Fresnel lens when the CCD camera was located at a distance of (a) 27 cm, (b) 50 cm, and (c) 76 cm behind the lens sample, respectively. Imaging properties of LC Fresnel lens at incident polarizations of (d) 0°, (e) 45°, and (f) 90° when the CCD camera was located at 27 cm behind the lens sample.
An imaging system was designed with the fabricated LC Fresnel lens as the focusing element, and the setup was described as follows. A printed paper was placed in front of the LC Fresnel lens as the object. The height of the capital letter “C” in the object was around 0.2 mm. A CCD camera with lens module was placed at a distance of 1 cm behind the LC Fresnel lens to capture the formed images of the object. The focal length of the lens module was set to infinite. The distance between the LC Fresnel lens and object was set to 50 cm, namely the primary focal length of LC Fresnel lens. A polarizer was placed between the LC Fresnel lens and object to adjust the incident polarization. When a voltage of 10 V was subject to the LC Fresnel lens (turned off), the defocused images are observed with various polarizations, as Figs. 8(a)–(c) have shown. As the LC Fresnel lens is turned on from 10 V to 2.3 V, the printed paper is focused and clear images can be captured. The captured images at various polarizations are similar due to the polarization-insensitive primary focus, as shown in Figs. 8(d)–(f). The blue tint of the images is attributed to the cool ambient light and quality of CCD camera.
Fig. 8. Defocused images at incident polarizations of (a) 0°, (b) 45°, and (c) 90° when the LC Fresnel lens is turned off; focused images at incident polarizations of (d) 0°, (e) 45°, and (f) 90° when the LC Fresnel lens is turned on. The red dash circle and arrow indicate the active area of LC Fresnel lens and the incident polarization direction, respectively.
4. Conclusion
This study demonstrates a highly efficient, polarization-insensitive, and electrically tunable LC Fresnel lens with a binary configuration of 90°-TN and VA LCs in the odd and even zones. After UV irradiation through a Fresnel zone plate, the interactions among the orthogonal rubbing treatment, self-assembly polymer gravels, and chirality of chiral dopant produces 90°-TN LCs in the odd zones. The 90°-TN LCs has been confirmed with measured and calculated V-T curves. On the contrary, the initial VA LCs are kept in the even zones. The fabricated LC Fresnel lens performs a maximum diffraction efficiency of ∼35.14% at 2.3 V, which is close to theoretical limit (∼41%) of binary-phase LC Fresnel lenses. The numerical calculations reveal that the diffraction loss is mainly attributed to the decreased phase differences with radial radius and the high LC twists at the boundary between the adjacent zones. If V > 2.3 V, the focus effect of the LC Fresnel lens is polarization-insensitive. As the V reaches 10 V, the focus effect vanishes. The diffractive focus of the LC Fresnel lens using the binary configuration has been calculated and the results reveal that the primary and higher order focus is polarization insensitive and sensitive, respectively. The fabricated LC Fresnel lens has been used in an imaging system to demonstrate the polarization-insensitive image performance. Compared with the DDLC Fresnel lens, the proposed LC Fresnel lens can avoid the color distortion that is favorable for imaging system.
Funding
Ministry of Science and Technology, Taiwan (110-2112-M-018-009, 110-2811-M-018-501).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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