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Abstract
In this paper we demonstrate fast-response Pancharatnam-Berry (PB) phase optical elements (PBOEs) based on polymer-stabilized liquid crystal (PSLC). First, a non-interferometric photo-alignment technique is employed to generate PB patterns in a dye-doped liquid crystal by green laser light. Then the samples are exposed to UV light to form polymer networks. Due to the greatly increased elastic constant in PSLC, all PBOEs can achieve submillisecond response time, while maintaining high diffraction efficiency (>90%). Furthermore, a varifocus PB lens (PBL) is implemented based on two identical PB lens elements and its application in fatigue free augmented-reality (AR) displays is verified. The fast response PBOEs based on PSLC hold great potential for various display and photonics applications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Pancharatnam-Berry phase optical elements (PBOEs), are basically half-wave plates with spatially varying optical axis [1,2]. Unlike conventional optical elements that modulate phase by optical path distance, PBOEs modulate phase by the spatial varying anisotropy. This allows for continuous optical phase shifts without introducing phase discontinuity at the boundaries, thus leading to high-efficiency diffraction [3–6]. PBOEs based on liquid crystals (LCs) offer additional electric tunability as well as low loss and low power consumption, and thus have been widely used as key components in display [6–12] and photonics applications [13–17].
As switchable optical elements, the response time of PBOEs is critical [18,19]. To improve the switching speed of PB LC devices, several approaches have been proposed. Wu et. al. used a thin cell (< 2 µm) filled with a low-viscosity LC material, and achieved a response time of 1.2 ms [20]. Hu et. al. demonstrated a fast PB grating using a dual-frequency LC [21]. By alternating the frequencies of applied voltages during the turn-on and turn-off processes, both rise and decay time have been significantly improved. Recently, Ma et. al. realized a PB lens (PBL) using a ferroelectric LC [22], which exhibits ~300 μs response with a low voltage.
In this paper, we demonstrate fast-response PBOEs based on polymer-stabilized liquid crystal (PSLC). First, PB phase patterns are formed on dye doped LC samples using a single-exposure photo-alignment method [23]. Then, polymer networks are formed to stabilize the LC alignment under UV light illumination. The strong polymer networks greatly increase the elastic constant of the LC mixtures and fasten the response time [24]. The fabricated PB LC gratings and lenses exhibit good electro-optical properties like submillisecond response time and high diffraction efficiency. We also realized a varifocus lens using two PBLs, and implement a fatigue-free augmented reality (AR) display based on it.
2. Materials and fabrication
Figures 1(a) and 1(b) show the fabrication process of PBOEs based on PSLC. The LC samples were made of a nematic host LC (E7, HCCH), a photosensitive azo dye methyl red (MR, Sigma Aldrich), a UV photo initiator (Irgacure 651, Ciba Specialty Chemicals), and a monomer (RM257, HCCH).
Fig. 1 Fabrication of PBOEs based on PSLC: (a) Optical setup of the single-exposure photo-alignment method and (b) polymer stabilization process by UV curing. (c) Normalized absorptance and transmittance of MR. Schematic distributions of LC directors in (d) a PB grating and (e) a PBL, respectively.
Frist, the optical setup in Fig. 1(a) is used to generate a two-dimensional linear polarization field (green laser 532 nm), which is used to photo-pattern LC alignment [23]. Next, as the sample is exposed to UV radiation, polymer networks are formed and LC alignments are stabilized, as shown in Fig. 1(b). Figure 1(c) shows the normalized transmittance spectrum and absorptance spectrum of MR, which has reasonably high absorption at 532 nm but almost no absorption below 400 nm. And the absorption peak of the UV initiator Irgacure 651 appears between 320 nm and 380 nm, but the absorptance above 400 nm is almost zero [25]. Therefore, the two exposures in Figs. 1(a) and 1(b) should not interference with each other. In PB gratings, LC director orientation can be controlled to vary from 0° to 180° with an increment of 30° in one period by loading a six-grey-level picture on a spatial light modulator (SLM) [23]. As for PBLs, twelve gray levels are chosen to mimic the continuous LC director change along radial axis. Schematic distributions of LC directors in a PB grating and a PBL are shown in Figs. 1(d) and 1(e), respectively. And the focal length of a PBL can be decided by Eq. (1) [26]:
where φ, λ, r, and f are the relative phase, wavelength, radial coordinate and focal length, respectively.In our experiment, to investigate the effect of monomer concentration, we prepared monomer/ LC mixtures with 6 wt.%, 7 wt.% and 8 wt.% RM257, respectively. Afterwards, ~1 wt.% MR and 0.1 wt.% UV photo initiator Irgacure 651 were added to the mixtures to form precursors. After being stirred, the precursors were injected into 3 µm indium-tin-oxide (ITO) coated cells with no alignment layer. All of the above steps were performed under total dark conditions. The sample was first exposed to the green laser light (532 nm, 60 J/cm2), and then cured by UV illumination (365 nm, 3 J/cm2). The SLM used in the experiment was a pure phase SLM (model: PLUTO-VIS, Holoeye) with 1920 X 1080 pixels and a pitch of 8 μm. The magnification of L1 is made “-1”.
3. Electro-optic properties of PBOEs
3.1 PB gratings
Figure 2(a) shows the microscopic image of a PB grating fabricated by the abovementioned 2-step method with 6 wt.% RM257. The grating period is approximately 48 μm as predicted. To prove the effect of polymer networks, we measured the electro-optical properties of the PB grating using a circular polarized (CP) beam from a He-Ne laser (632.8 nm). The first-order diffraction efficiency η of a PB grating is mainly determined by phase retardation Γ: η = sin2(Γ/2). And Γ = 2πδnd/λ, where δn is the refractive index difference between o- and e- waves, d is the cell gap and λ is the wavelength [23]. At room temperature, δn of E7 is about 0.225 (λ = 632.8 nm), and the cell gap is 3 μm, so Γ is approximately 2π and the first-order diffraction efficiency is almost zero. As a result, one can see that most of the energy is concentrated in the zero order, as shown in Fig. 2(b). As the applied voltage increases, LC direcors gradually tilt up, leading to decreased Γ. When Γ reaches ~π, the peak first-order diffraction efficiency is achieved as one can see from Fig. 2(c). The voltage required to achieve the peak diffraction efficiency for the first order is 18 Vrms, which is increased considerably compared to that of a PB grating without polymer networks, 1.6 Vrms [23]. And the peak diffraction efficiency of the PB grating using PSLC is 93.2%, indicating good LC alignment is maintained after UV exposure.
Fig. 2 (a) Microscopic image of a PB grating based on PSLC with 6 wt.% RM257. Diffraction patterns of the PB grating at (b) voltage-off and (c) voltage-on states.
The response times of the PB gratings with and without polymer networks are measured and shown in Fig. 3. The rise time and decay time of the PB grating with no polymer network are about 70 ms and 10 ms, respectively. And those of the PB grating with 6% RM257 are 276 µs and 526 µs, respectively. Approximately 20X improvement has been achieved for the decay time, which is mainly attributed to the increased elastic constant of the PSLC after UV curing.
The concentration of monomer plays an important role in determining the response time and driving voltage of the PB devices. With the monomer concentration increasing, the interaction between LC molecules and polymer networks is strengthened. Therefore, the free relaxation time is shortened while driving voltage increased [27–30]. Figure 4 shows the voltage-dependent first-order diffraction efficiency curves of PB gratings with different monomer concentrations. We find that all the PB gratings exhibit high diffraction efficiency (> 90%), and the driving voltages of 6 wt.%, 7 wt.% and 8 wt.% RM257 gratings are 18 Vrms, 24 Vrms and 28 Vrms, respectively. Table 1 shows the response times of these PB gratings. All gratings can achieve submillisecond response time, but the 8 wt.% RM257 grating exhibits the fastest response due to the highest monomer concentration. In consideration of both fast response time and relatively low driving voltage, we chose the optimal 6 wt.% RM257 sample to fabricate other PBOEs.
Fig. 4 Voltage-dependent first-order diffraction efficiency curves of PB gratings with different RM concentrations.
Table 1. Measured response times of PB gratings with different RM257 concentrations
3.2 PBL
We also fabricated a PBL with 6 wt.% RM257 by using the same exposure method. Figure 5(a) is the microscopic picture of the PBL. Figures 5(b) and 5(c) show the light patterns captured through the PBL in the focal plane (f~100 cm) at voltage-off and voltage-on states, respectively, when illuminated by CP laser light (632.8 nm). With an appropriate voltage (~18 Vrms), most of the light is focused to a bright point as shown in Fig. 5(c), indicating high diffraction efficiency. Figure 5(d) shows the measured response time of the PBL using an 18 Vrms alternative-current square-wave signal with a frequency of 60 Hz. The rise time is about 367 µs, and the decay time is about 464 µs.
Fig. 5 (a) Microscopic image of a PBL base on PSLC with 6 wt.% RM257. Diffraction patterns of the PBL at (b) voltage-off and (c) voltage-on states in the focal plane. (d) Response time of the PBL. Captured images through the PBL at (e) voltage-off and (f) voltage-on states.
The imaging capability of the PBL was investigated using a laptop screen, which had a black and red texture, as an object. A broadband circular polarizer (Edmund Optics) was inserted between the PBL and the laptop screen to generate circular polarization. And a mirrorless camera was placed behind the PBL to take photos. Figures 5(e) and 5(f) show the captured photos, when the PBL was turned off and on, respectively. Here, the PBL exhibited a positive optical power for this incident circular polarization. Since the object was placed within one focal length distance to the PBL, the image (Fig. 5(f)) was magnified by the PBL as expected.
4. Varifocus PB lens
Employing two identical PBLs, we further implemented a fast-response varifocus lens with four different focal lengths. For a PBL, the sign of its optical power depends on both the handedness of CP light and the direction of incident light. As Fig. 6 shows, the same PBL would function as a positive lens for left-handed CP light, but as a negative lens for right-handed CP light. Moreover, as CP light passes through a PBL, its handedness of the first-order diffracted light is changed to the opposite. More interestingly, as we can see from Fig. 6(a), when the left-handed CP light comes from the left side, the PBL is a positive lens, but when the same left-handed CP comes from the right side, the PBL is negative. Similarly, the right-handed CP light coming from the left and right sides encounters a negative PBL and a positive PBL, respectively as shown in Fig. 6(b). So we put a symbol ‘ + ’ on the side of a PBL that provides a positive optical power for left-handed CP light (negative optical power for right-handed CP light). And the other side of the PBL is marked with the symbol ‘-’, since it generates a negative optical power for left-handed CP light (positive optical power for right-handed CP light).
Fig. 6 Lensing effects of a PBL for (a) left-handed CP and (b) right-handed CP light coming from different sides.
Therefore, when two identical PBLs are closely stacked with the “-” sides facing each other as shown in Fig. 7, a varifocus lens with four different diopters could be implemented. The four different diopters cases when incident light is left-handed CP are shown in Figs. 7(a)-7(d), respectively. First, in Fig. 7(a), both two PBLs are turned on. PBL1 converges the left-handed CP light as a positive lens, and converted it into right-handed CP light with a high diffraction efficiency. PBL2, which has its “-” sign facing the incident light, also functions as a positive lens for the converted right-handed CP light. So the total effective focal length of the varifocus lens f is approximately a half of each PBL, + 50 cm ( + 2 diopters). Second, as Fig. 7(b) shows, when PBL1 is turned on while PBL2 is off, the effective focal length f is the same as a single PBL1, + 100 cm ( + 1 diopter). Third, Fig. 7(c) shows that when both PBLs are turned off, there is no lensing effect and the focal length f is ∞ (0 diopter). Last, Fig. 7(d) shows that when PBL1 is off and PBL2 is on, f = −100 cm (−1 diopter).
Fig. 7 Schematic diagrams of the varifocus lens when f = 50 cm (a), 100 cm (b), ∞ (c) and −100 cm (d), respectively. Beam spots with different sizes captured by a camera when f = 50 cm (e), 100 cm (f), ∞ (g) and −100 cm (h), respectively. LCP: left-handed circular polarizer. RS: Receiving screen.
Placing a receiving screen at 50 cm behind the varifocus lens, we can observe beam spots with different sizes for different diopters cases. As shown in Fig. 7(g), when the focal length of the varifocus lens f is ∞ (corresponding to the case depicted in Fig. 7(c)), the size of the beam spot on the receiving screen is the same as that of the incident beam. When f = 50 cm (corresponding to the case depicted in Fig. 7(a)), the beam is focused to a bright point with the smallest diameter on the receiving screen, as shown in Fig. 7(e). When f = 100 cm (corresponding to the case depicted in Fig. 7(b)), the size of the beam spot is slightly larger, but still smaller than that of the incident beam as Fig. 7(f) shows. And when the focal length is −100 cm (corresponding to the case depicted in Fig. 7(d)), the varifocus lens diverges the incident beam and an enlarged beam spot is observed on the screen as shown in Fig. 7(h). Thanks to the submillisecond response of the PBLs based on PSLC, the varifocus lens can change its optical power rapidly as well. Theoretically, if a varifocus lens is consisted of N PBLs, 2N different focal lengths could be realized.
Figure 8 depicts the design of a varifocus AR system we proposed based on the varifocus lens. A laptop screen, which displayed a picture containing red letters “SJTU”, was used as the image source. A broadband LCP was placed right in front of the image source to generate left-handed CP light. And a partial reflective mirror was used to combine the real scene with virtual images. A camera was placed in the eye position in Fig. 8 to capture photos. As the focal length of the varifocus lens changes, the virtual images are generated at different depths. Figures 9(a)–9(d) show pictures captured when the virtual letters “SJTU” were displayed at 28 cm, 40 cm, 67 cm, and 200 cm by the varifocus lens with the effective optical power being −1 diopter, 0 diopter, + 1 diopter and + 2 diopters, respectively. One can see that when the letters are clearly captured by the camera, the object placed in the same depth is also clear but those in different depths are blurred. For example, as Fig. 9(a) shows, when the camera was focused at 28 cm, both the virtual image “SJTU” and the first polarizer that was placed at 28 cm away from the camera are clear, while the second polarizer and the words (“SLIDES” and “Maya”) on two boxes are blurred. These phenomena indicate that correct accommodation depth cue is realized in this vary-focal plane AR display, which could solve the accommodation-convergence conflict issue and alleviate 3D visual fatigue. With the fast tuning capability, the varifocus lens based on PSLC could also be used for multi-plane AR displays [31], which require rapid changing of optical power to avoid image flickering. The faster the lens is, the more image depths can be generated, leading to higher depth resolution.
Fig. 9 Photographs taken through the vary-focal plane AR system when “SJTU” was rendered at (a) 28 cm, (b) 40 cm, (c) 67 cm and (d) 200 cm, respectively. The camera was always focused on “SJTU”.
5. Conclusion
In this paper, we have demonstrated fast response PB gratings and PBLs based on PSLC by a 2-step exposure method. First, a non-interferometric single-exposure photo-alignment technique is used to generate PB phase patterns. Second, polymer networks are formed by UV curing to stabilize the photo alignment. The fabricated PBOEs exhibit high diffraction efficiency and submillisecond response time. The decay time is significantly improved by a factor of ~20, compared with that of PBOEs without polymer networks. Based on two identical fast-response PBLs, we further implemented a varifocus lens that can generate four different optical powers: −1 diopter, 0 diopter, + 1 diopter and + 2 diopters. The feasibility of applying this varifocus lens in a fatigue-free AR display system is verified experimentally. The fast-response PBOEs based on PSLC have great potential for various applications such as optical switching, beam steering, AR displays and light-field displays.
Funding
National Natural Science Foundation of China (61727808); Shanghai Jiao Tong University (YG2016QN37); Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University (KJS1607).
References
1. S. Pancharatnam, “Generalized theory of interference and its applications,” Proc. Indian Acad. Sci. Sect. A Phys. Sci. 44(5), 247–262 (1956). [CrossRef]
2. L. Marruccia, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: Switchable helical mode generation,” Appl. Phys. Lett. 88(22), 221102 (2006). [CrossRef]
3. C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008). [CrossRef] [PubMed]
4. R. K. Komanduri and M. J. Escuti, “High efficiency reflective liquid crystal polarization gratings,” Appl. Phys. Lett. 95(9), 091106 (2009). [CrossRef]
5. J. Kim, C. Oh, S. Serati, and M. J. Escuti, “Wide-angle, nonmechanical beam steering with high throughput utilizing polarization gratings,” Appl. Opt. 50(17), 2636–2639 (2011). [CrossRef] [PubMed]
6. T. Zhan, Y. H. Lee, and S. T. Wu, “High-resolution additive light field near-eye display by switchable Pancharatnam-Berry phase lenses,” Opt. Express 26(4), 4863–4872 (2018). [CrossRef] [PubMed]
7. G. Tan, T. Zhan, Y. H. Lee, J. Xiong, and S. T. Wu, “Polarization-multiplexed multiplane display,” Opt. Lett. 43(22), 5651–5654 (2018). [CrossRef] [PubMed]
8. Z. He, Y. H. Lee, R. Chen, D. Chanda, and S. T. Wu, “Switchable Pancharatnam-Berry microlens array with nano-imprinted liquid crystal alignment,” Opt. Lett. 43(20), 5062–5065 (2018). [CrossRef] [PubMed]
9. Y. H. Lee, G. Tan, K. Yin, T. Zhan, and S. T. Wu, “Compact see-through near-eye display with depth adaption,” J. Soc. Inf. Disp. 26(2), 64–70 (2018). [CrossRef]
10. T. Ikeda and O. Tsutsumi, “Optical switching and image storage by means of azobenzene liquid-crystal films,” Science 268(5219), 1873–1875 (1995). [CrossRef] [PubMed]
11. H. Chen, Y. Weng, D. Xu, N. V. Tabiryan, and S. T. Wu, “Beam steering for virtual/augmented reality displays with a cycloidal diffractive waveplate,” Opt. Express 24(7), 7287–7298 (2016). [CrossRef] [PubMed]
12. Y. H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S. T. Wu, “Recent progress in Pancharatnam-Berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3(1), 79–88 (2017). [CrossRef]
13. P. Chen, Y. Q. Lu, and W. Hu, “Beam shaping via photopatterned liquid crystals,” Liq. Cryst. 43(13–15), 2051–2061 (2016). [CrossRef]
14. M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006). [CrossRef]
15. Y. Li, J. Kim, and M. J. Escuti, “Orbital angular momentum generation and mode transformation with high efficiency using forked polarization gratings,” Appl. Opt. 51(34), 8236–8245 (2012). [CrossRef] [PubMed]
16. X. Wang, D. Wilson, R. Muller, P. Maker, and D. Psaltis, “Liquid-crystal blazed-grating beam deflector,” Appl. Opt. 39(35), 6545–6555 (2000). [CrossRef] [PubMed]
17. L. Li, C. Liu, and Q. H. Wang, “Optical switch based on tunable aperture,” Opt. Lett. 37(16), 3306–3308 (2012). [CrossRef] [PubMed]
18. J. Yan, Y. Li, and S. T. Wu, “High-efficiency and fast-response tunable phase grating using a blue phase liquid crystal,” Opt. Lett. 36(8), 1404–1406 (2011). [CrossRef] [PubMed]
19. G. Carbone, P. Salter, S. J. Elston, P. Raynes, L. De Sio, S. Ferjani, G. Strangi, C. Umeton, and R. Bartolino, “Short pitch cholesteric electro-optical device based on periodic polymer structures,” Appl. Phys. Lett. 95(1), 011102 (2009). [CrossRef]
20. Y. H. Lee, T. Zhan, and S. T. Wu, “Enhancing the resolution of a near-eye display with a Pancharatnam-Berry phase deflector,” Opt. Lett. 42(22), 4732–4735 (2017). [CrossRef] [PubMed]
21. W. Duan, P. Chen, B. Y. Wei, S. J. Ge, X. Liang, W. Hu, and Y. Q. Lu, “Fast-response and high-efficiency optical switch based on dual-frequency liquid crystal polarization grating,” Opt. Mater. Express 6(2), 597–602 (2016). [CrossRef]
22. Y. Ma, A. M. W. Tam, X. T. Gan, L. Y. Shi, A. K. Srivastava, V. G. Chigrinov, H. S. Kwok, and J. L. Zhao, “Fast switching ferroelectric liquid crystal Pancharatnam-Berry lens,” Opt. Express 27(7), 10079–10086 (2019). [CrossRef] [PubMed]
23. Y. Li, Y. Liu, S. Li, P. Zhou, T. Zhan, Q. Chen, Y. Su, and S. T. Wu, “Single-exposure fabrication of tunable Pancharatnam-Berry devices using a dye-doped liquid crystal,” Opt. Express 27(6), 9054–9060 (2019). [CrossRef] [PubMed]
24. S. Liu, Y. Li, P. Zhou, X. Li, N. Rong, S. Huang, W. Lu, and Y. Su, “A multi-plane optical see-through head mounted display design for augmented reality applications,” J. Soc. Inf. Disp. 24(4), 246–251 (2016). [CrossRef]
25. W. Ruan, X. Wang, Y. Lian, Y. Huang, and A. Niu, “Superabsorbent hydrogel of acrylic acid/potassium acrylate copolymers by ultraviolet photopolymerization: Synthesis and properties,” J. Appl. Polym. Sci. 101(2), 1181–1187 (2006). [CrossRef]
26. T. Zhan, Y. H. Lee, G. Tan, J. Xiong, K. Yin, F. Gou, J. Zou, N. Zhang, D. Zhao, J. Yang, S. Liu, and S. T. Wu, “Pancharatnam-Berry optical elements for head-up and near-eye Displays,” J. Opt. Soc. Am. B 36(5), D52–D65 (2019). [CrossRef]
27. H. Ren, Y. H. Lin, Y. H. Fan, and S. T. Wu, “Polarization-independent phase modulation using a polymer-dispersed liquid crystal,” Appl. Phys. Lett. 86(14), 141110 (2005). [CrossRef]
28. H. Ren and S. T. Wu, “Reflective reversed-mode polymer stabilized cholesteric texture light switches,” J. Appl. Phys. 92(2), 797–800 (2002). [CrossRef]
29. I. Dierking, “Polymer network–stabilized liquid crystals,” Adv. Mater. 12(3), 167–181 (2000). [CrossRef]
30. J. Yan, Y. Chen, S. T. Wu, S. H. Liu, K. L. Cheng, and J. W. Shiu, “Dynamic response of a polymer-stabilized blue-phase liquid crystal,” J. Appl. Phys. 111(6), 063103 (2012). [CrossRef]
31. X. Hu and H. Hua, “Design and assessment of a depth-fused multi-focal-plane display prototype,” J. Disp. Technol. 10(4), 308–316 (2014). [CrossRef]
