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Abstract
An optical phase grating prototype based on the homeotropic aligned antiferroelectric liquid crystal (AFLC) is demonstrated. By applying an in-plane electric field using comb-like electrodes, the helical structure of AFLC is deformed with the molecules rotating parallel to the electric field because of dielectric anisotropy. This deformation is called the pre-transitional effect of AFLC and induces biaxiality. By using this effect, a switchable phase grating is constructed using a 40μm thick cell filled with (S)-MHPOBC at 85°C. For 532nm TM polarized incident light, the maximum diffraction efficiency of 37.0% is achieved at the electric field of 1.8V/μm for the ± 1st order diffraction. The rise and decay times for the 1st order diffraction pattern are 510μs and 210μs, respectively. The high diffraction efficiency achieved under low field makes it promising for future electro-optical applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Liquid crystals (LCs), have been widely applied to various photonic devices due to their easy tunability by electric fields. Among them, switchable gratings have been studied deeply in recent years due to their potential applications to displays and optical communication. So far, several approaches have been investigated to construct a grating profile. One approach is to exploit the natural helical structure of LC materials like cholesteric LCs [1]. This simple method, however, has a strict restriction on the material property and applicable wavelength. Another common method is to use nematic LCs combined with patterned electrodes [2]. Generally, they show slow response time due to the intrinsic property of nematic LCs. To improve the response speed of nematic liquid crystal devices, many attempts have been made including adjusting the material visco-elastic coefficient or adopting special driving electrode structures [3,4]. However, the response time of nematic liquid crystal devices are usually proportional to the cell thickness and the response time would increase inevitably if larger phase retardation value is desired. On the other hand, some novel LC materials including the blue phase LCs and ferroelectric liquid crystals(FLCs) [5,6] have attracted great attention due to their fast response time. In this work, a phase grating prototype based on homeotropic aligned AFLC is demonstrated.
AFLC is one kind of chiral smectic LCs discovered by Chandani et al. in 1988 [7]. Similar to FLC, AFLC has a helical structure and spontaneous polarization in each layer due to the chirality of the LC molecules. The molecules in adjacent layers tilt in almost opposite directions in AFLC so that the spontaneous polarization is canceled out. Several efforts to realize optical gratings using chiral smectic LCs have been made in the recent decades. One approach is based on the periodically aligned domains using the photo-alignment technique to generate periodic refractive index distribution [8]. Another approach is to mix FLC with photocurable liquid crystal monomer material and irradiate the sample by photomask to form a periodic grating profile [9]. However, these devices require a complicated fabrication process and a high-quality defect-free alignment for the planner chiral smectic LCs, which has always been a critical and challenging issue to overcome. To obtain a uniform texture, Another defect-free deformed helix of FLC mode in a homeotropic aligned configuration with in-plane electric field was put forward [10–12]. This preparation method enables uniform texture over a large area just by spin coating some alignment material and brings other desirable properties like analog gray scale, wide viewing angle, etc. To avoid these problems, we demonstrate a switchable optical grating based on the pre-transitional effect of homeotropic aligned AFLC with high efficiency, fast response time and easy fabrication process.
2. Physical principle
When an AFLC material is aligned perpendicular to the glass substrate (the smectic layer is parallel to the glass substrate), the average optical axis of AFLC is normal to the substrate plane due to the helical structure of the AFLC. When a sufficiently high in-plane field is applied, a field-induced phase transition to the FLC phase occurs because of the coupling between the polarization and the electric field. The helical pitch is unwinded and all molecules are tilted perpendicular to the electric field. However, when a weak electric field below the threshold value is applied, the molecular directors just rotate as they orient in the plane parallel to the field because of the dielectric anisotropy of anticlinic ordering and the helical structure is distorted. As a result, the field-induced birefringence appears. Such effect is one kind of dielectric response of the AFLC with fast response speed and is called the pre-transitional effect [13–15]. The polarization state of the output light can be invariant for the light with polarization either parallel or perpendicular to the electric field [15]. So for TM or TE polarized light, by applying an in-plane field using comb-like electrodes, the polarization state of the output light would be invariant in both areas with and without field, and only periodic phase modulation occurs. Based on this, we can prepare a pure phase grating using the homeotropic aligned AFLC cell (Fig. 1).
Fig. 1 Schematic cross-section diagrams of the in-plane switching of the AFLC based on the pre-transitional effect. The gray rods and the red arrows stand for the LC molecules and spontaneous polarization, respectively. The upper and lower substrates are common glass and ITO glass with patterned comb-like electrodes, respectively. (a) The helical structure of the homeotropic aligned AFLC when there is no electric field. The molecules in adjacent layers are oriented in almost opposite directions. (b) The molecules will rotate parallel to the electric field when a weak in-plane electric field (dashed line) is applied.
3. Experiment
In the experiment, (S)-MHPOBC (phase sequence: Iso-(148.0°C)-SmA*-(122.0°C)-SmC*α-(120.9°C)-SmC*β-(119.2°C)-SmC*γ-(118.4°C)-SmC*A-(84.0°C)-Cry), was used for testing [16]. This is one of the most well studied AFLC materials and in this paper, it is used to demonstrate the AFLC grating prototype. The helical pitch and spontaneous polarization of (S)-MHPOBC at 85°C are 7μm and 100nC/cm2, respectively [17]. The operating temperature can be further decreased by using other room-temperature AFLC materials [18]. A 40μm thick homeotropic aligned cell was prepared by sandwiching two glass substrates. One was a common glass substrate, and the other was an ITO glass substrate with patterned comb-like electrodes to generate an in-plane electric field. The substrates were spin coated with CYTOP (AGC Chemicals) to generate homeotropic alignment. The gap between the two adjacent electrodes and the width of the electrodes were set as 50μm and 50μm, respectively. And the thickness of the cell was kept with 40μm by film spacers.
The texture of the LC cell was observed using a full-wave retardation plate under a polarized-light microscope. A 100Hz square wave was applied to the sample at 85°C in a hot stage with a high-thermal stability of 0.01°C. After that, the TM linearly polarized green laser beam(λ = 532nm) was irradiated to the LC cell to generate the diffraction pattern and the pattern was detected in the far field at a distance of 40cm from the sample using a digital camera(Canon 60D) or a photo diode. The diffraction pattern intensities were evaluated by ImageJ using the FITS format files converted from the raw files obtained by the digital camera. A polarizer was inserted between the sample and the detector to check the polarization state of each diffraction order beam.
4. Results and discussion
From Fig. 2, we can see the texture is quite uniform without defect and optical isotropy due to the helical structure under zero field. The phase retardation enhances continuously with increasing field intensity, which proves the electric field is below the threshold value and the helix is deformed rather than unwinded [15]. The colors of the areas within or between the electrodes are quite uniform in the low field region so that we can regard the ideal square periodic phase retardation profile with 0.5 duty ratio is generated. For vertical aligned FLC materials, the focal conic defects can be observed near the electrode when a high field is applied. This is because the electric field near the electrode is not uniform and the electric field component perpendicular to the substrate causes extra strain to the molecule. In our experiment, the texture after the experiment is almost the same compared with the initial state because the maximum field applied in the experiment was low and no field-induced phase transition to the FLC phase occurs. The uniformity and reliability of the alignment can satisfy the high resolution requirement for future photonic applications. In this experiment, only TM polarized light is studied. The square periodic phase retardation distribution for the phase grating can be presented by the following equation:
where λ, z, w, d, and nx(n’x) stand for the wavelength of the incident light, cell thickness, width of the electrodes, the distance between two electrodes, and the refractive indices of LC materials in the x-direction in the area without(with) the in-plane electric field. Here, we define the in-plane field is applied in the x-direction and incident light propagates in the z-direction. The field distribution of the diffraction pattern in the far field can be calculated by Fourier transformation of the phase retardation distribution function of the LC cell. And for a binary phase grating, the intensity of each order is presented by the following equation:Fig. 2 Textures of the LC cell using a full wave retardation plate under the polarized-light microscope. A 100Hz square wave was applied to the sample and the LC cell was kept at 85 °C in a hot stage.
In our sample, since w and d are set to be equal, it is expected that only odd order diffraction patterns would appear and the 1st order diffraction is i2 times stronger than that of the ith order ones. From Fig. 3(a), in the initial state without the electric field, we can see only very week diffraction pattern due to the refractive index mismatch between the ITO layer and the glass. The laser power is mostly in the 0th order. When the field is below 1V/μm, the intensity of the ± 2nd order is so weak that they can hardly be observed. The intensity of the 1st order diffraction is around 9 times stronger than that of the 3rd order, as shown in Fig. 3(b). These confirm that the ideal square periodic phase retardation profile with 0.5 duty ratio was generated in the low field.
Fig. 3 (a) Diffraction patterns at 0V/μm, 1V/μm, 2V/μm and 2.5V/μm captured by the digital camera. (b) Diffraction intensity ratio of the 1st and 3rd order pattern at different electric fields. (c) The assumed phase distribution profile of the AFLC grating at low and high fields, respectively. (d) The zoomed-in texture using a full wave retardation plate under the polarized-light microscope and the schematic illustration of w1, w2, and w3 at 2.5V/μm.
On the other hand, the 2nd order starts to emerge when the electric field exceeds 1V/μm. The emergence of the 2nd order diffraction is accompanied by the slight change of the texture under the polarized-light microscope. The purple area of the texture at 2V/μm is a little narrower than that at 1V/μm, and we can see clear blue lines between purple and yellow areas. This is because the continuous change of the molecule directors and the electric field does not ideally emerge only between the electrodes. The LC molecules near the edge of the electrodes are also rotated by the electric field, which is unneglectable under high field circumstances. In this condition, the phase retardation profile can be treated as a trapezoid shape for simplification, as shown in Figs. 3(c) and 3(d). By measuring the phase retardation value and the length of each part of the trapezoid phase distribution profile from the texture under the polarized-light microscope, we can calculate the theoretical diffraction intensity of each order, which is illustrated in Fig. 4(a) together with the measured value. From Fig. 4(a), we can see the simulation value is well coincident with the measured value and predicts the appearance of the 2nd order diffraction in high field circumstances. The maximum efficiency for the ± 1 orders reaches 37.0% at 1.8V/μm and the minimum intensity of the 0th order reaches 5.3% at 2.3V/μm. The little difference between the simulation and experimental result may arise from the refractive index difference of ITO electrodes, which was not considered in the simulation.
Fig. 4 (a) Diffraction efficiency of the 0th, ± 1st and ± 2nd orders(simulation results are plotted in dashed lines). (b) Electro-optical response of the 0th and 1st order diffraction pattern intensity in the rise and decay processes upon application field of 2.0V/μm at 85°C. The response time is defined as the time between 10% and 90% of the final value. The measured diffraction order was selected by the iris and detected by the photo diode.
The diffraction angle of the 1st order was measured to be 0.31°. This value is small because the field-induced biaxiality of (S)-MHPOBC is small so that a thick IPS cell with large electrode periodicity was needed to generate enough phase retardation. This also results in high operating voltages. For this type of AFLC phase grating, there are three possible ways to increase the diffraction angle and reduce the operating voltages. The first is to increase the field-induced biaxiality value so that a smaller grating periodicity can be used. According to the model put forward by Jones [13], the helix distortion is proportional to the effective electric field value EPs/γ, in which E, Ps, and γ stand for the electric field, spontaneous polarization and antiferroelectric interaction strength. So by choosing material with larger spontaneous polarization, tilt angle, birefringence and smaller antiferroelectric interaction strength, we can expect larger biaxiality value. Another strategy is related to manipulate the anchoring energy of the substrate by means of “slippery interfaces” [19]. The general idea is that the impurities with surface affinity weaken or melt the liquid crystalline order near the interface. Therefore, the anchoring effect disappears and molecular motion is lubricated by the slippery interfaces. This method can also be used to reduce the operating voltage without reducing the response speed. The third method is to adopt double-electrode structure both on the top and bottom substrates to provide better uniformity of the electric field [20].
The response time for this switchable grating was also measured. From Fig. 4(b), we can see the rise and decay time for the 1st order pattern are 510μs and 210μs, respectively. The response speed is quite fast compared with common nematic LCs since the pre-transitional effect is one kind of dielectric response of the AFLC with fast response speed. The fast response speed is preserved even though a thick cell was used in this experiment, which is an advantage compared with the common nematic liquid crystal gratings. Besides, the polarization state of each order beam is examined. The polarization direction of the output beam is rotated for around 5°, which can be explained by the optical rotational power of AFLC.
5. Conclusion
To make a summary, a phase grating prototype based on the pre-transitional effect of AFLC materials is proposed and demonstrated by experiments. The maximum efficiency for the ± 1 orders reaches 37.0% at 1.8V/μm for the TM polarized 532nm incident light, which is very close to the theoretical value (40.5% derived from Eq. (2)). The rise and decay time are measured to be 510μs and 210μs, which is much faster compared with common nematic liquid crystals devices. Though the diffraction angle is small and the operating temperature is high for this prototype using (S)MHPOBC, these parameters can be improved by selecting other more proper AFLC materials. The high efficiency, fast response independent with the cell thickness, and easy fabrication process make it possible for high performance and wide optoelectronic applications in the future.
References
1. K. Kondo, H. Takezoe, A. Fukuda, and E. Kuze, “Temperature sensitive helical pitches and wall anchoring effects in homogeneous monodomains of ferroelectric SmC* liquid crystals, nobambc (n= 6-10),” Jpn. J. Appl. Phys. 21(2), 224–229 (1982). [CrossRef]
2. C. Brown, E. E. Kriezis, and S. Elston, “Optical diffraction from a liquid crystal phase grating,” J. Appl. Phys. 91(6), 3495–3500 (2002). [CrossRef]
3. H. Xianyu, S. Gauza, and S.-T. Wu, “Sub-millisecond response phase modulator using a low crossover frequency dual-frequency liquid crystal,” Liq. Cryst. 35(12), 1409–1413 (2008). [CrossRef]
4. T. Matsushima, K. Seki, S. Kimura, Y. Iwakabe, T. Yata, Y. Watanabe, S. Komura, M. Uchida, and T. Nakamura, “51-1: Optimal fast-response lcd for high-definition virtual reality head mounted display,” in SID Symposium Digest of Technical Papers, 49, pp. 667–670 (2018). [CrossRef]
5. Y. Ma, X. Wang, A. K. Srivastava, V. G. Chigrinov, and H.-S. Kwok, “Fast switchable ferroelectric liquid crystal gratings with two electro-optical modes,” AIP Adv. 6(3), 035207 (2016). [CrossRef]
6. A. K. Srivastava, E. Pozhidaev, V. G. Chigrinov, and R. Manohar, “Single walled carbon nano-tube, ferroelectric liquid crystal composites: Excellent diffractive tool,” Appl. Phys. Lett. 99(20), 201106 (2011). [CrossRef]
7. T. Chandani, T. Hagiwara, Y. Suzuki, Y. Ouchi, H. Takezoe, and A. Fukuda, “Tristable switching in surface stabilized ferroelectric liquid crystals with a large spontaneous polarization,” Jpn. J. Appl. Phys. 27(5), L729–L732 (1988). [CrossRef]
8. A. Srivastava, W. Hu, V. Chigrinov, A. Kiselev, and Y.-Q. Lu, “Fast switchable grating based on orthogonal photo alignments of ferroelectric liquid crystals,” Appl. Phys. Lett. 101(3), 031112 (2012). [CrossRef]
9. S. Matsumoto, M. Goto, S.-W. Choi, Y. Takanishi, K. Ishikawa, H. Takezoe, G. Kawamura, I. Nishiyama, and H. Takada, “Phase grating using a ferroelectric liquid-crystal mixture with a photocurable liquid crystal,” J. Appl. Phys. 99(11), 113709 (2006). [CrossRef]
10. D.-W. Kim, E. Jang, Y.-W. Lim, and S.-D. Lee, “Defect-free deformed-helix ferroelectric liquid-crystal mode in a vertically aligned configuration,” J. Soc. Inf. Disp. 16(9), 947–952 (2008). [CrossRef]
11. E. P. Pozhidaev, A. D. Kiselev, A. K. Srivastava, V. G. Chigrinov, H.-S. Kwok, and M. V. Minchenko, “Orientational Kerr effect and phase modulation of light in deformed-helix ferroelectric liquid crystals with subwavelength pitch,” Phys. Rev. E. 87(5), 052502 (2013). [CrossRef] [PubMed]
12. J.-H. Lee, D.-W. Kim, Y.-H. Wu, C.-J. Yu, S.-D. Lee, and S.-T. Wu, “High-speed infrared phase modulators using short helical pitch ferroelectric liquid crystals,” Opt. Express 13(20), 7732–7740 (2005). [CrossRef] [PubMed]
13. L. A. Parry-Jones and S. J. Elston, “Field-driven helix unwinding in antiferroelectric liquid crystal cells,” Phys. Rev. E. 63(5), 050701 (2001). [CrossRef] [PubMed]
14. Y. Takanishi, S. Noma, and J. Yamamoto, “Novel display mode using dielectric response of antiferroelectric liquid crystals,” Appl. Phys. Express 6(8), 081701 (2013). [CrossRef]
15. Z. Feng and K. Ishikawa, “Phase modulator mode based on the pre-transitional effect of antiferroelectric liquid crystals,” Opt. Lett. 43(2), 251–254 (2018). [CrossRef] [PubMed]
16. H. Takezoe, E. Gorecka, and M. Cepic, “Antiferroelectric liquid crystals: interplay of simplicity and complexity,” Rev. Mod. Phys. 82(1), 897–937 (2010). [CrossRef]
17. A. Singh and S. Singh, “Thermodynamic model for the electro-optical and structural properties of sm c* a phase in antiferroelectric liquid crystal mhpobc,” J. Mater. Chem. 21(6), 1991–1996 (2011). [CrossRef]
18. E. Pozhidaev, V. Vashchenko, V. V. Mikhailenko, A. I. Krivoshey, V. Barbashov, L. Shi, A. K. Srivastava, V. G. Chigrinov, and H. S. Kwok, “Ultrashort helix pitch antiferroelectric liquid crystals based on chiral esters of terphenyldicarboxylic acid,” J. Mater. Chem. C 4(43), 10339–10346 (2016). [CrossRef]
19. J. Yamamoto and I. Nishiyama, “Slippery interfaces: control and evaluation of the anchoring effect for the reduction of driving voltage (conference presentation),” in Liquid Crystals XXII, vol. 10735 (International Society for Optics and Photonics, 2018), p. 107350V.
20. A. K. Srivastava, V. G. Chigrinov, and H. S. Kwok, “Ferroelectric liquid crystals: Excellent tool for modern displays and photonics,” J. Soc. Inf. Disp. 23(6), 253–272 (2015). [CrossRef]
