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Abstract
A large-angle polarization volume grating (PVG) with circular-polarization selectivity is demonstrated using a three-dimensional chiral liquid crystal with simple cubic symmetry – the blue phase (BP) II. We confirm defect-free alignment of the BP crystal on a periodically patterned substrate down to a period of 700 nm, with Kossel diagrams and far-field diffraction patterns suggesting that the lattice becomes slanted within the cell to accommodate to the imprinted pattern. We further demonstrate a tunable PVG by exploiting the external field-responsivity of BPs, making this PVG attractive for a wide range of applications from tunable photonics to augmented reality.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The development of miniature optical elements with advanced functionalities to control light is in strong demand for various applications such as portable and wearable devices. One of the intensively investigated subjects is holographic optical elements (HOEs) that enable the manipulation of light in a flat and thin film. Conventional HOEs have been fabricated by the holographic interference method in which an interference pattern of light is recorded on holographic recording materials such as photo-polymers [1]. Liquid crystals (LCs) have recently emerged as attractive materials for HOEs, since they enable high light-conversion efficiency and solution-processability [2]. In particular, cholesteric LCs (ChLCs) in which the LC director self-organizes into a helical structure have been widely adopted for the fabrication of reflective volume HOEs based on the Bragg-Berry (BB) effect [3–5]. For a light illuminated from normalcy on the device, full 0-2π phase control in Bragg reflected light is enabled through a 0-π phase modulation of the LC director on a substrate. This concept has been applied to the fabrication of reflective volume HOEs, such as polarization gratings [3,5–7], lenses [3], holograms [8,9], and vortex beam generators [4,10], using photo-patterning technologies for spatially controlling the LC director on a substrate. Such devices diffract only a circular-polarized (CP) light with same handedness as the helix due to the sinusoidal modulation of the dielectric tensor [11], opening the possibility of exploiting light polarization to tune or miniaturize optical systems.
Blue phase (BP) LCs, which possess three-dimensional (3D) helical structures, are also candidates for realizing reflective HOEs. BPs are composed of double twist cylinders (DTCs) in which the average orientation of the LC molecules, or the director, is twisted in 360-degree directions. Depending on the packing symmetry of the DTCs, BPs are categorized into two types of periodic structures with body-centered cubic (BP I) and simple cubic (BP II) symmetry [12]. They typically possess a lattice constant of a few hundred nm, resulting in CP-selective Bragg reflection from the ultraviolet to the visible light region [13–15]. Recently, it has been revealed that BPs also show the BB effect when its azimuthal orientation is varied on a substrate [16,17]. A BB volume grating was experimentally demonstrated, confirming the theoretical prediction; however, the grating period was large owing to the limited resolution of the photo-patterning process, limiting the deflection angle as small as approximately 1° [16].
In this study, we report the fabrication and characterization of a large-angle (41.7° at 460 nm) polarization volume grating (PVG) based on a simple cubic BP II. The device is achieved by introducing a short-pitch periodic modulation in the LC molecules on a substrate through photoalignment with polarization holography. We suggest a possible configuration of the BP crystal within the patterned cell through the observation of Kossel diagrams and far-field diffraction patterns, and discuss its theoretical and experimental diffraction properties. We further investigate the effect of electric field on the PVG, and show that in contrast to cholesteric PVGs, the reflection wavelength can be tuned continuously, owing to the soft nature of the 3D crystalline structure to change its lattice constant without disturbing the alignment pattern. In contrast to the ChLC-based PVGs, the device proposed here possesses unique features such as omnidirectional CP selectivity arising from the 3D helical structure, narrow reflection bandwidth, and reversible external field-responsivity on their structure, making them attractive for practical applications such as light-coupler of waveguide devices.
2. Experimental sections
2.1 Cell fabrication
A sandwiched cell with a gap of 8 µm was prepared by assembling two ITO-coated glass substrates, which were covered by a photo-alignment agent. The photo-alignment material is based on azo-benzene, which enables the long axis of LC molecules to be aligned perpendicular to the incident linear polarization. The photo-patterning process was conducted by polarization holography method [5,18].
2.2 Photo-alignment with polarization holography method
A diode laser (Coherent, Sapphire SF 488) with a wavelength (λ) of 488 nm was used as a light source for polarization holography. The polarization of the light was converted to left-circular polarization (LCP) using an isolator (also act as a polarizer) and a Barbinet-Soleil (BS) compensator. The LCP light was enlarged to a beam size of 1 cm through a beam expander, and passed through a quarter-wave plate (QWP) and reflected by a dielectric mirror, again passed through the same QWP to maintain the polarization of reflected light as LCP light. Two counter-propagating LCP light are superimposed on each other, creating a periodically rotating linear polarized (LP) light with a periodicity given by Λ = λ/2sinθ, where θ is the angle of the device normal from the beam. In experiment, the sandwiched cell was placed between the BS compensator and the QWP, and rotated by 20°, giving a theoretical grating period of 713 nm. The dosage of the laser illumination was 14 J/cm2.
2.3 Materials
A BP mixture was prepared by blending two types of host nematic LCs (MLC-2140 and 5CB, both from Merck) with positive dielectric anisotropy, and a left-handed chiral dopant (S-5011, HCCH) at a weight concentration of 48.45:48.45:3.1. The phase sequence of the mixture in the cooling process was isotropic – BP II (47.5°C) – BP I (45.9°C) – cholesteric (43.5°C). The mixture was filled in the photo-patterned cell at 50°C and cooled to a temperature where the BP II appears (46.1°C), at a rate of 0.2°C/min. The temperature of the device was controlled using a commercial hotplate (Linkam, TS350). A square wave electric field with a frequency of 1kHz was applied between the two substrates using a function generator (33210A, Agilent) connected to a × 30 amplifier.
3. Results
Figure 1 shows a model of the BP lattice in the proposed device. The surface anchoring imposed on the substrate causes the BP lattice to be rotated azimuthally depending on position [16]. However, considering the elasticity of BPs, a possible configuration of the BP lattice as a whole is to rotate its unit cell to maintain the cubic structure, at the cost of some transitional layer near the surface that follows the anchoring profile. In this case, the tilt angle α in the bulk will be given by α = sin−1(a/Λ) = sin−1(2asin(θ)/λ), where a is the lattice constant of the BP II, to satisfy the periodic anchoring condition imposed on the surface. The tilt causes the central wavelength of the Bragg reflection (λc) to be shifted by a factor of cos(α) from a BP II with the [100] axis perpendicular to the surface. Thus, the λc of the proposed device for normal incidence is expressed as
Fig. 1. Schematic illustration of the proposed BP. The device has the [100] crystal axis slanted from the device normal at an angle of α.
We note that the theoretical diffraction angle according to the pure BB effect, i.e., when the BP is not tilted, is identical with Eq. (2) and is only determined by λc and Λ. Although we focus here on the optical properties of the fabricated PVG, investigation using advanced microscopic methods such as confocal laser scanning microscopy [19] and transmission electron microscopy [12] should enable characterization of the microscopic alignment of BPs in a patterned cell.
Figure 2(a) shows a polarized optical microscope (POM) image and its magnified image, taken in reflection mode under the illumination of LCP light, of the device obtained by cooling from the isotropic state. It is confirmed that a macroscopic defect-free BP crystal is obtained with a periodic modulation in the reflectivity with Λ ∼ 690 nm. The intensity modulation originates from the periodic change in the optical phase of Bragg reflected light from the device, which corresponds to the patterning period of the device (the slight difference between the theoretical and experimental grating period is due to the mismatch of 0.5° in the rotation angle of the device during the patterning process). Figure 2(b) shows the transmission spectrum of the device upon LCP and right-CP (RCP) illumination. The Bragg reflection appears for only LCP light with λc of 465 nm, giving a ∼ 154 nm and α ∼ 12.9° according to Eqs. (1) and (2), when the no and ne are assumed to have values of 1.50 and 1.65, respectively.
Fig. 2. Optical characteristics of the fabricated PVG. (a) POM image observed in reflection mode upon LCP illumination, and its magnified image. (b) Transmission spectra upon LCP and RCP illumination. Experimental (c) and simulated (d) Kossel diagrams. The white circles in (c) and (d) indicate the maximum collection angle of the objective, and the dashed line in (d) shows simulated Kossel line.
Figures 2(c) and (d) show experimental and simulated Kossel patterns of the device illuminated by light with a wavelength of 460 nm (for experiments, the bandwidth of illuminated light is ± 5 nm). Hereafter, we refer to BP II with the (h k l) crystal plane oriented parallel to the substrate as BP II(hkl). It is well-known that the Kossel pattern of a BP II(100) typically appears as a centered circle in the back focal plane, reflecting the incident angle dependence of Bragg reflection from the (100) plane set [20]. In our device, the circular Kossel line shifts toward the edge of the back focal plane by an angle of 19.5°, which provides direct evidence of light diffraction by the fine-pitch patterning of BP (The strong light spot at the center of the back focal plane is attributed to the Fresnel reflection from the glass substrate). As described previously, the diffraction property of the patterned BP can be analyzed by considering a tilted lattice structure; thus, the Kossel pattern is reproduced numerically by assuming a simple cubic structure with the same values of a and na as above, and tilting its [100] axis by α from the substrate normal (Fig. 2(d)).
BPs are suited for a candidate of tunable PVGs because their lattice structure can be easily modulated by external stimuli such as heat [21], electric field [22,23], and light [24,25]. Here, we examine the response of the patterned BP structure to an application of electric field. Figure 3(a) shows the evolution in the POM images, Kossel diagrams, and schematics of the device as an electric field is gradually increased with a step of 0.19 V/µm per min up to homeotropic (H) state, and removed. Up until a field of 2.1 V/µm, the reflected intensity modulation in the POM image is observed, and the reflection color is red-shifted. The corresponding Kossel diagrams show enlarged circular patterns without changing the shift angle. This implies that the lattice constant is increased along the direction parallel to the applied field, but the diffraction property is still maintained. At a field of 3.0 V/µm, the intensity modulation in POM image disappears, and the circular Kossel pattern becomes centered at the back focal plane. BP II is known to undergo a field-induced phase-transition to the body-centered tetragonal BP X [26]; however, judging from the Kossel pattern of the BP II, which still has primitive tetragonal symmetry, suggests that an anchoring breaking had occurred, causing the BP II to become uniformly aligned on the substrate. Further increase of the field induces a phase transition to the H phase (at 5.3 V/µm), in which the helical structure is completely unwound and the director is uniformly aligned along the applied field. The original structure reappears when the field is removed, demonstrating the capability to switch the slanted BP structure.
Fig. 3. Mechanism on the lattice distortion of BP crystal upon applying electric field. (a) Evolution of the POM images, Kossel diagrams, and schematics at various electric field. (b) Applied field dependent λc as the field is increased with a rate of 0.19 V/µm per min. The dashed line indicates an applied field of 2.3 V/µm. (c) Transmission spectra before applying and after removing the electric field.
Figure 3(b) plots the measured λc with respect to the applied field at the device. The λc red-shifts monotonically up to 2.3 V/µm, which is attributed to the distortion of the lattice structure. A discontinuous change in the λc from 490 nm to 507 nm is observed at 2.3 V/µm because of the aforementioned anchoring breaking. When the electric field is removed from the H phase, the Bragg reflection reappears at a same wavelength with the initial BP (Fig. 3(c)), enabling a tunable and switchable PVG by the application of electric field.
A laser setup shown in Fig. 4(a) was used to evaluate the tunablility of light diffraction from our device. A super-continuum laser (SuperK COMPACT, NKT Photonics) was separated by a beam splitter and passed through two different band-pass filters with a bandwidth of 10 nm to select two probe beam wavelengths. The two beams were combined through another beam splitter and illuminated on the BP after controlling its polarization to LCP and RCP lights using a polarizer and a quarter-wave plate. The reflected light spots were observed on a screen placed at a distance of 13 cm from the device.
Fig. 4. Observations of diffracted light spot from the device. (a) Schematic of the laser set up. BS: Beam splitters; BF: band-pass filters (the central wavelengths of BF1 and BF2 are 460 and 480 nm, respectively, with a bandwidth of 10 nm); M: dielectric mirrors; P: polarizer; QWP: quarter-wave plate; Sc: screen. (b) Diffracted light spots at 0 V upon LCP and RCP illumination by light with a wavelength of 460 (± 5) nm. (c) Time-dependent applied electric field for observations of tunable diffraction characteristics of the PVG. (d) Diffracted light spots at various field intensities when illuminated by LCP light with wavelengths of 460 (± 5) and 480 (± 5) nm. In (b) and (d), the light spots on the right are the diffracted light spots and those on the left are zero-order reflections.
Figure 4(b) shows the diffraction spot when light with wavelength of 460 (± 5) nm is incident from normalcy on the device with no applied field. Because the device shows CP-selective reflection due to the double-twist structure of LC molecules [11], a strong reflection spot is observed only for LCP illumination at a distance of 11.6 cm from the zero-order spot, giving a deflection angle of 41.7°. This value well-matches with the theoretical prediction (41.9°) given by Eq. (2). The elongation of the diffraction beam spot is because the incident light is not single-wavelength, but has a bandwidth of 10 nm. When illuminated by LCP light, the conversion efficiency, which is defined as the intensity ratio between the incident and diffracted lights, in Fig. 4(b) is measured as 54.7%. The value is similar to the reflectance of the BP (∼ 60%, see Fig. 2(b)), with losses attributed to the Fresnel reflection at the glass-air interface and imperfections in the patterning. The circular dichroic ratio of light diffraction between LCP and RCP illumination was approximately 103:1. Figures 4(c) and (d) show the tunability of diffraction spots from the device upon the application of electric field. An AC electric field (1kHz) was applied with a sequence of 0 V – 2.1 V/µm – 5.3 V/µm – 0 V as shown in Fig. 4(c), and diffraction profile was measured at each stage. For this experiment, the device was illuminated by LCP light with wavelength of 460 and 480 nm (± 5 nm for both), which overlap with the Bragg reflection bands of the BP at 0 V and 2.1 V/µm, respectively. As shown in Fig. 4(d), the reflection color is tuned at 2.1 V/µm, and hence the deflection spot is shifted away from the zero-order spot according to Eq. (2). Moreover, on-off switching of the diffraction is enabled by inducing a phase transition to the H phase (5.3 V/µm). As such, it is demonstrated that the diffraction light from the BP-based PVG can be tuned or switched through the control of electric field.
4. Discussion
In this paper, we demonstrated a large-angle, circular-polarized, and field-tunable PVG based on the photo-patterned BP II. An interesting difference of BP-based PVGs compared to ChLC-based PVGs is their exceptionally wide-angle CP dependence originating from the high symmetry of the cubic structure [17] and reversible tunablilty on their helical structure upon an application of electric field. The semi-transparency caused by the CP selectivity makes our proposed device useful for light-couplers in augmented reality system where the capability of seeing through the device is required. We expect that the device operating in a wide temperature range can be achieved using polymer-stabilization method [27] or by adding a small amount of bent-core molecules in BPs [28]. We also believe that PVGs with similar diffraction characteristics can be obtained using BP I with appropriate techniques to control the crystal orientation, such as field-assisted directed self-assembly [17] and the use of nano-patterned substrates [29]. On the other hand, we have discovered a previously unreported phenomenon of anchoring breaking at moderate electric fields. Our work is a step towards understanding how the frustration between surface anchoring and self-organization can lead to unexpected material behavior.
Funding
The Ministry of Education, Culture, Sports, Science and Technology (LEADER Program); Japan Society for the Promotion of Science (JP19H02581, JP20H00391, JP20H04672, JP20K21154).
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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