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Abstract
We report the ferroelectric liquid crystal (FLC) Pancharatnam-Berry lenses (PBLs) with rapid transmittance tunability. The FLC PBLs were fabricated using a single-step holographic exposure system based on a spatial light modulator working as numerous polarization retarders, providing a simple way to fabricate FLC continuous aligning structures. A state-selection sector containing a binary FLC switch was utilized for fast changing input light’s polarization handedness. Thus, when light passes through a FLC PBL, the output light’s polarization handedness can be switched accordingly. In this case, FLC PBLs can function as concave/convex lenses with rapidly switching speed. Photo sensitive azo-dye material was used as the aligning layer for both FLC PBLs and FLC switches. The fabricated FLC PBLs and the FLC switches show fast switching-on times of 150μs and 50μs respectively. The FLC PBLs combining with the state-selection sector can have potential applications on varies displays and augmented reality.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Pancharatnam-Berry lens (PBL) plays an important role in optical science and engineering community where the circular polarization-dependent devices are well utilized including the capacity of optical communication system [1,2], virtual and augmented reality displays [3–6]. The PBLs fabricated with liquid crystals (LCs) are potential candidates because their inherent photoelectric properties, large optical birefringence and controllable continuous orientation [7,8]. The complex structure of PB phase prevents the use of common rubbing method to align LCs. Several photopatterning systems have been developed. One is photo patterning through static photo masks which cannot be reconfigured once fabricated [9–12]. Other mask-free approaches using DMD (digital mirror device) [13–16], or direct laser writing [17–19] were also reported. Both techniques failed to provide single-step exposure. Recently, a single-step exposure system was used to fabricate PB gratings and q-plate based on spatial light modulator (SLM) [20]. However, the existing LC-PBLs exhibited slow switching speed limited to the level of millisecond. Furthermore, polarization of incident light beam can modulate PBLs into concave lenses/ convex lenses. Slow output light’s handedness selection between two states, that is, focusing and scattering states, is another challenge for its industrial use. Several options including blue phase liquid crystals [21], cholesteric liquid crystals [22,23] to improve switching speed still suffer from high voltage and material processing problem. On the other hand, ferroelectric liquid crystals (FLCs) utilizing photo-alignment technology [24–27] represent a promising way for PBLs with sub-millisecond responses [28–30]. However, patterns are difficult to change due to the requirement of masks as original patterns, meanwhile focusing and scattering states also requires manual selection.
In this paper, we utilized a single-exposure system containing spatial light modulator (SLM) to realize FLCPBLs. Deformed helix FLCs (DHFLCs) [31] are selected because they can offer fast response and continuously changing of light transmittance [32,33]. Moreover, when circular light passes through a state-selection sector containing a FLC switch, the FLCPBLs can switch between focusing and scattering states within sub-millisecond. The diffraction efficiency of FLCPBLs can rapidly change with switching-on time 150$\mathrm{\mu }\textrm{s}$ at $4\textrm{V}/\mathrm{\mu }\textrm{m}$ and their two states can switch with only 50$\mathrm{\mu }\textrm{s}$ at $6.67\textrm{V}/\mathrm{\mu }\textrm{m}$. Furthermore, FLCPBL arrays are also demonstrated to show good alignment and focusing properties.
2. Fabrication system
2.1 Single-step exposure
To align FLC molecules in complex structures, a polarization photosensitive alignment material namely sulphonic azo-dye (SD1) is chosen as the aligning material for its high anchoring energy, lack of mechanical damages and minimized unwanted electronic charges. Under exposure from a polarized light source in the UV-to-blue spectrum, the SD1 molecules tend to orient perpendicularly to the polarization of the incident light. Its working principle and molecular structure are shown in Figs.1(b)–1(c). To generate polarized light patterns using as exposure light on SD1, here we use a non-interferometric single-step exposure system based on a phase SLM as several phase retardations on pixel level. This approach had been used in realization of LC polymer PB devices and nematic LC PB devices [20,34] and is first used to produce FLC PBLs.
The exposure system based on SLM is depicted in Fig. 1(a), which consists of a 450nm laser, two optical lenses (lens1 and lens2), a half-wave plate (HWP), a right-angle prism, a SLM and a quarter-wave plate (QWP). The expanded blue light beam along y axis passes through a HWP with fast axis 22.5° to z direction, a SLM with fast axis parallel to x- axis and a QWP with fast axis 45° to z direction. The SLM includes 1920 × 1200 pixels and each pixel is treated as an independent phase retarder. Based on Jones Matrix, the output vector in one pixel denoted as AaBb (0<a≤1920, 0<b≤1200) can be derived as:
Fig. 1. (a) Experimental setup of the single-step holographic exposure system used for a photo-sensitive azo dye material SD1. (b) SD1 with (c) its formula providing alignment direction perpendicular to the exposure polarization of the incident light.
2.2 Fabrication of FLC PBLs
The PB lens has a lens-like phase profile entirely established using PB phase. The transmission function of the general LC-PB optical elements is given by,
Fig. 2. Simulation results of optical axis orientations and grayscale images loaded on the SLM for a $2 \times 2$ PBLA (b) and a $4 \times 4$ PBLA (c). (a) is the structure of a DHFLC cell and the rotating directions of the FLC molecules with external electric field.
Another variable that affects transmittance in Eq. (2) is the expression Γ = 2πΔneffd/λ, where Δn is the effective index of LC cell, and d is the thickness of the LC layer. In this paper, deformed helix FLC (DHFLC) is selected. In the schematic of a typical DHFLC cell shown in upper picture of Fig. 1(a) when there is no electric field, helix exists with helix pitch denoted as P0 and one important requirement for DHF effect existence is $d \gg {P_0}$. When there is an external electric field to DHFLC molecules in Fig. 1(a), the fast axis changes accordance with the absolute value of electric field. Moreover, when we consider the electrically induced biaxiality of DHFLC molecule [33], these in-plane and out-of-plane axis change both decide Δneff. [28]. Thus, the transmittance of DHFLC PBL can be expressed by Eq. (2) in terms of Δneff and α(x, z).
From the optical axis orientations α(x, z) = α(r) = πr2/2fλ, the helix orientations of the FLC molecules change continuously from 0 to $\mathrm{\pi }$ from the center to the edge of the FLCPBL. Similarly, the FLCPBL arrays (FLC PBLAs) which consist of several FLCPBLs have the same optical axis orientations in each FLCPBL. The simulation result of a 2 × 2 PBLA is shown in the left figure of Fig. 2(b). The color bar from blue to red represents the helical aligning directions of FLC molecules from 0 to $\mathrm{\pi }$. The designed incident wavelength is 633nm and the focal distance is 10$\textrm{cm}$. In the right figure of Fig. 2(b), the grayscale image was calculated according to the relationship of the grayscales on the SLM, the output light-polarizations and aligning directions of SD1. The simulation result and grayscale image for a 4 × 4 PBLA were calculated in the same way shown in Fig. 2(c)
In this work, DHFLC 587 (from P. N. Lebedev Physical Institute of Russian Academy of Sciences) is selected as the material for its high transmission in the visible spectrum and fast switching. The phase transitions sequence of this LC during heating up from the solid crystalline phase is Cr→12°C →SmC*→110°C→SmA*→127°C→Is, while cooling from smectic C* phase crystallization occurs around −10°C–15°C. The spontaneous polarization Ps and the tilt angle θ at room temperature are 150nC/cm2 and 36.5°, respectively. Two optically flat indium tin oxide-coated glass plates coated with SD1 were used for preparing a sandwich-type sample holder with cell thickness of 5μm. Designed pattern was exposed on the cell using SLM exposure system. FLC was then filled into the cell.
3. Fast state-selection sector for FLC PBLs
Knowing from Eq. (3), when half wave condition is satisfied in the FLCPBLs, the argument inside the complex exponential indicates that the lens will behave as a concave/convex lens denoted as focusing and scattering states with a focal length +/- f for the left-handed circular (LHC)/ right-hand circular (RHC) polarized light. 5μm cell gap for the FLCPBLs is chosen to meet their third half wave condition. We use another FLC switching sector as state-selection sector for FLCPBLs shown in Fig. 3(a). In this sector, the FLC switch is only required to operate in two states, changing incident light into LHC/RHC output light. An Electric suppressed helix FLC (ESHFLC) is used as a key element in the state-selection sector for its intrinsic ability of fast operation in two helix directions. Figure 3(b) shows the schematic of a FLC cell in which FLC helix is aligned along with the aligning direction where molecules rotate by the sematic layer around helix with no voltage applied. When there is voltage applied, FLC molecules rotate on the helical cone surface shown in Fig. 3(c). The directions can be decided by applied electric field polarizations.
Fig. 3. (a) Optical setup for fast switching states of the FLC PBLs. (b) Structure of a ESHFLC cell. (c) illustration of the rotating directions of the FLC molecules with external electric field.
Material FD4004N (DIC, Japan) is chosen for these FLC switches with phase transition scheme as SmC* → SmA → N* →Iso at temperatures of 72°C, 85°C and 105°C, respectively. At room temperature, the helix pitch is P0 = 350nm, spontaneous polarization Ps = 61nC/cm2 and tilt angle θ ≈ 22.5°.As depicted in Fig. 3(a), a state-selection sector compresses a QWP, a FLC switch and another QWP. By passing through the first QWP, a circular polarized light is transferred into a linear polarized light with polarization direction along z-axis as well as parallel to helix aligning direction of the FLC switch. When external electrical field is provided, FLC molecules rotate θ in plane x-z with regarding to electric polarities. In this system, half wave condition of the FLC switch is satisfied which rotates a linearly polarized light with ±2θ to z axis. After passing through a QWP with fast axis parallel to x axis, the input circular polarized light can finally be changed into LHC or RHC polarized light. Thus, one big reason we choose FLC FD4004N is its cone angle close to 45°, achieving highest efficiency of changing incident light handedness. Afterwards, the fabricated FLCPBLs can be fast switched between focusing and scattering states. The purpose of using circularly-polarized input light in this state-selection sector is to directly employ it after any PB device.
4. Results and discussion
For both DHFLCs and ESHFLCs, there exists the critical electric potential Ec with unit V/m,
where Ps denotes the spontaneous polarization of FLC material and q0 = 2π/P0 with P0 representing the helix pitch.The main difference of operating DHFLC and ESHFLC is the electric operation range. DHFLC cells should be operated in the range of -Ec < E < Ec. The switching times can be expressed as: τ = γφ/K22q02 where γφ represents rotational viscosity and K22 is elastic constant of FLCs. Whereas, ESHFLC cells should be operated in the range of E > Ec. The switching time is calculated using τ=γφ/PsE, where E is the absolute value on ESHFLC cells.
Figure 4 shows the electro-optical responses of a 5μm DHFLC cell and a 1.5μm ESHFLC cell, where the inserts (c) and (d) depict the microphotographs of a ESHFLC cell and a DHFLC cell under crossed polarizers, respectively, to prove their good alignment quality. The ESHFLC cell was sandwiched between crossed polarizer and analyzer with an angle θ between its helix axis and the polarization of the polarizer. The DHFLC cell was placed between the crossed polarizer and analyzer with its helix axis parallel to the polarization of the polarizer illustrated in Fig. 4(a) and 4(b). τon is defined as the switching time when light transmittance is changing from 10% to 90% and τoff is defined as the switching time when light transmittance is changing from 90% to 10%. For both ESHFLCs and DHFLCs, when operating in their required electric range, τon ≅ τoff. The switching-on time for the fabricated FLCPBLs is around 150μs. Transmittance performance of a 5μm FLC PBL was tested and depicts in Fig. 4(e). Under 500 Hz applied electric field shown in above figure, the FLCPBL can reach its highest transmittance with saturated range. The states-select sector can change from RHC polarized light to LHC polarized light at speed about 50μs at electric field 10 V.
Fig. 4. Switching time of a typical 1.5μm ESHFLC (FD4004N) cell and a 5μm DHFLC (587) cell on applied electric field. The inserted images (a) and (b) are illustrations of a ESHFLC cell and a DHFLC cell placed under crossed polarizers for switching time measurement. (c) and (d) are microscopic pictures of a typical ESHFLC cell and DHFLC cell. (e) is the transmittance performance in the below figure using a 5μm FLC 587 cell under applied voltage in the above figure.
The microscopic images of a 2 × 2 PBLA cell and a 4 × 4 PBLA cell with scale bar 200μm are shown in Figs. 5(a) and 5(b). The focal length of each lens is set to 10 $\textrm{cm}$ and the incident wavelength is 633 nm. Figures 5(c) and 5(d) show photographs of laser beam after passing through the state-selection sector and the FLCPBLs captured by a camera. When the state-selection sector turns the input light into right-circular polarized light, the FLCPBLs function as convex lenses observing small bright dots on the screen. When the state-selection sector turns the input light into left-circular polarized light, the FLCPBLs act as concave lenses that enlarge the beam. A L-letter image was zoomed in and out through FLCPBL system to show its ability for information transmission in Figs. 5(e) and 5(f).
Fig. 5. Microphotographs of (a) a 2${\times} 2$ DHFLC PBLA cell and (b) a 4${\times} 4$ DHFLC PBLA cell. Light patterns was captured by a CCD camera: focusing state with RHC polarized input light from (c) a 2${\times} 2$ DHFLC PBLA cell and (d) a 4${\times} 4$ DHFLC PBLA cell, images with RHC polarized input light (e) and LHC polarized input light (f). The line scale bar of (a) and (b) represents 200 $\mathrm{\mu }\textrm{m}$.
5. Conclusion
In conclusion, we have demonstrated the DHFLC-PB lenses using a single-step holographic exposure setup based on a SLM as a polarization controller in pixel level. This fabrication process for the FLC PBLs is cost effective and time efficient since the continuous alignment profile has been realized from a single step exposure. The FLC PBLs can be rapidly switched between focusing state and scattering state through a state-selection sector using a ESHFLC switch as the key element. Theoretical analyses on how the exposure system and state-selection sector work were discussed. The DHFLC PBLs provide fast response time of 150µs at 2 V/µm and their focusing/scattering states can be switched with speed of 50µs at 6.7 V/µm. These properties make them suitable for applications in imaging, display, beam manipulation and various optical setups that require fast response.
Funding
National Key Research and Development Program of China (2017YFA0303800); National Natural Science Foundation of China (61805035, 61805202); Fundamental Research Funds for the Central Universities (20D210401); DHU Distinguished Young Professor Program; Russian Science Foundation (20-19-00201).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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