Recently, Spatial Light Modulators (SLMs) with high modulation bandwidth in both spatial and time domains received great interest. Especially SLMs with small pixel size and continuous 2π phase modulation are in great demand for applications such as Light Detection and Ranging (LiDAR), holographic display, AR/VR, optical tweezers, correction in digital photo-lithography, wave-front correctors, 3D printing, and correlator in free space optical calculation, communications, and many more1-10. Such SLMs can also be used in the blocks of optical information processors, high-resolution microscopy, and display applications11. For instance, it can be used in Adaptive Optics (AO), which is paving the way for high-resolution microscopy, and aberration correction in biomedical imaging including the biological tissue specimens, cell structure, and pico-scale devices14.
The SLMs can be categorized into two types. First, micro-mirrors based devices that include Micro-electro Mechanical systems (MEMS) and bimorph deformable mirrors16. These are generally employed for binary modulation offering high-frequency operations (f < 20 kHz) with fixed amplitude and phase by addressing the light reflection. Digital Micromirror Devices (DMD) SLMs are effective for direct-laser-projection (DLP), 3D printing and aberrations correction in two-photon imaging19. However, the non-solid structure and binary modulation are serious barriers for applications that require frame rate above kHz, multi-phase-level, and reconfigurable phase modulators. On the other hand, there are modulators based on Liquid Crystals (LC). These modulators are tuneable with highly flexible patterns20-22. LC SLMs use LC’s ability to respond to external stimuli, mostly applied electric fields. In contrast to the DMD SLMs, the LC-based SLMs have advantages in generating complex phase patterns. Moreover, it can potentially find application in multi-photon microscope that requires a correction element in the illumination path12. Besides, the LC SLMs can readily be employed in two-photon fluorescence microscopes since phase modulation is necessary for the laser beam, not the fluorescence output13,23-25. Apart from AO, phase modulation has been extensively explored for hologram and beam steering. Recently, the Polymer-stabilized Blue Phase Liquid Crystals (PSBPLC) and standing helix Cholesteric Liquid Crystals (CLC) based SLMs were reported for display applications26,27.
Liquid crystal on silicon (LCoS) technology can be utilized for developing SLMs based on Nematic LC (NLC) or FLC. However, the NLCs can only achieve low-frequency phase modulations due to its slow switching time, typically < 180 Hz28. The LCoS using Surface Stabilized Ferroelectric Liquid Crystal (SSFLCoS) usually provides fast (~10 kHz)29,30, with only binary phase modulation31-32,33.
The Deformed Helix Ferroelectric Liquid Crystal (DHFLC) with sub-wavelength helix pitch can provide continuous amplitude modulation without fringe field effect (FFE.)34,35. The DHFLC, on applying the electric fields, shows a continuous change of effective birefringence and the optical axis, resulting in analog grayscale 36. However, there are certain limitations, such as loss of light due to the imperfect alignment in the DHFLC that limits the efficiency and contrast ratio in these devices36. Additionally, the effective birefringence and effective optical axis change simultaneously32,35. The variation of the retardation limits the multi-phase level and phase modulation depth. Furthermore, the phase modulation depth depends on the rotation cone of the DHFLC optical axis, and the required cone angle of FLC should be close to 90º, which usually increases the rotational viscosity and limits the response time of the FLC31.
Bottlenecks
The minimum pixel size, resolution, FFE., response time of LC, and the driving voltages are the critical attributes of a high-performing LCoS. Currently, LCoS occupies the market of the most competitive phase modulators with 2π phase modulation range such as Wavelength Selective Switch (WSS) and near-eye holographic displays. Due to growing demand in high-resolution imaging and photonic devices, people are aiming to archive LCoS pixel size ~ 1 μm without any artifact. However, reducing the pixel size of LCoS is challenging for NLC due to strong FFE. (crosstalk)34. A relatively large pixel size results in low diffraction efficiency, a small deflection angle, and a hologram with a limited viewing zone.
The FFE. is a common issue in devices with an electrode array that has voltage distribution in 1D, 2D, or 3D patterns, which is also referred to as the cross-talk effect between neighboring pixels. It becomes a serious issue for devices using a vertical electric field as a driving force, such as twisted nematic LC, pi-cell LC (O.C.B.), and nonlinear optical materials, especially when the thickness of the LC is comparable to the pixel size. To evaluate the severity of the FFE. in modern high-resolution devices, a common Electrical Controlled Birefringence (ECB.) LC cell (cell gap = 4.3 µm) filled with nematic MLC2144 (Merck & Co. Inc)39 condition is simulated using the LCD master simulation software, see Fig. 1a. Ideally, the phase depth should reach 2π in the absence of FFE. and should not have disclination lines, but these two factors are inevitable for NLCs34. Specifically when the pixel size is 3.54 μm with 0.2 μm electrode gaps for 4K LCoS devices. Here two kinds of FFE. are considered38. Firstly, the FFE. induced by the horizontal electric field, results in the disclination line. Secondly, the FFE. induced by the vertical electric field , which results in the cross-talk between pixels. In Fig. 1a, on applying different voltages on neighbouring pixels, the phase modulation depth drops by 30% and serious disclination lines show up at driving voltage 0.79 V. On comparing it with the ideal phase modulation profile on each electrode, we found a clear mismatch and disclination lines. In spite of several efforts, the FFE. and slow response times remains the two main issues for modern NLC based SLMs. These limitation results in, insufficient spatial frequency, deflection angle (< 2˚), efficiency and refresh rate stopping NLS based LCoS towards a lots of applications such as hologram, WSSs, and LiDARs40.
In 2020, our group showed that the DHFLC based spatial light modulators are inherently immune to FFE. 34. The DHFLC shows a clear electrode edge without any noticeable FFE. or disclination lines, whereas these effects are serious in NLCs34. The POM. images of NLCs and DHFLCs are shown in Fig. 1b. Fig. 1c and d depicts the configuration of FLC cell, the FFE. is primarily absent due to the coupling between the electric field and spontaneous polarization (). The in-plane direction of alongs the FLC helix axis, the Ex does not couple with , and therefore, FLC molecules do not respond to the . Conversely, the electric field projections are perpendicular to the helix axis couple with FLC molecules. However, unlike the ECB. in NLC and Kerr effect in vertical aligned deformed helix ferroelectric liquid crystal, planar aligned FLC shows limited performance in phase modulation because of the hysteresis and limited modulation ability. In 2022, Nabadda et al proposed an optimized binary phase modulation using the SSFLC mode. Optimizations related to the FLC materials and optics are still on going41. Kotova, S. P. et al proposed a continuous phase modulation by using DHFLC while the cell gap is around 50 μm for visible light, for which the alignment quality and FFE. should be discussed and optimized32.
In this article, a fast continuous 2π geometrical phase modulator on the basis of dynamic rotation of the short-pitch Ferroelectric Liquid Crystal (FLC) is proposed. A continuous multi-level (8 bit) phase modulation with 1.9π phase modulation depth, fast switching time (<250 μs), low operating voltage (< 7 V) and high diffraction efficiency (> 77%) is achieved based on defect-free Deformed Helix Ferroelectric Liquid Crystal (DHFLC) for the first time while the minimum distinguishable feature size is 1 μm, without FFE. We also discussed the unwinding process of the helix, linear working region of DHFLC for pure phase modulation, using rotation of the effective optical axis, and non-linear phase modulation region using the change of the effective birefringence, are shown as the limitation and introduction of the dynamic unwinding of DHFLC. We synthesized a new series of FLC material with fast response and cone ~ 85º for short pitch DHFLC. Later, we designed a compensation film to enlarge the phase modulation depth in and beyond the material aspect of DHFLC. We also illustrated that DHFLC is a promising candidate for LiDAR, real-time holograms and other spatial light modulator applications requiring fast response and super high pixel density.
Material Design
To design a suitable short pitch FLC, we used the guest host approach, wherein the achiral host is mixed with one or multiple chiral guest molecules. The chiral components were synthesized using the similar approach described in Ref 42. The details of FLC materials synthesis are given in Supplementary Materials 1.1-1.3.
General requirements of the high-performing DHF. materials for the electro-optical application includes short helix-pitch () (i) to avoid Bragg diffraction of light, at any angle of incident, must be <125-130 nm; (ii) and maintain high elastic energy during the whole operational range43. The induced helix-pitch of FLC, based on guest host approach, depends on concentration () of the chiral component (CC) and its helical twisting power (HTP.), which can be written as p–1 = H.T.P. ×c×ee, where ee is enantiomeric excess of CC.
Typically, the viscosity of FLC increases with the concentration of CC. Thus, a chiral compound with high H.T.P. is required that can achieve short helix-pitch at relatively lower content of CC in achiral host. To achieve a maximum phase modulation depth, tilt angle should be 45°. However, a slightly small , even ~ 40°, still provides reasonably high phase modulation range and diffraction efficiency. Furthermore, to meet the higher resolution SLM. limitations on the driving voltage, the spontaneous polarization () of the FLC should be high, which adds additional constraints on the concentration of the CC.
We started from the mixture FLC 58742 and considered as our reference material. The FLC 587 show FFE-free phase and amplitude modulation34. This mixture is composed of binary biphenylpyrimidine host (BPP-6587) and 24 mol.% of CC FOTDA-6, see Table 1. Since BPP-6587 melts at 36°C, to have a non-crystallized FLC mixtures at room temperature, we compose new 6-component host, BPP-73, which melts at 21°C. We suppose that an additional dipole to the structure of the CC can enforce the inter-molecular interaction with host molecules and thereby improve H.T.P. and P.S., we synthesised o-diflouro analog of FODTA, compound DFT-TFA-6. Indeed, DFT-TFA-6 shows increased H.T.P. (by ~10%), whereas P.S. value remains almost unchanged, c.f. 9074 with 9075. However, unexpectedly new CC induced higher tilt angle (~ 42.5° at room temperature). Further variation of chemical structure of FODTA, namely exchange terminal of benzene rings with pyridine ones, passing to PDN-TFA-6 CC, resulted in further enhancement of the CC performance: H.T.P., and especially , see Table 2. Apparently, the pyridine rings increase the inter-molecular coupling not only due to dipole-dipole interaction, but being of the basic nature, also by specific interaction with surrounding molecules.