Multi-dimensional multiplexing optical secret sharing framework with cascaded liquid crystal holograms

Secret sharing is a promising technology for information encryption by splitting the secret information into different shares.However,the traditional scheme suffers from information leakage in decryption process since the amount of available information channels is limited.Herein,we propose and demonstrate an optical secret sharing framework based on the multi-dimensional multiplexing liquid crystal(LC)holograms.The LC holograms are used as spatially separated shares to carry secret images.The polarization of the incident light and the distance between different shares are served as secret keys,which can significantly improve the information security and capacity.Besides,the decryption condition is also restricted by the applied external voltage due to the variant diffraction efficiency,which further increases the information security.In implementation,an artificial neural network(ANN)model is developed to carefully design the phase distribution of each LC hologram.With the advantage of high security,high capacity and simple configuration,our optical secret sharing framework has great potentials in optical encryption and dynamic holographic display.

Liquid crystal-integrated metasurfaces for an active photonic platform

Metasurfaces have opened the door to next-generation optical devices due to their ability to dramatically modulate electromagnetic waves at will using periodically arranged nanostructures.However,metasurfaces typically have static optical responses with fixed geometries of nanostructures,which poses challenges for implementing transition to technology by replacing conventional optical components.To solve this problem,liquid crystals(LCs)have been actively employed for designing tunable metasurfaces using their adjustable birefringent in real time.Here,we review recent studies on LCpowered tunable metasurfaces,which are categorized as wavefront tuning and spectral tuning.Compared to numerous reviews on tunable metasurfaces,this review intensively explores recent development of LC-integrated metasurfaces.At the end of this review,we briefly introduce the latest research trends on LC-powered metasurfaces and suggest further directions for improving LCs.We hope that this review will accelerate the development of new and innovative LC-powered devices.

Dielectric anisotropy in liquid crystal mixtures with nematic and smectic phases

The modulation of dielectric anisotropy(△ε)is pivotal for elucidating molecular interactions and directing the alignment of liquid crystals.In this study,we combine liquid crystals with opposing dielectric anisotropies to explore the impact of varying concentrations on their properties.We report the sign-reversal of△εin both the nematic and smectic A phases of these mixed liquid crystals,alongside a dual-frequency behaviour across a broad temperature spectrum.Our research further quantifies the influence of mixture ratios under various temperatures and electric field frequencies.This exploration may pave the way for the discovery of new physical phenomena.

Liquid crystal droplets formation and stabilization during phase transition process

The study of phase transition processes in liquid crystals(LCs)remains challenging.Most thermotropic LCs exhibit a narrow temperature range and a rapid phase transition from the isotropic(ISO)to the nematic(N)phase,which make it difficult to capture and manipulate the phase transition process.In this study,we observed the evolution of small droplets during the ISO–N phase transition in ferroelectric nematic(NF)LC RM734.After doping with metal nanoparticles(NPs),the temperature range of the phase transition broadened,and the droplets formed during the phase transition remained stable,with their diameter increasing linearly with temperature.In addition,droplets doped with NPs can be well controlled by an external electric field.This discovery not only aids in understanding the fundamental mechanisms of LC phase transitions but also provides a simple alternative method for preparing droplets,which is potentially valuable for applications in optoelectronic devices and sensors.

Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers,micro-motors,medical equipments,and so on.Currently,numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency.However,numerical methods are burdened by intricate computations and limited precision,hindering comprehensive investigations into self-oscillating systems.In this paper,the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied,and analytical solutions for the amplitude and frequency are determined.Initially,we establish the governing equations of self-oscillation,elucidate two motion regimes,and reveal the underlying mechanism.Subsequently,we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency.The results show agreement between the multi-scale and numerical methods.This research contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.

THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.

ENERGY CONSERVATION FOR THE WEAK SOLUTIONS TO THE 3D COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

In this paper,we establish some regularity conditions on the density and velocity fields to guarantee the energy conservation of the weak solutions for the three-dimensional compressible nematic liquid crystal flow in the periodic domain.

Advances in Liquid Crystal Epoxy:Molecular Structures,Thermal Conductivity,and Promising Applications in Thermal Management

Traditional heat conductive epoxy composites often fall short in meeting the escalating heat dissipation demands of large-power,high-frequency,and highvoltage insulating packaging applications,due to the challenge of achieving high thermal conductivity(k),desirable dielectric performance,and robust thermomechanical properties simultaneously.Liquid crystal epoxy(LCE)emerges as a unique epoxy,exhibiting inherently high k achieved through the self-assembly of mesogenic units into ordered structures.This characteristic enables liquid crystal epoxy to retain all the beneficial physical properties of pristine epoxy,while demonstrating a prominently enhanced k.As such,liquid crystal epoxy materials represent a promising solution for thermal management,with potential to tackle the critical issues and technical bottlenecks impeding the increasing miniaturization of microelectronic devices and electrical equipment.This article provides a comprehensive review on recent advances in liquid crystal epoxy,emphasizing the correlation between liquid crystal epoxy’s microscopic arrangement,organized mesoscopic domain,k,and relevant physical properties.The impacts of LC units and curing agents on the development of ordered structure are discussed,alongside the consequent effects on the k,dielectric,thermal,and other properties.External processing factors such as temperature and pressure and their influence on the formation and organization of structured domains are also evaluated.Finally,potential applications that could benefit from the emergence of liquid crystal epoxy are reviewed.

WEAK-STRONG UNIQUENESS FOR THREE DIMENSIONAL INCOMPRESSIBLE ACTIVE LIQUID CRYSTALS

The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.

Creating a bionic scaffold via light-curing liquid crystal ink to reveal the role of osteoid-like microenvironment in osteogenesis

Osteoid plays a crucial role in directing cell behavior and osteogenesis through its unique characteristics,including viscoelasticity and liquid crystal(LC)state.Thus,integrating osteoid-like features into 3D printing scaffolds proves to be a promising approach for personalized bone repair.Despite extensive research on viscoelasticity,the role of LC state in bone repair has been largely overlooked due to the scarcity of suitable LC materials.Moreover,the intricate interplay between LC state and viscoelasticity in osteogenesis remains poorly understood.Here,we developed innovative hydrogel scaffolds with osteoid-like LC state and viscoelasticity using digital light processing with a custom LC ink.By utilizing these LC scaffolds as 3D research models,we discovered that LC state mediates high protein clustering to expose accessible RGD motifs to trigger cell-protein interactions and osteogenic differentiation,while viscoelasticity operates via mechanotransduction pathways.Additionally,our investigation revealed a synergistic effect between LC state and viscoelasticity,amplifying cellprotein interactions and osteogenic mechanotransduction processes.Furthermore,the interesting mechanochromic response observed in the LC hydrogel scaffolds suggests their potential application in mechanosensing.Our findings shed light on the mechanisms and synergistic effects of LC state and viscoelasticity in osteoid on osteogenesis,offering valuable insights for the biomimetic design of bone repair scaffolds.

Influence of the Powder on the Properties of the Liquid Crystal Emulsions

The purpose of study was to evaluate the effect of four powder including titanium dioxide,bismuth oxychloride,silica,and kaolin on the properties of the liquid crystal emulsions.The results show that the addition of titanium dioxide and bismuth oxychloride had no obvious effect on the liquid crystal structure.In addition,the addition of Kaolin and silica have an effect on the stability of the liquid crystal structure.Sensory evaluation and Texture analyzer results shown that the addition of titanium dioxide and bismuth oxychloride had no obvious effect on the spreadability of liquid crystal system.The addition of silica and Kaolin was increased the hardness and adhesive of the liquid crystal system.Rheological experiments shown that the kaolin system had lower structural stability.the system with titanium dioxide,bismuth oxychloride,and silica has good stability.This paper provides data support for the application of powders in the formulation of liquid crystal system,which aims to provide a data basis for the preparation and applications of liquid crystal emulsion.

Color holographic display based on azo-dye-doped liquid crystal(Invited Paper)

A multiplexed holographic display video has been achieved by using a passive azo-dye-doped liquid crystal （LC） cell. Holograms formed in this cell can be refreshed in the order of several milliseconds. By angular multiplexing technique, dynamically multiplexed holographic videos are realized. Moreover, the reconstructed RGB images are merged into a color image, which illustrates the possibility of a color holographic three-dimensional （3D） display by holographic multiplexing of the LC cell.

Bichromatic coherent random lasing from dye-doped polymer stabilized blue phase liquid crystals controlled by pump light polarization

In this paper,we investigate the bichromatic coherent random lasing actions from the dye-doped polymer stabilized blue phase liquid crystals.Two groups of lasing peaks,of which the full widith at half maximum is about 0.3 nm,are clearly observed.The shorter-and longer-wavelength modes are associated with the excitation of the single laser dye（DCM） monomers and dimers respectively.The experimental results show that the competition between the two groups of the lasing peaks can be controlled by varying the polarization of the pump light.When the polarization of the pump light is rotated from 0？to 90？,the intensity of the shorter-wavelength lasing peak group reduces while the intensity of the longer-wavelength lasing peak group increases.In addition,a red shift of the longer-wavelength modes is also observed and the physical mechanisms behind the red-shift phenomenon are discussed.

Random lasing in dye-doped polymer dispersed liquid crystal film

A dye-doped polymer-dispersed liquid crystal film was designed and fabricated,and random lasing action was studied.A mixture of laser dye,nematic liquid crystal,chiral dopant,and PVA was used to prepare the dye-doped polymer-dispersed liquid crystal film by means of microcapsules.Scanning electron microscopy analysis showed that most liquid crystal droplets in the polymer matrix ranged from 30 μm to 40 μm,the size of the liquid crystal droplets was small.Under frequency doubled 532 nm Nd：YAG laser-pumped optical excitation,a plurality of discrete and sharp random laser radiation peaks could be measured in the range of 575–590 nm.The line-width of the lasing peak was 0.2 nm and the threshold of the random lasing was 9 m J.Under heating,the emission peaks of random lasing disappeared.By detecting the emission light spot energy distribution,the mechanism of radiation was found to be random lasing.The random lasing radiation mechanism was then analyzed and discussed.Experimental results indicated that the size of the liquid crystal droplets is the decisive factor that influences the lasing mechanism.The surface anchor role can be ignored when the size of the liquid crystal droplets in the polymer matrix is small,which is beneficial to form multiple scattering.The transmission path of photons is similar to that in a ring cavity,providing feedback to obtain random lasing output.

Random lasing from dye-doped negative liquid crystals using ZnO nanoparticles as tunable scatters

This work demonstrates the realization of a lasing in scattering media,which contains dispersive solution of Zn O nanoparticles（NPs） and laser dye 4-dicyanomethylene-2-methyle-6-（p-dimethylaminostyryl）-4H-pyran（DCM） in negative liquid crystals（LCs） that was injected into a cell.The lasing intensity of the dye-doped negative LC laser can be tuned from low to high if the NPs concentration is increased.The tunability of the laser is attributable to the clusters-sensitive feature in effective refractive index of the negative LCs.Such a tunable negative liquid crystal laser can be used in the fabrication of new optical sources,optical communication,and liquid crystal laser displays.

Flat multifunctional liquid crystal elements through multi-dimensional information multiplexing

Flat optical elements have attracted enormous attentions and act as promising candidates for the next generation of optical components.As one of the most outstanding representatives,liquid crystal(LC)has been widely applied in flat panel display industries and inspires the wavefront modulation with the development of LC alignment techniques.However,most LC elements perform only one type of optical manipulation and are difficult to realize the multifunctionality and light integration.Here,flat multifunctional liquid crystal elements(FMLCEs),merely composed of anisotropic LC molecules with space-variant orientations,are presented for multichannel information manipulation by means of polarization,space and wavelength multiplexing.Specifically,benefiting from the unique light response with the change of the incident polarization,observation plane,and working wavelength,a series of FMLCEs are demonstrated to achieve distinct near-and far-field display functions.The proposed strategy takes full advantage of basic optical parameters as the decrypted keys to improve the information capacity and security,and we expect it to find potential applications in information encryption,optical anti-counterfeiting,virtual/augmented reality,etc.

A review of liquid crystal spatial light modulators:devices and applications

Spatial light modulators,as dynamic flat-panel optical devices,have witnessed rapid development over the past two decades,concomitant with the advancements in micro-and opto-electronic integration technology.In particular,liquid-crystal spatial light modulator(LC-SLM)technologies have been regarded as versatile tools for generating arbitrary optical fields and tailoring all degrees of freedom beyond just phase and amplitude.These devices have gained significant interest in the nascent field of structured light in space and time,facilitated by their ease of use and real-time light manipulation,fueling both fundamental research and practical applications.Here we provide an overview of the key working principles of LC-SLMs and review the significant progress made to date in their deployment for various applications,covering topics as diverse as beam shaping and steering,holography,optical trapping and tweezers,measurement,wavefront coding,optical vortex,and quantum optics.Finally,we conclude with an outlook on the potential opportunities and technical challenges in this rapidly developing field.

Singularity Formation forthe General Poiseuille Flow of Nematic Liquid Crystals

We consider the Poiseuille flow of nematic liquid crystals via the full Ericksen-Leslie model.The model is described by a coupled system consisting of a heat equation and a quasilinear wave equation.In this paper,we will construct an example with a finite time cusp singularity due to the quasilinearity of the wave equation,extended from an earlier resultonaspecial case.

Smart beam via electrically addressing the dye-doped and polymer-stabilized cholesteric liquid crystals

Smart beams play a vital role in modern intelligent vehicles and have recently attracted significant attention.A spatial light modulator with high optical efficiency,low cost,and compact size is crucial for designing smart beams.Here,we mix cholesteric liquid crystals with dichroic black dye and a monomer.After UV polymerization,the sample exhibits a low driving voltage of 26 V,a high transmittance of over 70%,and an On-off ratio over 280,thanks to the joint contribution of both the absorption and the scattering effect.A smart beam device is demonstrated by electrically addressing the dye-doped and polymer-stabilized cholesteric liquid crystal with pixelated electrodes.Light patterns with arbitrary designs are projected dynamically.The switching time reaches several tens of milliseconds.This strategy brings new designs to intelligent vehicles and may also inspire applications in public information displays,advertising,and even AR/VR displays.

Preparation and improved photocatalytic activity of ordered mesoporous TiO_2 by evaporation induced self-assembly technique using liquid crystal as template

Ordered mesoporous TiO2 （OMPT） was prepared by an evaporation induced self-assembly technique using liquid crystal as template. The key factors affecting the methylene blue （MB） oxidation efficiency were investigated, including the initial concentration of MB, pH value and catalyst concentration. The results show that the obtained OMPT has high thermal stability and shows a 2D hexagonal mesostructure with the small particle size and high surface area, which lead to higher degradation efficiency than commercial P25 or nanoparticle TiO2 （NPT） fabricated by sol-gel process. The optimal conditions are 5 mg/L MB, pH 6 and 1.5 g/L OMPT for the fastest rate of MB degradation. Total organic carbon （TOC） analysis indicates complete mineralization of MB in 240 min by OMPT, with rate constant higher than NPT or P25.