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.

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.

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.

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.

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.

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.

Magneto and Electro-Optic Intensity Modulator Based on Liquid Crystal and Magnetic Fluid Filled Photonic Crystal Fiber

We propose a novel light intensity modulator based on magnetic fluid and liquid crystal（LC） filled photonic crystal fibers（PCFs）. The influences of electric and magnetic fields on the transmission intensity are theoretically and experimentally analyzed and investigated. Both the electric and magnetic fields can manipulate the molecular arrangement of LC to array a certain angle without changing the refractive index of the LC. Therefore, light loss in the PCF varies with the electric and magnetic fields whereas the peak wavelengths remain constant. The experimental results show that the transmission intensity decreases with the increase of the electric and magnetic fields. The cut-off electric field is 0.899 V/um at 20 Hz and the cut-off magnetic field is 195 m T. This simple and compacted optical modulator will have a great prospect in sensing applications.

A dark hollow beam from a selectively liquid-filled photonic crystal fibre

This paper reports that, based on the electromagnetic scattering theory of the multipole method, a high-quality hollow beam is produced through a selectively liquid-filled photonic crystal fibre. Instead of a doughnut shape, a typical hollow beam is produced by other methods; the mode-field images of the hollow-beam photonic crystal fibre satisfy sixth-order rotation symmetry, according to the symmetry of the photonic crystal fibre （PCF） structure. A dark spot size of the liquid-filled photonic crystal fibre-generated hollow beam can be tuned by inserting liquid into the cladding region and varying the photonic crystal fibre structure parameters. The liquid-filled PCF makes a convenient and flexible tool for the guiding and trapping of atoms and the creation of all-fibre optical tweezers.

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.

Synthesis and Characterization of Side-Chain Liquid Crystalline Polysiloxanes

Side chain liquid crystalline golysiloxanes conta ing biphenyl and benzyl ether mesogen were synthesized by the hydrosilation of poly(methylhydrcsiloxane) with 4-(4-allyloxybenzytoxy)-4'- methoxybiphenyl(M_1),4-(4-allyloxybenzyloxy)-4'-ethoxybiphenyl(M_2),4-(4-allyloxybenzyloxy)-4'- propoxybiphenyl(M_3),4-(4-allyloxybenzyloxy)-4'-butoxybiphenyl(M_4),4-(4-allyloxybenzyloxy)-4'- pentyloxybiphenyl(M_5).The phase behavior of monomeric and polymeric liquid crystals was chararcterized by differential scanning calorimetry and optical polarization microscopy.Both the monomeric and polymeric liquid crystals exhibit liquid crystal behaviors.

Circuit-Level Analysis on Opto-Electronic Characteristics of Ferroelectric Liquid Crystal

We propose an electronic model in Spice, instead of traditional mathematical analysis, for analyzing the performance of ferroelectric liquid crystal （FLC） under various working conditions. Using this equivalent circuit model,it is easy to simulate and analyze the behavior of an FLC layer in three different typical parameters,including temperature, input light wavelength, and the frequency of driving voltage. We conclude that the response velocity drops as the wavelength increases in the range of visible light, and for the parameter of temperature, the velocity reaches its lowest value when the temperature reaches a certain degree,meanwhile,the frequency of driving voltage exerts important effects on the response velocity only when the frequency is beyond a critical value. Excellent agreement is achieved between simulation and experimental results.

Self-assembly and UV-curing Property of Polymerized Lyotropic Liquid Crystal Monomer of Sodium 3,4,5-tris（ll-acryloxyundecyloxy）benzoate

A polymerized lyotropic liquid crystal monomer of sodium 3,4,5-tris（11-acryloxyundecyloxy）- benzoate was synthesized by a convenient route starting from 3,4,5-trihydroxybenzoic acid via esterification followed by etherification, acylation and finally neutralization. The chemi- cal structure was confirmed by Fourier transform infrared （FT-IR） and 1H nuclear magnetic resonance spectral analysis. The self-organization behavior of the monomer with deionized water in methanol at room temperature was also demonstrated. The assemblies were char- acterized by polarized optical microscope and X-ray diffraction. The results show that a solution containing 80：20 of the monomer to water was found to be able to self-organize into Lamellar （La） phase and 92：8 with inverted hexagonal （H]I） phase, which was in ac- cordance with the theoretical calculation of critical packing parameter. It suggests that the concentration of the monomer was the key factor to influence assembly structure. Addi- tionally, the acrylate conversion with different photoinitiators and nanostructure retention after polymerization were investigated. The research shows that the acrylate conversion of the monomer with Darocur2959 could reach up to 78% when irradiated by 30 mW/cm2 UV light of 365 nm for 30 min characterized by Real-time FT-IR as well as the sol-gel method. Meanwhile, the La and HII phase nanostructures were both retained after polymerization.

Liquid Crystal Motion Picture Projector

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Photoreaction Behaviors of Two Liquid Crystalline Cinnamoyl Compounds with Different Phase in Solution and Mesomorphic States

A novel nelnatic liquid crystal compound containing a cinnamoyl moiety （PCPC） and a typically cholesteric liquid crystal cholesteryl cinnamate （CC） were synthesized to explore the mechanism ofcinnamoyl compounds, and the chemical structures of photodimerization were confirmed by Fourier transform infrared spectroscopy and 1H nuclear magnetic resonance spectral analysis. The photoreaction behaviors of these two cinnamoyl compounds in mesomorphic state and solution were investigated, UV-Vis spectral analysis was used to analyze the photoproduct. The results show that the photochemistry of PCPC in nematic state involves both photodimerization and photoisomerization, while CC shows a complex reaction which can be divided into three parts, and this has enabled us to present new data and interpretations regarding the [2＋2] photocycloaddition reaction. Additionally, the results of UV-Vis spectral analysis in solutions strongly suggest that UV-Vis spectral analysis can be used to study the kinetic behaviors of cinnamoyl moiety photoreaction.

Development of hydrometallurgical process for indium recovery from waste liquid crystal display using Cyphos IL 101

The main goal of this study was to recover indium from the waste liquid crystal display(LCD)panel.In this context,an ionic liquid Cyphos IL 101 was explored.The extraction parameters such as equilibration period,acid concentration,chloride ion concentration,hydrogen ion concentration were examined on the extraction efficiency of Cyphos IL 101 towards In(III).Quantitative extraction of indium was found at 2.0 mol/L HCl using 0.005 mol/L Cyphos IL 101 and quantitative stripping with 1.0 mol/L H2SO4.Job’s method was used to determine the extracted species and R3R'PInCl4(R=C6H13;R′=C14H29)was proposed.Based on the observations on multi-metal studies,Cyphos IL 101 was further employed for the removal of indium,tin and copper from the leach liquors of waste LCDs.Optimized conditions were generated for the recovery of indium from waste LCDs.McCabe−Thiele diagram analysis,counter-current extraction and selective stripping were carried out to separate the metal ions,i.e.,indium,tin and copper.Two stages at O/A ratio of 1:3 were required for complete removal of tin from the feed and selective stripping of In and Sn was achieved using 0.1 mol/L H2SO4.A scheme for separating indium from the waste LCDs was proposed.