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.

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.

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.

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.

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.

Liquid Crystal Motion Picture Projector

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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.

Odd-even Effect on Liquid Crystalline Behavior for C_3-Cyclotriveratrylene(CTV) Derivatives Containing Alkoxies with Different Lengths as Peripheral Groups

A series of bowlic cyclotriveratrylenes（CTV） with peripheral groups with different lengths were synthesized.These compounds were investigated by diferential scanning calorimetry and hot stage coupled polarizing microscopy.Several CTV derivatives show thermotropic liquid crystalline properties.The experimental results of their thermotropic liquid crystalline behavior indicate that the clear points,the entropy changes of melting points,the crystallization temperatures,and their entropy changes all exhibited an evident odd-even effect except the melting points,which decreased monotonously with the increase of the length of the alkoxy groups.The parameter values of CTVs with even number carbon atoms were larger than those of CTVs with odd number.When the length of alkoxyl chains was even longer,a monotonous decrease occured.Nevertheless,in the case of the entropy changes of both melting points and crystallization temperatures,the effect was valid for all the six species,and therefore,the whole curves presented as a zig-zag form.

ORGANOMETALLIC FERROELECTRIC LIQUID CRYSTALS Ⅰ. LIQUID CRYSTAL PROPERTIES OF ORTHO—PALLADATED BINUCLEAR COMPLEXES OF AZINE, IMINE AND AZO DERIVATIVES

The mesomorphie properties of title complexes are investigated by means of DSC and polarizing microscopy. The mesophase temperature ranges of complexes are wider than that of corresponding organic ligands. The bridging groups of the complexes have profoand effects on the mesomorphic behavior, When the bridging groups are opticallhy active. the compleve show chiral smectic

INCOMPRESSIBLE LIMIT OF A COMPRESSIBLE LIQUID CRYSTALS SYSTEM

This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space R^N and a bounded domain of R^N with Dirichlet boundary conditions. Here we set the number of dimension N = 2 or 3.

Fixation for the helical structure of a glassy cholesteric liquid crystal reflective film

The planar texture of glassy cholesteric siloxane cyclic side-chain liquid crystals was fixed by quenching initially. Then the polymer network formed by the optically active polymerizable monomers imposed additional constraints on the motion of chain segments of the glassy liquid crystal and then further stabilized the molecule arrangement. A cholesteric liquid crystal film with stable optical properties was developed by this method.

MECHANICAL PERTURBATION INDUCED MOLECULAR ALIGNMENTS IN A SIDE-CHAIN LIQUID CRYSTALLINE POLYACETYLENE, POLY{10-[4-(4'-METHOXYPHENOXY-CARBOML)PHENOXYCARBONYL]-1-DECYNE}

A new liquid crystalline polyacetylene containing a phenyl benzoate mesogen (5) is synthesized,whose mesomorphic properties are found to be easily 'tunab1e' by simple mechanical perturbation. Thepolymerization of 10- [ 4 - (4' -methoxyphenoxycarbonyl )phenoxycarbonyl] - 1 -decyne (4 ) in itiated by theWCl_6-Ph_4Sn/dioxane complex yields polymer 5 with a M_w of 28400. The molecular structure of 5 ischaracterized by NMR, IR, and UV spectroscopy and its liquid crystalline behavior is investigated by DSC,POM, and XRD analysis. Upon mechanical perturbation, 5 exhibits unusual agitation-induced high-strengthdisclinations, shear-induced inversion walls, and solidification-induced banded textures. Such phenomenahave been observed in the main-chain liquid crystalline polymers with rigid backbones, but have seldom beenreported for the side-chain liquid crystalline polymers with flexible backbones, suggesting that the rigidpolyacetylene backbone of 5 plays a constructive role in inducing the novel molecular alignments.