Generation of orbital angular momentum hologram using a modified U-net

Orbital angular momentum(OAM)holography has become a promising technique in information encryption,data storage and opto-electronic computing,owing to the infinite topological charge of one single OAM mode and the orthogonality of different OAM modes.In this paper,we propose a novel OAM hologram generation method based on a densely connected U-net(DCU),where the densely connected convolution blocks(DCB)replace the convolution blocks of the U-net.Importantly,the reconstruction process of the OAM hologram is integrated into DCU as its output layer,so as to eliminate the requirement to prepare training data for the OAM hologram,which is required by conventional neural networks through an iterative algorithm.The experimental and simulation results show that the OAM hologram can rapidly be generated with the well-trained DCU,and the reconstructed image's quality from the generated OAM hologram is significantly improved in comparison with those from the Gerchberg-Saxton generation method,the Gerchberg-Saxton based generation method and the U-net method.In addition,a 10-bit OAM multiplexing hologram scheme is numerically demonstrated to have a high capacity with OAM hologram.

Multiphase cooperation for multilevel strain accommodation in a single-crystalline BiFeO3 thin film

The functionalities and diverse metastable phases of multiferroic BiFeO3(BFO)thin films depend on the misfit strain.Although mixed phase-induced strain relaxation in multiphase BFO thin films is well known,it is unclear whether a singlecrystalline BFO thin film can accommodate misfit strain without the involvement of its polymorphs.Thus,understanding the strain relaxation behavior is key to elucidating the lattice strain–property relationship.In this study,a correlative strain analysis based on dark-field inline electron holography(DIH)and quantitative scanning transmission electron microscopy(STEM)was performed to reveal the structural mechanism for strain accommodation of a single-crystalline BFO thin film.The nanoscale DIH strain analysis results indicated a random combination of multiple strain states that acted as a primary strain relief,forming irregularly strained nanodomains.The STEM-based bond length measurement of the corresponding strained nanodomains revealed a unique strain accommodation behavior achieved by a statistical combination of multiple modes of distorted structures on the unit-cell scale.The globally integrated strain for each nanodomain was estimated to be close to1.5%,irrespective of the nanoscale strain states,which was consistent with the fully strained BFO film on the SrTiO3 substrate.Density functional theory calculations suggested that strain accommodation by the combination of metastable phases was energetically favored compared to single-phase-mediated relaxation.This discovery allows a comprehensive understanding of strain accommodation behavior in ferroelectric oxide films,such as BFO,with various low-symmetry polymorphs.

Accelerated generation of holograms with ultra-low memory symmetrically high-compressed look-up table

Computer-generated holography technology has been widely applied,and as research in this field deepens,the demand for memory and computational power in small AR and VR devices continues to increase.This paper presents a hologram generation method,i.e.,a symmetrically high-compressed look-up table method,which can reduce memory usage by50%.In offline computing,half of the basic horizontal and vertical modulation factors are stored,halving the memory requirements without affecting inline speed.Currently,its potential extends to various holographic applications,including the production of optical diffraction elements.

Bessel–Gaussian beam-based orbital angular momentum holography

Orbital angular momentum(OAM), as a new degree of freedom, has recently been applied in holography technology.Due to the infinite helical mode index of OAM mode, a large number of holographic images can be reconstructed from an OAM-multiplexing hologram. However, the traditional design of an OAM hologram is constrained by the helical mode index of the selected OAM mode, for a larger helical mode index OAM mode has a bigger sampling distance, and the crosstalk is produced for different sampling distances for different OAM modes. In this paper, we present the design of the OAM hologram based on a Bessel–Gaussian beam, which is non-diffractive and has a self-healing property during its propagation. The Fourier transform of the Bessel–Gaussian beam is the perfect vortex mode that has the fixed ring radius for different OAM modes. The results of simulation and experiment have demonstrated the feasibility of the generation of the OAM hologram with the Bessel–Gaussian beam. The quality of the reconstructed holographic image is increased, and the security is enhanced. Additionally, the anti-interference property is improved owing to its self-healing property of the Bessel-OAM holography.

Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography

An electron vortex beam(EVB) carrying orbital angular momentum(OAM) plays a key role in a series of fundamental scientific researches, such as chiral energy-loss spectroscopy and magnetic dichroism spectroscopy. So far, almost all the experimentally created EVBs manifest isotropic doughnut intensity patterns. Here, based on the correlation between local divergence angle of electron beam and phase gradient along azimuthal direction, we show that free electrons can be tailored to EVBs with customizable intensity patterns independent of the carried OAM. As proof-of-concept, by using computer generated hologram and designing phase masks to shape the incident free electrons in the transmission electron microscope, three structured EVBs carrying identical OAM are tailored to exhibit completely different intensity patterns. Furthermore, through the modal decomposition, we quantitatively investigate their OAM spectral distributions and reveal that structured EVBs present a superposition of a series of different eigenstates induced by the locally varied geometries. These results not only generalize the concept of EVB, but also demonstrate an extra highly controllable degree of freedom for electron beam manipulation in addition to OAM.

Towards 6D Little String Theory of Particles

A model for particles based on preons in chiral, vector and tensor/graviton supermultiplets of unbroken global supersymmetry is engineered. The framework of the model is little string theory. Phenomenological predictions are discussed.

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.

4K-DMDNet:diffraction model-driven network for 4K computer-generated holography

Deep learning offers a novel opportunity to achieve both high-quality and high-speed computer-generated holography(CGH).Current data-driven deep learning algorithms face the challenge that the labeled training datasets limit the training performance and generalization.The model-driven deep learning introduces the diffraction model into the neural network.It eliminates the need for the labeled training dataset and has been extensively applied to hologram generation.However,the existing model-driven deep learning algorithms face the problem of insufficient constraints.In this study,we propose a model-driven neural network capable of high-fidelity 4K computer-generated hologram generation,called 4K Diffraction Model-driven Network(4K-DMDNet).The constraint of the reconstructed images in the frequency domain is strengthened.And a network structure that combines the residual method and sub-pixel convolution method is built,which effectively enhances the fitting ability of the network for inverse problems.The generalization of the 4K-DMDNet is demonstrated with binary,grayscale and 3D images.High-quality full-color optical reconstructions of the 4K holograms have been achieved at the wavelengths of 450 nm,520 nm,and 638 nm.

Time-sequential color code division multiplexing holographic display with metasurface

Color metasurface holograms are powerful and versatile platforms for modulating the amplitude,phase,polarization,and other properties of light at multiple operating wavelengths.However,the current color metasurface holography can only realize static manipulation.In this study,we propose and demonstrate a multiplexing metasurface technique combined with multiwavelength code-division multiplexing(CDM)to realize dynamic manipulation.Multicolor code references are utilized to record information within a single metasurface and increase the information capacity and security for anticracks.A total of 48 monochrome images consisting of pure color characters and multilevel color video frames were reconstructed in dual polarization channels of the birefringent metasurface to exhibit high information density,and a video was displayed via sequential illumination of the corresponding code patterns to verify the ability of dynamic manipulation.Our approach demonstrates significant application potential in optical data storage,optical encryption,multiwavelengthversatile diffractive optical elements,and stimulated emission depletion microscopy.

Planar peristrophic multiplexing metasurfaces

As a promising counterpart of two-dimensional metamaterials,metasurfaces enable to arbitrarily control the wavefront of light at subwavelength scale and hold promise for planar holography and applicable multiplexing devices.Nevertheless,the degrees of freedom(DoF)to orthogonally multiplex data have been almost exhausted.Compared with state-of-theart methods that extensively employ the orthogonal basis such as wavelength,polarization or orbital angular momentum,we propose an unprecedented method of peristrophic multiplexing by combining the spatial frequency orthogonality with the subwavelength detour phase principle.The orthogonal relationship between the spatial frequency of incident light and the locally shifted building blocks of metasurfaces can be regarded as an additional DoF.We experimentally demonstrate the viability of the multiplexed holograms.Moreover,this newly-explored orthogonality is compatible with conventional DoFs.Our findings will contribute to the development of multiplexing metasurfaces and provide a novel solution to nanophotonics,such as large-capacity chip-scale devices and highly integrated communication.

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.

Direct field-to-pattern monolithic design of holographic metasurface via residual encoderdecoder convolutional neural network

Complex-amplitude holographic metasurfaces(CAHMs)with the flexibility in modulating phase and amplitude profiles have been used to manipulate the propagation of wavefront with an unprecedented level,leading to higher image-reconstruction quality compared with their natural counterparts.However,prevailing design methods of CAHMs are based on Huygens-Fresnel theory,meta-atom optimization,numerical simulation and experimental verification,which results in a consumption of computing resources.Here,we applied residual encoder-decoder convolutional neural network to directly map the electric field distributions and input images for monolithic metasurface design.A pretrained network is firstly trained by the electric field distributions calculated by diffraction theory,which is subsequently migrated as transfer learning framework to map the simulated electric field distributions and input images.The training results show that the normalized mean pixel error is about 3%on dataset.As verification,the metasurface prototypes are fabricated,simulated and measured.The reconstructed electric field of reverse-engineered metasurface exhibits high similarity to the target electric field,which demonstrates the effectiveness of our design.Encouragingly,this work provides a monolithic field-to-pattern design method for CAHMs,which paves a new route for the direct reconstruction of metasurfaces.

Deep learning assisted variational Hilbert quantitative phase imaging

We propose a high-accuracy artifacts-free single-frame digital holographic phase demodulation scheme for relatively lowcarrier frequency holograms-deep learning assisted variational Hilbert quantitative phase imaging(DL-VHQPI).The method,incorporating a conventional deep neural network into a complete physical model utilizing the idea of residual compensation,reliably and robustly recovers the quantitative phase information of the test objects.It can significantly alleviate spectrum-overlapping-caused phase artifacts under the slightly off-axis digital holographic system.Compared to the conventional end-to-end networks(without a physical model),the proposed method can reduce the dataset size dramatically while maintaining the imaging quality and model generalization.The DL-VHQPI is quantitatively studied by numerical simulation.The live-cell experiment is designed to demonstrate the method's practicality in biological research.The proposed idea of the deep learning-assisted physical model might be extended to diverse computational imaging techniques.

Multi-channel generation of vortex beams with controllable polarization states and orbital angular momentum

Optical vortices with tunable polarization states and topological charges are widely investigated in various physical systems and practical devices for high-capacity optical communication.However,this kind of structured light beams is usually generated using several polarization and spatial phase devices,which decreases the configurability of optical systems.Here,we have designed a kind of polarized optical multi-vortices generator based on the Stokes-Mueller formalism and cross-phase modulation.In our scheme,multi-channel generation of polarized vortex beams can be realized through a single optical element and a single-input Gaussian beam.The polarization states and orbital angular momentum of the generated light beams are all-optically controllable.Furthermore,the proposed polarized optical multi-vortices generator has also been demonstrated experimentally through one-step holographic recording in an azobenzene liquid-crystalline film and the experimental results agree with theoretical analysis.

Extension of sound field reconstruction based on element radiation superposition method in a sparsity framework

Nearfield acoustic holography(NAH)is a powerful tool for realizing source identification and sound field reconstruction.The wave superposition(WS)-based NAH is appropriate for the spatially extended sources and does not require the complex numerical integrals.Equivalent source method(ESM),as a classical WS approach,is widely used due to its simplicity and efficiency.In the ESM,a virtual source surface is introduced,on which the virtual point sources are taken as the assumed sources,and an optimal retreat distance needs to be considered.A newly proposed WS-based approach,the element radiation superposition method(ERSM),uses piston surface source as the assumed source with no need to choose a virtual source surface.To satisfy the application conditions of piston pressure formula,the sizes of pistons are assumed to be as small as possible,which results in a large number of pistons and sampling points.In this paper,transfer matrix modes(TMMs),which are composed of the singular vectors of the vibro-acoustic transfer matrix,are used as the sparse basis of piston normal velocities.Then,the compressive ERSM based on TMMs is proposed.Compared with the conventional ERSM,the proposed method maintains a good pressure reconstruction when the number of sampling points and pistons are both reduced.Besides,the proposed method is compared with the compressive ESM in a mathematical sense.Both simulations and experiments for a rectangular plate demonstrate the advantage of the proposed method over the existing methods.

Experimental study on the desulfurization and evaporation characteristics of Ca(OH)_(2) droplets

The experiments were conducted to focus on the desulfurization and evaporation characteristics of lime slurry droplets at 298-383 K. We designed an evaporation-reaction chamber with quartz glass windows.The monodisperse slurry droplet stream was injected into the evaporation reaction chamber, and the inlet gas components(air, air + SO_(2)) were introduced into the chamber. We applied the magnified digital in-line holography to measure the droplet parameters and calculated the evaporation rate. The effects of temperature, droplet concentration, and SO_(2) concentration on the evaporation rate of Ca(OH)_(2) droplets were discussed. Moreover, the Ca(OH)_(2) droplets under different experimental conditions were sampled,and the droplets were observed and analyzed using an off-line microscope. The evaporation rate of the Ca(OH)_(2) droplet increased at first, and then decreased during the falling process, and remained constant at last. The average evaporation rate of the Ca(OH)_(2) droplets increased significantly with the temperature increasing.

用全息观点看农业生态经济系统

用全息观点看农业生态经济系统曹志平（北京农业大学生物学院，１０００９４）ＡｎａｌｙｓｉｓｏｆＡｇｒｏ－ＥｃｏｌｏｍｉｃＳｙｓｔｅｍＦｒｏｍｔｈｅＶｉｅｗｐｏｉｎｔｓｏｆＨｏｌｏｇｒａｐｂｙ．￥ＣａｏＺｈｉｐｉｎｇ（ＣｏｌｌｅｇｅｏｆＢｉｏｌｏｇｙ，Ｂ...

Method for eliminating zero-order image in digital holography

For eliminating the zero-order image in digital holography, a new method using the differential of the hologram intensity instead of the hologram itself for numerical reconstruction is proposed. This method is based on digital image processing. By analyzing the spatial spectrum of the off-axis digital hologram, it theoretically proves that the zero-order image can be effectively eliminated by differential before reconstruction. Then, the detected hologram is processed in the program with differential and reconstruction. Both the theoretical analysis and digital reconstruction results show that it can effectively eliminate the large bright spot in the center of the reconstructed image caused by the zero-order image, improve the image quality significantly, and render a better contrast of the reconstructed image. This method is very simple and convenient due to no superfluous optical elements and requiring only one time record.

Size-Dependent Oxidation-Induced Phase Engineering for MOFs Derivatives Via Spatial Confinement Strategy Toward Enhanced Microwave Absorption

Precisely reducing the size of metal-organic frameworks(MOFs)derivatives is an effective strategy to manipulate their phase engineering owing to size-dependent oxidation;however,the underlying relationship between the size of derivatives and phase engineering has not been clarified so far.Herein,a spatial confined growth strategy is proposed to encapsulate small-size MOFs derivatives into hollow carbon nanocages.It realizes that the hollow cavity shows a significant spatial confinement effect on the size of confined MOFs crystals and subsequently affects the dielectric polarization due to the phase hybridization with tunable coherent interfaces and heterojunctions owing to size-dependent oxidation motion,yielding to satisfied microwave attenuation with an optimal reflection loss of-50.6 d B and effective bandwidth of 6.6 GHz.Meanwhile,the effect of phase hybridization on dielectric polarization is deeply visualized,and the simulated calculation and electron holograms demonstrate that dielectric polarization is shown to be dominant dissipation mechanism in determining microwave absorption.This spatial confined growth strategy provides a versatile methodology for manipulating the size of MOFs derivatives and the understanding of size-dependent oxidation-induced phase hybridization offers a precise inspiration in optimizing dielectric polarization and microwave attenuation in theory.

Self‑Assembly MXene‑rGO/CoNi Film with Massive Continuous Heterointerfaces and Enhanced Magnetic Coupling for Superior Microwave Absorber

MXene, as a rising star of two-dimensional(2 D) materials, has been widely applied in fields of microwave absorption and electromagnetic shielding to cope with the arrival of the 5 G era. However, challenges arise due to the excessively high permittivity and the difficulty of surface modification of few-layered MXenes severely, which infect the microwave absorption performance. Herein, for the first time, a carefully designed and optimized electrostatic selfassembly strategy to fabricate magnetized MXene-r GO/Co Ni film was reported. Inside the synthesized composite film, r GO nanosheets decorated with highly dispersed Co Ni nanoparticles are interclacted into MXene layers, which effectively suppresses the originally self-restacked of MXene nanosheets, resulting in a reduction of high permittivity. In addition, owing to the strong magnetic coupling between the magnetic Fe Co alloy nanoparticles on the r GO substrate, the entire MXener GO/Co Ni film exhibits a strong magnetic loss capability. Moreover, the local dielectric polarized fields exist at the continuous heterointerfaces between 2 D MXene and r GO further improve the capacity of microwave loss. Hence, the synthesized composite film exhibits excellent microwave absorption property with a maximum reflection loss value of-54.1 d B at 13.28 GHz. The electromagnetic synergy strategy is expected to guide future exploration of high-efficiency MXene-based microwave absorption materials.