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GENERAL

Research on pulse transmission dynamics in optical fiber based on intelligent algorithms
LI Jun, SU Jin, HAN Xiaoxiang, ZHU Weijie, YANG Ruixia, ZHANG Haiyang, YAN Xiang’an, ZHANG Yunjie, WANG Feiran
2025, 74 (6): 060201. doi: 10.7498/aps.74.20241473
Abstract +
Nonlinear Schrödinger equation (NLSE) has important applications in quantum mechanics, nonlinear optics, plasma physics, condensed matter physics, optical fiber communication and laser system design, and its accurate solution is very important for understanding complex physical phenomena. Here, the traditional finite difference method (FDM), the split-step Fourier (SSF) method and the physics-informed neural network (PINN) method are studied, aiming to analyze in depth the solving mechanisms of various algorithms, and then realize the efficient and accurate solution of complex NLSE in optical fiber. Initially, the steps, process and results of PINN in solving the NLSE for pulse under the condition of short-distance transmission are described, and the errors of these methods are quantitatively evaluated by comparing them with the errors of PINN, FDM and SSF. On this basis, the key factors affecting the accuracy of NLSE solution for pulse under long-distance transmission are further discussed. Then, the effects of different networks, activation functions, hidden layers and the number of neurons in PINN on the accuracy of NLSE solution are discussed. It is found that selecting a suitable combination of activation functions and network types can significantly reduce the error, and the combination of FNN and tanh activation functions is particularly good. The effectiveness of ensemble learning strategy is also verified, that is, by combining the advantages of traditional numerical methods and PINN, the accuracy of NLSE solution is improved. Finally, the evolution characteristics of Airy pulse with different chirps in fiber and the solution of vector NLSE corresponding to polarization-maintaining fiber are studied by using the above algorithm. This study explores the solving mechanisms of FDM, SSF and PINN in complex NLSE, compares and analyzes the error characteristics of those methods in various transmission scenarios, proposes and verifies the ensemble learning strategy, thus providing a solid theoretical basis for studying pulse transmission dynamics and data-driven simulation.

GENERAL

Cluster behavior and spontaneous velocity alignment of active Brownian particles with attractive interactions
CHEN Jianli, LI Jiajian, AI Baoquan
2025, 74 (6): 060501. doi: 10.7498/aps.74.20241746
Abstract +
Spontaneous velocity alignment can occur in active particle systems. As a fundamental inter-particle interaction, the attractive interaction is shown to significantly affect the collective behavior of active particles. However, the mechanisms by which attractive interactions induce and affect velocity alignment are still unclear. To solve this problem, we conduct numerical simulations by using the stochastic Euler method to investigate cluster behavior and spontaneous global velocity alignment in active particle systems with attractive interactions. The local area fraction of particles and its corresponding probability distribution function are computed to capture the system’s cluster behavior. The global velocity alignment order parameter and the polar average parameter are also calculated to characterize the particle velocity directions. Based on whether motion-induced phase separation and crystallization can be achieved, the system is categorized into low, medium, and high packing fraction regimes, and the cluster behavior and velocity alignment within each regime are systematically investigated.Spontaneous velocity alignment results from the coupling of self-propulsion and attractive interactions. During the persistent time, feedback regulation involving particle velocities, relative positions, and interaction forces operates simultaneously among neighboring particles. This process leads to the alignment of particle velocities with those of their neighbors, ultimately achieving large-scale alignment. The closer the particles’ arrangement, the more conducive it is to the coupling of self-propulsion and spatial interactions, thus promoting large-scale spontaneous velocity alignment. The competition between these two effects governs the formation and structure of clusters, ultimately affecting global velocity alignment.At low and medium packing fractions, when the attractive interaction dominates and self-propulsion is negligible, particles attract each other to form discrete banded clusters due to the strong attraction and limited range of interaction. Over time, these clusters connect to form a network-like cluster. Small differences in particle velocity are amplified by the banded structure, hindering velocity alignment. In the systems with low packing fractions, a thin network-like cluster forms, whereas in systems with medium packing fractions, a thicker network-like cluster forms, leading to lower velocity alignment in the former. As self-propulsion becomes more dominant, the network structure loosens, causing the particle bands to break and reconnect until a more stable block-like cluster structure is formed. The system transitions from a network-like cluster to a block-like cluster, with particles becoming closely packed, resulting in global velocity alignment. When self-propulsion dominates and attraction is negligible, particle motion is mainly driven by self-propulsion, resulting in sparse particle distribution or unstable clusters, leading to disordered velocity. Thus, as self-propulsion competes with attractive interactions and becomes dominant, the global velocity alignment increases from low values to a higher plateau and then decreases, approaching zero.At high packing fractions, the initial distribution of particles is dense. Even when the attractive interaction dominates and self-propulsion is negligible, the system forms a block-like cluster, leading to global velocity alignment. As self-propulsion becomes dominant, the instability of the clusters partially hinders spontaneous velocity alignment. Nevertheless, the particles remain densely packed, resulting in local velocity alignment. Thus, as self-propulsion transitions from weak to dominant in competition with attractive interactions, global velocity alignment first plateaus at a higher value, then decreases, but remains above 0.5.It is important to note that the spontaneous velocity alignment discussed here exhibits a finite size effect. In experimental setups and applications involving active particles, smaller systems are usually studied. By modulating the balance between self-propulsion and attractive interactions in these systems, a broader range of spontaneous velocity alignment can be achieved, which may even lead to global velocity alignment.

GENERAL

Quantum dynamics of machine learning
WANG Peng, MAIMAITINIYAZI Maimaitiabudula
2025, 74 (6): 060701. doi: 10.7498/aps.74.20240999
Abstract +
In order to solve the current lack of rigorous theoretical models in the machine learning process, in this paper the iterative motion process of machine learning is modeled by using quantum dynamic method based on the principles of first-principles thinking. This approach treats the iterative evolution of algorithms as a physical motion process, defines a generalized objective function in the parameter space of machine learning algorithms, and regards the iterative process of machine learning as the process of seeking the optimal value of this generalized objective function. In physical terms, this process corresponds to the system reaching its ground energy state. Since the dynamic equation of a quantum system is the Schrödinger equation, we can obtain the quantum dynamic equation that describes the iterative process of machine learning by treating the generalized objective function as the potential energy term in the Schrödinger equation. Therefore, machine learning is the process of seeking the ground energy state of the quantum system constrained by a generalized objective function. The quantum dynamic equation for machine learning transforms the iterative process into a time-dependent partial differential equation for precise mathematical representation, enabling the use of physical and mathematical theories to study the iterative process of machine learning. This provides theoretical support for implementing the iterative process of machine learning by using quantum computers. In order to further explain the iterative process of machine learning on classical computers by using quantum dynamic equation, the Wick rotation is used to transform the quantum dynamic equation into a thermodynamic equation, demonstrating the convergence of the time evolution process in machine learning. The system will be transformed into the ground energy state as time approaches infinity. Taylor expansion is used to approximate the generalized objective function, which has no analytical expression in the parameter space. Under the zero-order Taylor approximation of the generalized objective function, the quantum dynamic equation and thermodynamic equation for machine learning degrade into the free-particle equation and diffusion equation, respectively. This result indicates that the most basic dynamic processes during the iteration of machine learning on quantum computers and classical computers are wave packet dispersion and wave packet diffusion, respectively, thereby explaining, from a dynamic perspective, the basic principles of diffusion models that have been successfully utilized in the generative neural networks in recent years. Diffusion models indirectly realize the thermal diffusion process in the parameter space by adding Gaussian noise to and removing Gaussian noise from the image, thereby optimizing the generalized objective function in the parameter space. The diffusion process is the dynamic process in the zero-order approximation of the generalized objective function. Meanwhile, we also use the thermodynamic equation of machine learning to derive the Softmax function and Sigmoid function, which are commonly used in artificial intelligence. These results show that the quantum dynamic method is an effective theoretical approach to studying the iterative process of machine learning, which provides a rigorous mathematical and physical model for studying the iterative process of machine learning on both quantum computers and classical computers.

NUCLEAR PHYSICS

Consistency analysis and nuclear data validation for two series of beryllium reflector critical benchmark experiments
CHEN Shengli, WANG Tianxiang
2025, 74 (6): 062801. doi: 10.7498/aps.74.20241685
Abstract +
Beryllium metal and beryllium oxide are important nuclear materials, with neutron-induced nuclear reaction data on beryllium playing a crucial role in nuclear energy research and development. Macroscopic validation is an essential step in the nuclear data evaluation process, providing a means to assess the reliability and accuracy of such data. Critical benchmark experiments serve as the most important references for this validation. However, discrepancies have been observed in two closely related series of beryllium-reflector fast-spectrum critical benchmark experiments, HMF-058 and HMF-066, which are widely used in current nuclear data validation. A previous systematic study indicates that these two series of experiments reache contradictory conclusions in validating the neutron-induced nuclear reaction data of beryllium, creating ambiguity in improving beryllium nuclear data. As a result, the total of 14 experiments in these two series cannot currently support high-accuracy validation of nuclear data. Although most researches on nuclear data validation and adjustment mainly focus on cross sections, the angular distribution of emitted neutrons is a key factor in reactor physics calculations. In this work, we address these inconsistencies by improving the secondary angular distributions of the (n, n) and (n, 2n) reactions of beryllium, thereby making the theoretical calculations (C) and experimental results (E) of these two series more consistent, and reducing the cumulative χ2 value from 7.58 using the ENDF/B-VII.1 evaluation to 4.52. All calculations based on the improved nuclear data agree with the experimental measurements within 1σ experimental uncertainty. With these enhancements, the consistency between the HMF-058 and HMF-066 series cannot be rejected within the 1σ experimental uncertainty. Based on the latest comprehensive evaluation of uranium nuclear data, this consistency is slightly improved, and the cumulative χ2 value decreases to 4.36 once again. Despite these advances, systematic differences in the expected values of C/E between the two series still exist. The C/E values of the HMF-066 series are generally 230–330 pcm lower than those of the HMF-058 series, comparable to their experimental uncertainties of 200–400 pcm. Therefore, drawing a definitive conclusion about this systematic difference remains challenging. If the current improvement of differential nuclear data based on experimental data of 9Be is accurate, then the HMF-058 series experiments seem to be more reliable than the HMF-066 series. Ultimately, to achieve this goal, either reducing experimental uncertainty or designing and executing higher-precision integral experiments is required.

ATOMIC AND MOLECULAR PHYSICS

Dissociation mechanism of ethane dication via three-body fragmentation
ZHANG Ziqi, YAN Shuncheng, TAO Chenyu, YU Xuan, ZHANG Shaofeng, MA Xinwen
2025, 74 (6): 063401. doi: 10.7498/aps.74.20250008
Abstract +
Molecular ions are widely distributed in the ionosphere of planetary atmospheres, and their fragmentations can generate different ions and neutral fragments. Studying the kinetic energy distribution and generation mechanism of the final products is helpful in understanding fundamental phenomena in astrophysics and plasma physics. In particular, ethane is an important molecule found in Titan and comet, and its fragmentation may be involved in the generation of complex hydrocarbons, as well as the atmospheric escape processes on Titan.In this paper, the experiment on ethane fragmentation by electron impact is carried out, focusing on the three-body fragmentation channel from $ {{\text{C}}_2}{\text{H}}_6^{2 + } $ to $ {\text{CH}}_3^ + /{\text{CH}}_2^ + /{\text{H}} $. The three-dimensional momenta of $ {\text{CH}}_3^ + $ and $ {\text{CH}}_2^ + $ ions are measured, and then the momentum of the H atom is reconstructed using momentum conservation law. Based on these analyses, the kinetic energy release (KER) spectrum and the fragmentation mechanisms are investigated.The time-of-flight (TOF) coincidence map of the ions shows two channels: channel (1) that represents the two-body dissociation generating $ {\text{CH}}_3^ + $/$ {\text{CH}}_3^ + $, and channel (2) that refers to the three-body dissociation generating $ {\text{CH}}_3^ + /{\text{CH}}_2^ + /{\text{H}} $. It is found that the neutral H from channel (2) has a wide kinetic energy distribution, ranging from 0 eV to more than 10 eV. This feature indicates that the dissociation of the C－H bond is from multiple electronic states. Since the escape threshold of H in Titan’s ionosphere is 0.02 eV, the vast majority of the H atoms produced in channel (2) can escape into outer space. In addition, the kinetic energy sum of $ {\text{CH}}_3^ + $ and $ {\text{CH}}_2^ + $ in channel (2) is found to be similar to the KER of channel (1), indicating that the C－H dissociation presents limited influence on the energy sum of the CH2+ and $ {\text{CH}}_3^ + $.The corresponding fragmentation mechanism of channel (2) is also analyzed in this work. the overall KER spectrum is divided into three parts: 0–6 eV, 6–9 eV, and 9–11 eV, and the respective Dalitz plots and Newton diagrams are reconstructed under different KER conditions. In all Dalitz plots, there are a bright spot representing the concerted dissociation and a horizontal belt representing the sequential dissociation. The concerted dissociation is considered as the main mechanism, while the sequential dissociation plays a secondary role.The bright spot in the Dalitz plot shifts from the center to the left as the KER increases. This feature arises from the fact that the $ {\text{CH}}_2^ + $ lies between the H and the $ {\text{CH}}_3^ + $ in the concerted dissociation, and it feels the recoil both from H and from $ {\text{CH}}_3^ + $. Considering that the Coulomb potential from $ {\text{CH}}_3^ + $ is constant, the increase of the C－H dissociation energy will reduce the $ {\text{CH}}_2^ + $ kinetic energy. The belt in the Dalitz indicates that the sequential dissociation is a two-step process, with the first step being the dissociation of $ {{\text{C}}_2}{\text{H}}_6^{2 + } $ to generate H and metastable $ {{\text{C}}_2}{\text{H}}_5^{2 + } $, and the second step being the fragmentation of $ {{\text{C}}_2}{\text{H}}_5^{2 + } $ into $ {\text{CH}}_3^ + $ and $ {\text{CH}}_2^ + $.The Newton diagrams under different KER conditions are also reconstructed to give further evidence of the sequential dissociation from the metastable $ {{\text{C}}_2}{\text{H}}_5^{2 + } $, rather than from the metastable $ {\text{CH}}_3^ + $ or $ {\text{CH}}_4^ + $. In fact, for the former case, the center positions of the two half circles in the Newton diagram are correct. Oppositely, for the latter two cases, the center positions notably deviate from the expected values. This means the sequential dissociation from $ {{\text{C}}_2}{\text{H}}_5^{2 + } $ is dominant, which agrees excellently with the conclusion from the Dalitz plots.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

Generation and independent-manipulation of multi-channel high-capacity perfect vector vortex beams based on geometric metasurfaces
ZHANG Shenglan, TIAN Ximin, XU Junwei, XU Yaning, LI Liang, LIU Jielong
2025, 74 (6): 064201. doi: 10.7498/aps.74.20241725
Abstract +
Perfect vector vortex beams (PVVBs), which are characterized by spiral phase, donut-shaped intensity profile and inhomogeneous polarization of a light beam carrying spin angular momentum (SAM) and orbital angular momentum (OAM), have a constant bright ring radius and ring width which are unaffected by the changes of their carrying topological charge (TC), thus making them highly valuable in many optical fields. Metasurfaces, as planar optical devices composed of subwavelength nanostructures, can precisely control the phase, polarization, and amplitude of electromagnetic waves, providing a revolutionary solution for integrated vector field manipulation devices. However, existing metasurfaces still encounter significant challenges in generating high-capacity, polarization- and orbital angular momentum-independent controlled perfect vector vortex beams. In order to solve this problem, in this work a spin-multiplexing scheme based on pure geometric phase modulation on a metasurface platform is used to achieve high-capacity polarization- and OAM-independent controlled PVVBs. The metasurfaces with a combined phase profile of a spiral phase plate, an axicon, and a focusing (Fourier) lens are spatially encoded by rectangular Ge2Sb2Se4Te1 (GSST) nanopillar with various orientations on a CaF2 square substrate. When illuminated by circularly polarized light with opposite chirality, the metasurfaces can generate various perfect vector vortex beams (PVBs) with arbitrary topological charges. For linearly polarized incidence, the metasurface is employed to induce PVVBs by coherently superposing PVBs with spin-opposite OAM modes. The polarization states and polarization orders of the generated PVVBs can be flexibly customized by controlling the initial phase difference, amplitude ratio, and topological charges of the two orthogonal PVB components. Notably, through precisely designing the metasurface’s phase distribution and the propagation path of the generated beams, the space and polarization multiplexing can be realized in a compact manner of spatial PVVB arrays, significantly increasing both information channels and dimensions for the development of vortex communication capacity. With these findings, we demonstrate an innovative optical information encryption scheme by using a single metasurface to encode personalized polarization states and OAM in parallel channels embedded within multiple PVVBs. This work aims to establish an ultra-compact, robust platform for generating multi-channel high-capacity polarization- and OAM-independent controlled PVVBs in the mid-infrared range, and promote their applications in optical encryption, particle manipulation, and quantum optics.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

Vortex key decoding based on logarithmic coordinate transformation
LI Lang, ZHOU Shiyun, GAO Chunqing, FU Shiyao
2025, 74 (6): 064202. doi: 10.7498/aps.74.20241612
Abstract +
Orbital angular momentum (OAM), as a novel high-dimensional degree of freedom, shows great potential applications in optical communication in improving system channel capacity and solving the problem of scarce communication resources. However, the effective recognition and detection of OAM modes are the core challenges for achieving efficient communication in such systems. In this work, an OAM decoding system consisting of a designed coordinate transformation device, a phase corrector, and a Fourier transform lens is presented based on log-polar coordinate transformation. The coordinate transformation device fabricated by liquid crystal polymer is utilized to map the incident vortex beam from polar coordinates into Cartesian coordinates, followed by the phase corrector to compensate for phase distortions into a collimated beam. Finally, the Fourier transform lens is used to separate the OAM modes at different space positions in its rear focal plane. The performance of the system is numerically evaluated in several ablation studies, and the influence of various grating parameters on beam separation efficiency is analyzed. Experimentally, the system successfully achieves the decoding of OAM modes ranging from –35 to +31 orders. Furthermore, a free-space optical communication demonstration system is constructed based on this OAM decoding system. By introducing specifically designed decoding rules, the system effectively mitigates the adjacent mode crosstalk inherent in logarithmic polar coordinate transformation and successfully transmitted 748934 symbols without errors. These favorable results highlight the capabilities of the proposed OAM-based optical communication system and provide valuable insights for developing future high-capacity optical communication networks.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

Optical properties of ensemble of complex externally mixed aerosol particles under different relative humidity conditions
WANG Mingjun, YU Jihua, BAI Liangliang, ZHOU Yiming
2025, 74 (6): 064203. doi: 10.7498/aps.74.20241140
Abstract +
Microphysical quantities (particle shape, composition, size, density, complex refractive index, size distribution model, aspect ratio, hygroscopic parameter, etc.) of the ensemble of complex externally mixed aerosol particles vary greatly in humid environments (sea fog, water mist, haze, etc.). These microphysical quantities directly affect the transmission and scattering characteristics of laser. The optical properties (extinction coefficient, absorption coefficient, backscattering coefficient, phase function, etc.) of the ensemble of complex externally mixed aerosol particles directly determine the propagation properties of laser signals in the atmosphere, as well as the intensity and shape of echo signals. Therefore, studying the optical properties of the ensemble of complex externally mixed aerosol particles in humid environments is of significant importance for engineering applications such as autonomous driving, mapping, and remote sensing detection.Based on the various possibilities of aerosol particles existing in humid environments, the physicochemical properties of aerosol particles, including their shapes (sphere, oblate spheroid, prolate spheroid, and irregular), size distributions, complex refractive indices, densities, aspect ratios, their distribution models, and hygroscopicity parameters, are all taken into consideration in this work. Therefore, a scattering model of the ensemble of complex externally mixed aerosol particles is presented. Based on the presented complex aerosol scattering model, the influences of different mixing ratios (MR), and relative humidity (RH) on the optical properties, such as extinction coefficient, single scattering albedo, scattering phase matrix, asymmetry factor, backscattering coefficient, lidar ratio, and linear depolarization ratio, are numerically analyzed at typical incident laser wavelengths (0.78, 0.905, 1.064, 1.55, and 2.1 μm).In order to verify and demonstrate the rationality of the complex aerosol scattering model presented in this work, this model is compared with the scattering model of maritime pollution aerosol in optical properties of aerosols and clouds (OPAC). The results show that the optical properties of these two different aerosol scattering models vary similarly with wavelengths, although differences exist, but they are relatively small. Therefore, the influences of MR on the optical properties of the ensemble of complex internally mixed aerosol particles are analyzed. The influences of RH on the optical properties of the ensemble of complex internally mixed aerosol particles are also analyzed. The numerical results indicate that the extinction coefficient and phase function P11 exhibit strong sensitivity to both the MR and RH. As RH increases, the extinction coefficient and the forward scattering of P11 also increase. Compared with MR, single scattering albedo and asymmetry factor are more sensitive to RH. Significant differences in the sensitivity to RH and wavelength between linear and circular polarization properties are observed at different scattering angles. The backscattering coefficient is found to be inversely proportional to the lidar ratio, and the backscattering coefficient and the lidar ratio are both sensitive to MR and RH. It is observed that RH has a more pronounced effect on the linear depolarization ratio, while the influence of MR is weaker. The complex scattering model presented in this work further expands the study of aerosol optical properties and provides theoretical support for studying engineering applications involving lasers in different RHs environments. It is worth emphasizing that this work only focuses on external mixing. Therefore, the optical properties of the ensemble of complex internally mixed aerosol particles under different RHs will be discussed in the future.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

In-situ reconstruction of step phase based on orthogonal holograms
HAO Aihua, HUANG Jingyan, ZHANG Shiji, WANG Zhijun, WANG Xiaolong
2025, 74 (6): 064204. doi: 10.7498/aps.74.20241629
Abstract +
Filtering technology is the key to accurate phase reconstruction in off-axis digital holography. Due to the limitations of resolution of charge coupled device (CCD) and off-axis digital holography itself, the filtering process of the step-phase objects is often accompanied by spectral loss, spectral aliasing and spectral leakage when non-integer periods are intercepted. At present, much research has been done on adaptive filtering in the frequency domain, but the above problems have not been fundamentally solved. In this work, the influence of spatial filtering on the accuracy of step-phase reconstruction is first analyzed theoretically. The analysis shows that even if the size of the filter window is equal to the sampling frequency of the CCD, the reconstructed object cannot retain all the spectral information of the object due to the limitation of the resolution power of the CCD itself. In addition, in the off-axis holographic recording process, considering the interference of zero-order terms and conjugate terms, the actual filter width is usually only 1/24 of the sampling frequency of the CCD, at which the average absolute error of the step is about 10% of the height of the step, the oscillation is relatively severe, and after further smoothing filtering, the details of the object are lost, the edge is blurred, and the tiny structure cannot be resolved. Second, according to the definition of discrete Fourier transform, the one-dimensional Fourier transform of a two-dimensional function integrates only in one direction, while the other dimension remains unchanged. When performing one-dimensional Fourier transform along the direction perpendicular to the holographic interference fringes and performing one-dimensional full-spectrum filtering, the distribution of reconstructed object light waves in the direction parallel to the fringes follows the original distribution, is not affected by the filtering, and has high accuracy. Therefore, by combining the reconstructed light waves obtained from one-dimensional full-spectrum filtering of two orthogonal off-axis holograms, an accurate two-dimensional differential phase can be obtained, which provides a basic guarantee for the accurate phase unwinding of Poisson equation. On this basis, a spectral lossless phase reconstruction algorithm based on orthogonal holography and optical experiment method is proposed. In this paper, the ideal sample simulation, including irregular shapes such as gear, circle, V, diamond, drop, hexagon and pentagram, and the corresponding experiment based on USFA1951 standard plate and silicon wafer are carried out. The AFM-calibrated average step heights of the standard plate and the silicon wafer are 100 nm and 240 nm, respectively. The experimental results show that compared with the currently widely used adaptive filter phase reconstruction, the proposed method naturally avoids spectrum loss, spectrum aliasing and spectrum leakage caused by filtering, the reconstruction accuracy is high, and it is suitable for three-dimensional contour reconstruction of any shape step object, which provides a practical way for reconstructing the high-precision phase of off-axis holography.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

Orbital angular momentum multiplexing three-dimensional encrypted hologram
FANG Guoquan, LIN Han, WANG Siyue, PENG Pu, FANG Zheyu
2025, 74 (6): 064205. doi: 10.7498/aps.74.20241444
Abstract +
After decades of development, holography has evolved into a sophisticated optical technology for information display. Traditional holographic techniques, which rely solely on the wavelength and polarization of light as information carriers, are limited in both security and capacity of information. The introduction of orbital angular momentum (OAM) as an additional optical dimension into holography effectively addresses these challenges. In order to maintain the OAM mode characteristics of the original image, spatial discrete sampling must be performed first. The sampled image undergoes Fourier transform to generate a discrete hologram. An OAM-selective hologram is then constructed by multiplying the discrete hologram with a spiral phase factor. By superimposing multiple selective holograms with varying topological charges, an OAM-multiplexing hologram is generated.Using this approach, computer simulations of OAM-based holography demonstrate the encryption of multiple two-dimensional images with different topological charges ($ {l}_{i} $) into an OAM-multiplexing hologram for storage. Decryption is achieved by illuminating the multiplexing hologram with a reproduction beam of a specific topological charge. When the condition ($ l'_{i}+{l}_{i}= 0 $) is satisfied, the original image associated with the corresponding topological charge is successfully reproduced.Furthermore, a three-dimensional object, such as a rose in the article, can be decomposed into multiple two-dimensional planes by using a layering method. Holograms for each layer are generated based on their spatial positions and a custom function f that assigns topological charges ($ {l}_{j} $). These holograms are stored in a phase array through OAM-multiplexing holography, effectively reducing the dimensionality of information storage. By setting different reproduction charges ($ l'_{j} $), the holograms are successfully reconstructed. The spatial position of each layer is determined by the function f, enabling the replicating and stacking of layers to achieve a three-dimensional reconstruction of the rose, including its petals, from different perspectives. This process realizes three-dimensional holography. Notably, the combination of topological charge and the function f servesacts as a cryptographic key, significantly enhancing the security of information transmission. This OAM-selective holography technology not only improves security, but also achieves higher information throughput, indicating its enormous potential in various applications.
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