Conventional metasurfaces incorporating phase-change materials (PCMs) are typically limited to small-range adjustments of the orbital angular momentum (OAM) carried by optical vortex beams. This study presents a metasurface design paradigm for the reconfigurable, broad range generation of vortex beams across a broad range of topological charges. The design utilizes low-loss, non-volatile antimony trisulfide (Sb 2 S 3 ) as the active PCM at an operational wavelength of 800 nm. We identified eight distinct crystallinity levels of Sb 2 S 3 that collectively provide a full 0−2 π phase coverage under a fixed geometry, with a phase step of π /4 between adjacent levels. By optically stimulating the metasurface, we locally tune the crystallinity of its nanopillars, thereby imparting a phase profile that forms the desired spiral phase gradient. Under illumination by a linearly polarized Gaussian beam, the co-polarized transmitted light is thereby converted into a vortex beam with the desired OAM order. Results indicate that beams generated in low-order modes exhibit high mode purity, whereas higher-order modes show reduced purity due to a limited number of meta-atoms, and we further verified that the mode purity improves significantly as the array size increases. Furthermore, the proposed structure exhibits considerable tolerance to nanofabrication-induced dimensional errors and the performance of the PCM-based metasurface remains robust even under coarse crystallinity control, relaxing experimental constraints. This reconfigurable metasurface offers a promising pathway toward reconfigurable integrated photonic systems for advanced optical manipulation and communication.

Wavefront estimation under long-distance, strong atmospheric turbulence remains a critical challenge in free-space optical communication (FSOC). Conventional approaches always suffer from high computational cost and latency. To address this issue, we proposed a lightweight high-precision neural network (LHP-Net), a compact yet accurate model that directly predicts Zernike coefficients from single-frame distorted images under long-distance, strong atmospheric turbulence. The architecture combines an optimized convolutional backbone with a lightweight Zernike-aware attention (LZA) module, enhancing the sensitivity to turbulence-induced aberrations while minimizing computational cost. To rigorously evaluate performance, a large-scale dataset using spectral phase screen simulations was obtained, covering propagation distances up to 10 km and turbulence intensity ranging from weak to strong. Simulation results indicate that LHP-Net achieves up to 92.4% lower prediction error and 37.5% faster inference, exhibiting better performance than a conventional convolutional neural network (CNN). Furthermore, our hybrid training strategy significantly enhances the generalization across different turbulence intensities. Remarkably, LHP-Net maintains robust performance even under extreme turbulence, exhibiting minimal prediction error, providing potential for real-time adaptive optics in next-generation free-space optical systems.

Most existing ground-motion models (GMMs) provide spectral acceleration (Sa) predictions only up to about 10 s, limiting their use for structures sensitive to motions at periods greater than 10 s. To address this, this study develops a record-fusion ground-motion modeling framework that covers 0.01–16 s, using 7804 collocated acceleration-velocity record pairs from 126 earthquakes in Southern California, USA. The framework integrates Bayesian optimization of fusion weights with staged GMM term search. The resulting GMM extends Sa prediction beyond 10 s and exhibits physically reasonable magnitude scaling, distance attenuation, and site-condition scaling over the modeled period range. Between-event, site-to-site, and remaining within-event residuals are generally centered near zero across all periods and show no clear systematic bias. Comparisons with four benchmark NGA-West2 GMMs indicate that, although the dataset is smaller than those used for the benchmarks, particularly for large-magnitude events, the developed GMM produces median predictions within 0.01–10 s, broadly consistent with the benchmark models. Further comparisons with observed Sa and representative earthquake cases show that predictions within 0.01–16 s remain consistent with observed trends and show no evident attenuation instability or divergence, confirming the effectiveness of the proposed framework and the stable predictive behavior of the resulting GMM across the modeled period range.

Currently, significant progress has been made in the development of in-plane symmetry-protected BIC sensors, but research on out-of-plane symmetry-protected BIC sensors has received much less attention. In this work, we introduce an approach where the tilt angle of rectangular holes is adjusted to break vertical mirror symmetry, successfully exciting the out-of-plane BIC mode. Our results show that increasing the tilt angle enhances electric field confinement at the BIC resonance, while promoting radiation leakage and facilitating stronger coupling to free space. Further analysis reveals that the gold coating significantly enhances the quality factor for tilt angles smaller than 5°, without compromising the sensor’s detection sensitivity. These findings highlight the potential of out-of-plane symmetry-broken BIC metamaterials as highly sensitive platforms for THz refractive index and thickness sensing, driving advancements in this emerging field. Investigation of out-of-plane symmetry-protected bound states in the continuum in terahertz metamaterials.

Longitudinal turbulence profiling remains a fundamental challenge in atmospheric optics, with traditional methods constrained by inherent trade-offs between longitudinal spatial resolution, measurement precision, and system complexity. Here, we propose a deep learning-enabled longitudinal turbulence profiling approach using Trajectory-engineered Airy Beams (TABs). The TABs with tunable focus act as probe beams for turbulence strength sensing along the beam path, yielding different modal powers at the receiving plane. A Joint Convolutional Channel Attention One-dimensional Network (JCCA-1DNet) is proposed to learn the mapping between the longitudinal turbulence strengths and the corresponding modal powers of TABs. Our simulations establish the effectiveness of the proposed method for longitudinal turbulence profiling across a broad range of turbulence conditions, whereas the experiments validate its feasibility. This work may provide a promising route toward accurate and efficient longitudinal turbulence profiling in atmospheric environments.

Robust scaling laws governing high-energy laser (HEL) slant-path propagation through a non-Kolmogorov marine atmosphere are critical for rapid performance prediction in laser engineering applications. However, the derivation of accurate scaling laws remains highly challenging due to the variable application scenarios and the precision limitations of traditional scaling law models. To address this, we developed a scaling law for Gaussian beam propagation along slant paths in non-Kolmogorov marine environments by introducing the zenith angle dependence. By combining the least-squares method (LSM) and the genetic algorithm (GA) optimization method, the numerical simulation reveals distinct behaviors under independent turbulence and thermal blooming conditions. Although the zenith angle exhibits almost negligible impact on turbulence-induced beam spreading, it introduces nonlinear coupling effects with thermal blooming. To rigorously characterize these effects, we employed a modified root-sum-square (MRSS) model to establish the scaling law on the consideration of the coupling effect of turbulence and thermal blooming. Results indicate that the proposed scaling law achieves remarkable consistency with numerical simulations, with relative deviations constrained below 5.00%. This comprehensive approach not only extends the applicability of scaling laws to previously unexplored marine atmospheric conditions but also establishes what we believe to be a new benchmark for accuracy in laser propagation modeling through its integration of the zenith angle.

In spectral beam combining (SBC) of high-power fiber lasers, the excitation of higher-order linearly polarized (LP) modes becomes increasingly pronounced since the output power from a single fiber arises. To address this, we proposed a full two-dimensional (2D) diffraction integral model of SBC, enabling a comprehensive modeling and correction of such higher-order LP modes. Furthermore, a matrix multiplication method was used to reduce the computation complexity from O(n6) to O(n3). Using this framework, the detrimental effects of higher-order LP modes on the beam quality of the combined beam were analyzed, and the improvement of beam quality via a wavefront sensor-less adaptive optics (AO) method was illustrated. We hope this work can provide useful reference for the beam quality analysis and control in SBC systems.

Metasurface is a kind of artificial structure which can efficiently control the amplitude, phase, frequency, and polarization of the light field. Metasurface polarization holographic encryption is a holographic encryption technology with the polarization state as a key, which has been widely concerned in recent years with advantages such as sub-wavelength pixels, precision adjustment, and high security factor. In this paper, the design and optimization of the unit structure of metasurface have been carried out, and the clear double-channel holographic image reproduction and good encryption effects have been realized afterwards. The results show that the relatively good polarization holographic encryption can be achieved by employing the designed Si nanorods with the length of 148 nm and width of 55 nm, respectively, which have been beforehand grown on SiO2 substrates. Note that the periodic angle deflection around the Z axis was adopted by using the dual-channel optical rotation incidence with the wavelength of 632.8 nm. It has been theoretically demonstrated that information transmittance loss should be less and the image restoration effect should be satisfactory. A novel encryption method has also been proposed for the optical information processing and optical encryption, and the huge application potential of our theme has been revealed as the next-generation optical control platform in the near future.

Noise, usually undesired yet inevitable, can be harnessed to suppress channel crosstalk in multiplexed holography and thus increase information capacity. Existing noise-engineering strategies, however, rely predominantly on one-dimensional engineered noise, whose limited degrees of freedom severely constrain the key space and, in turn, the scalability and flexibility of holographic encryption. Here we propose and experimentally demonstrate a generalized orthogonality principle based on high-dimensional noise that overcomes this fundamental limitation. By exploiting the intrinsic orthogonality of high-dimensional random noise, we establish a channel-isolation mechanism for holographic multiplexing that substantially enlarges the available channel space while preserving low crosstalk. We further integrated a conditional generative adversarial network (pix2pix) to recover high-fidelity images from low-signal-to-noise reconstructions. This work provides a robust and scalable route towards ultrahigh-capacity, ultrasecure holography.

In space-based gravitational wave detection systems,ultra-long laser interferometry arms are established between three communication satellites to detect the gravitational wave,requiring the space telescopes to perform both laser transmission and reception functions.However,the extreme weakness of gravitational wave signals imposes stringent requirements on optical path stability and backward stray light suppression in these telescopes,that is,the backward stray light must be less than 10-10 of the output laser.The primary source of backward stray light from space telescopes arises from surface scattering.Even in ultra-smooth optical elements(roughness less than 1 nm),the surface scattering inevitably occurs during laser transmission,generating backward-scattered light that affects the gravitational wave detection.Therefore,precise characterization of ultra-smooth optical surfaces is critical for analyzing and suppressing telescope backward stray light levels.However,conventional non-contact measurement methods face significant challenges,including complex instrument structure,high experimental cost,and insufficient accuracy,making it difficult to achieve rapid and high-precision measurement of ultra-smooth optical surface.Consequently,there is an urgent need to develop a surface quality assessment method for ultra-smooth optical elements to meet the extraordinary precision requirements of gravitational wave space telescopes. For high-precision scattering measurement of ultra-smooth optical elements,Li B C's team proposed a method based on multi-channel cavity ring down technique.This method obtains the surface scattering rate by analyzing multi-channel ring-down signals,offering advantages including absolute measurement,immunity to laser source intensity fluctuation,and exceptional measurement accuracy.This work further combines the cavity ring-down-based scattering measurement technique with the Generalized Beckmann-Kirchhoff(GBK)scalar scattering model,to establish a method for estimating the surface parameters of ultra-smooth optical elements.In this method,the GBK scattering model is used to establish the scattering rate database of the optical elements,and the scattering rate of the ultra-smooth optical elements at different solid angles is measured based on the cavity ring down technique.Then,the scattering rate distribution measured by cavity ring down method is numerically fitted with the scattering rate database to obtain the surface parameters of the ultra-smooth optical elements,which provides a reference for the scattering characteristics analysis and stray light suppression of the ultra-smooth optical elements of space telescopes. The scattering rate distribution of ultra-smooth optical element measured by the cavity ring down technique was simulated and calculated,with the measured data numerically fitted through our proposed surface parameter estimation approach.As shown in Figure 3,the fitting achieves remarkable precision with an error of 0.16%and a goodness of fit of 0.999 8.Further evaluation of the method's performance across different parameters demonstrates that within the applicable range of GBK theory,the method can achieve an error of below 4%(typically<0.5%),while the goodness of fit is greater than 0.96(often>0.999).In addition,to address measurement errors induced by scattering overlap during bidirectional beam propagation in standing-wave cavity ring-down experiments,we analyzed key influencing factors.By integrating these findings with our predictive model,we quantified scattering overlap effects at various measurement angles and derived an optimized angular selection scheme to minimize interference. This work proposes a novel method for estimating surface parameters of ultra-smooth optical elements by combining GBK scalar scattering theory with cavity ring-down scattering measurement techniques.The simulation analysis shows that,within the scope of application of GBK scalar theory,the relative error of this method is less than 4%,and the fitting degree is greater than 0.96,confirming its high accuracy for rapid and precise measurement of surface quality parameters.In addition,aiming at the error caused by the scattering overlap of the back and forth propagation of the beam in the scattering measurement experiment of the standing wave cavity ring down method,we propose a measurement angle selection scheme considering both the signal-to-noise ratio and the measurement accuracy,so as to reduce the influence of the scattering overlap of the forward and backward propagation on the scattering measurement and subsequent surface quality estimation.

A novel beamforming method is proposed to address mutual-coupling-induced beam misalignments in phased arrays interleaved by coupled subarrays (PAICS). By establishing a signal-coupling model, subarray port currents are related to decoupled incident voltages via a generalized impedance matrix (GIM), which is used to correct the ideal steering vector (ISV) in beamforming. Compared with optimization-based methods, this analytical method notably reduces computational overhead and response time. A C-band PAICS comprising seven subarrays was designed and implemented with integrated measurement-and-control circuitry, enabling efficient data acquisition required for GIM determination. Experiments on the prototype demonstrate high angular accuracy in direction-of-arrival (DoA) estimation and beam steering over ranges of ±55° and ±50°, respectively. The tested 1.5-ms latency of beamforming-weight calculation proves its potential for real-time embedded implementation.

Structured optical fields with tailored propagation properties are of significant interest for applications in optical manipulation, imaging, laser processing, and remote optical delivery. However, traditional non-diffracting and self-focusing beams generally lack the flexibility to simultaneously tailor the on-axis intensity evolution and transverse beam profile according to the application requirements. To address this limitation, we propose a generalized phase-gradient method for constructing diffraction-resistant structured beams with controllable axial and transverse propagation characteristics. By directly engineering arbitrary smooth radial phase gradients, continuously distributed inward transverse wavevectors are generated to sustain stable axial focusing during propagation. Consequently, different phase-gradient functions further lead to distinct transverse wavevector redistribution behaviors, enabling flexible control of the transverse main-lobe evolution. Based on the resulting stationary-phase mapping relation, an analytical expression for amplitude compensation is further derived to achieve any desired on-axis intensity profile. Simulations and experiments both confirm the programmable axial intensity evolutions, controllable main-lobe dynamics, and robust self-healing behaviors, in excellent agreement with theoretical predictions. The proposed approach provides a flexible method for engineering structured optical fields with customizable propagation dynamics.

Spectral beam combining (SBC) is promising for power scaling of fiber lasers while maintaining beam quality. However, the combined beam quality is severely degraded by the coupling of multiple factors, including pointing and divergence angle deviations of the fiber array and thermal effects of the grating and internal channel. In this work, in order to analyze the influence of multi-factors coupling and to explore the optimization strategy for SBC systems, a multi-physics coupling model based on the Fourier propagation method and the equivalent phase screen method is established. Our simulation results reveal that beam quality degradation under multi-factor coupling conditions is significantly more severe than that caused by any individual factor alone. In addition, the adaptive optics (AO) can effectively mitigate the low-order aberrations induced by thermal effects and divergence angle variations, whereas its capability to correct the non-common-path aberrations induced by pointing angle deviations is somewhat limited. We believe this work offers valuable guidance for the design and optimization of high-power, high-beam-quality SBC systems.

Metasurface orbital angular momentum (OAM) holography has great potential in high-capacity information storage and encryption from its unbounded orthogonal helical modes and nanometer-scale resolution. However, this multiplexing technique currently remains at the single degree of freedom (DoF) level, and its inherent diffraction causes the beam spreading as the OAM spiral mode index increases, which limits its applicability in areas such as high-capacity information storage and high-security encryption. Addressing this, we propose the concept of metasurface OAM holography with multi-spatial modal basis multiplexing (MSMBM), which provides a multi-DoF control method by using the multiple dimensions of spatial modal basis and OAM helical mode index to expand the information capacity of holographic display devices. Under the same OAM spiral mode index, the method can integrate OAM with different spatial mode bases as a high-dimensional information carrier, and realize control of multiple independent DOF while maintaining image resolution. As a proof of concept, we experimentally demonstrate a meta-hologram using a noninterleaved metasurface, which enables the reconstruction of a unique sequence of OAM-dependent holographic images, and the information capacity is twice that of traditional OAM multiplexed holography. This breakthrough enhances information capacity and security, enabling ultra-high-capacity data storage and optical encryption applications.

The metasurface possesses great potential in a 3D holographic display due to its powerful ability to manipulate optical fields, ultracompact structure, and extraordinary information capacity. However, the in-plane and inter plane crosstalk caused by the coupling between the meta-atoms of the current 3D holographic metasurface limits the quality of the reconstructed image, which has become a significant obstacle to high-performance 3D display applications. Additionally, the interleaved or multilayer design strategy of metasurfaces increases the complexity of structural design and manufacturing, facing challenges in meeting the requirements for miniaturization and low cost-effectiveness. Here, we propose a strategy for a free-space 3D multiplane color holographic multiplex display based on a single-cell metasurface. By utilizing a modified holographic optimization strategy, multiple holographic information is encoded into three mutually independent bases of incident photons and integrated into a metasurface, thereby creating high-quality 3D vectorial metaholography with minimal crosstalk across the visible spectrum. The proposed metasurface has great potential for applications in augmented reality/virtual reality devices, polarization imaging, holographic data encryption, and information storage. (c) 2025 Chinese Laser Press

The increasing demand for data security in the digital age has exposed the limitations of traditional data-at-rest encryption, including vulnerabilities in key management and insufficient ability to withstand attacks. Here, we propose a hybrid optical cryptography framework that integrates dynamic optical hardware with algorithmic codesign to provide multi-level protection. In the encryption process, the target information is encrypted using the single pixel imaging (SPI) principle, and the ciphertext is generated by mixing the false information with the bucket signal obtained by SPI. The decryption key is generated by the reconfigurable metasurface. This metasurface is based on the phase change material (PCM) Sb2Se3, which can be laser-induced to enable key switching for each encryption process, thus realizing "one-time pad" (OTP). In the decryption process, the key obtained from loading at the metasurface can decrypt the information from the ciphertext. The target image is finally decrypted through different channels using Visual Secret Sharing (VSS) scheme. Decryption requires superposition of all shares, thereby enhancing resistance against brute-force and eavesdropping attacks. Furthermore, we analyze the reconfigurability of the metasurface as well as the fabrication tolerance. The results show the strong robustness and high security of our encryption scheme. This approach not only addresses the limitations of fixed-function metasurfaces but also establishes a scalable paradigm for high-security optical encryption in real applications.

In recent years, the propagation characteristics of Gaussian beams in anisotropic nonKolmogorov maritime atmospheric turbulence have attracted significant attention. However, beam spreading is inevitable upon propagation, leading to the decrease of beam quality of Gaussian beams in far field. The analysis of beam spreading of Gaussian beams, using the power spectrum inversion and the multi-layer phase screen method, is quite time-consuming and challenging to efficiently address the rapid and accurate prediction of beam spreading in practical applications. Although many researches have been focused on the propagation characteristics of Gaussian beams in maritime atmospheric turbulence, the scaling law for beam spreading is still lacking. Especially, compared to terrestrial environments, the maritime environment exhibits distinct characteristics, including higher humidity levels and temperature variations. These environmental differences lead to variations in the propagation characteristics of Gaussian beams. Consequently, establishing scaling law is essential for predicting the beam spreading of Gaussian beams in maritime atmospheric turbulence. To effectively predict and evaluate the impact of maritime atmospheric turbulence on the beam spreading, this study investigates the scaling law for beam spreading of Gaussian beams in maritime atmospheric conditions. A comprehensive physical model has been developed to characterize maritime turbulence using the power spectrum inversion method to generate the turbulence phase screen. Subsequently, numerical simulations have been carried out by the use of the multi-layer phase screen method. Based on the Kolmogorov turbulence spectrum and taking into account the atmospheric coherence length for nonKolmogorov scenarios, the scaling law for beam spreading of Gaussian beams in maritime atmospheric turbulence has been established. The effects of key parameters, including atmospheric anisotropy, spectral power index, initial beam quality, and wavelength, on the beam spreading of Gaussian beams propagating through maritime turbulence have been investigated. Simulation results, obtained under various parameter settings, yield curves that represent beam spreading and calibration factors under different parameters. The least squares method was then employed to fit these results, leading to the derivation of a beam spreading calibration formula. Furthermore, an error analysis has been performed on all numerical calculation data in relation to the derived calibration formula to validate the effectiveness and applicability of the proposed calibration approach. The results indicate that, within the wavelength range from 1 mu m to 4 mu m, the initial beam quality from 1 to 3, the refractive index structure from 5x10(-16 )to 5x10(-13) m(3-alpha) , the anisotropy factor from 1 to 4, and the spectral power index from 3.1 to 3.8, the error between the predicted beam spreading and the numerical calculation results remains within 15 degrees o. Upon these results, the calibration formula exhibits a maximum error of approximately 14.4 degrees o, with an average error of around 2.82 degrees o. Particularly, in cases where beta(0)>1 or zeta>1, the maximum error is reduced to below 10 degrees o. This reduction arises from the amplified impact of the initial beam quality on beam spreading as initial quality of the laser beam deteriorates. Furthermore, as anisotropy factor increases, the influence of turbulence on beam spreading decreases, augmenting the relative impact of the initial beam quality and consequently reducing the error of the scaling law. The scaling law was proposed to predict the beam spreading of Gaussian beam in anisotropic nonKolmogorov maritime atmospheric turbulence rapidly and accurately. Firstly, the variations of beam spreading with laser and turbulence parameters, including atmospheric anisotropy, spectral power index, initial beam quality, and wavelength, were analyzed in detail. Then, the simulation results yield curves that represent beam spreading and calibration factors under different parameters. Subsequently, the least squares method was employed to fit these results, leading to the derivation of the scaling law. Furthermore, the errors between the results predicted by the scaling formula and the simulation results were analyzed. The results show that, within the specified parameter range, the errors are less than 14.4 degrees o, with the average error below 2.82 degrees o.