By introducing noncanonical vortex pairs to partially coherent beams, spatial correlation singularity (SCS) and orbital angular momenta (OAM) of the resulting beams are studied using the Fraunhofer diffraction integra...By introducing noncanonical vortex pairs to partially coherent beams, spatial correlation singularity (SCS) and orbital angular momenta (OAM) of the resulting beams are studied using the Fraunhofer diffraction integral. The effect of noncanonical strength, off-axis distance and vortex sign on spatial correlation singularities in far field is stressed. Furthermore, far-field OAM spectra and densities are also investigated, and the OAM detection and crosstalk probabilities are discussed. The results show that the number of dislocations of SCS always equals the sum of absolute values of topological charges for canonical or noncanonical vortex pairs. Although the sum of the product of each OAM mode and its power weight equals the algebraic sum of topological charges for canonical vortex pairs, the relationship no longer holds in the noncanonical case except for opposite-charge vortex pairs. The changes of off-axis distance, noncanonical strength or coherence length can lead to a more dominant power in adjacent mode than that in center detection mode, which also indicates that crosstalk probabilities of adjacent modes exceed the center detection probability. This work may provide potential applications in OAM-based optical communication, imaging, sensing and computing.展开更多
On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1...On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.展开更多
Optical singularities are topological defects of electromagnetic fields;they include phase singularity in scalar fields,polarization singularity in vector fields,and three-dimensional(3D)singularities such as optical ...Optical singularities are topological defects of electromagnetic fields;they include phase singularity in scalar fields,polarization singularity in vector fields,and three-dimensional(3D)singularities such as optical skyrmions.The exploitation of photonic microstructures to generate and manipulate optical singularities has attracted wide research interest in recent years,with many photonic microstructures having been devised to this end.Accompanying these designs,scattered phenomenological theories have been proposed to expound the working mechanisms behind individual designs.In this work,instead of focusing on a specific type of microstructure,we concentrate on the most common geometric features of these microstructures—namely,symmetries—and revisit the process of generating optical singularities in microstructures from a symmetry viewpoint.By systematically employing the projection operator technique in group theory,we develop a widely applicable theoretical scheme to explore optical singularities in microstructures with rosette(i.e.,rotational and reflection)symmetries.Our scheme agrees well with previously reported works and further reveals that the eigenmodes of a symmetric microstructure can support multiplexed phase singularities in different components,such as out-of-plane,radial,azimuthal,and left-and right-handed circular components.Based on these phase singularities,more complicated optical singularities may be synthesized,including C points,V points,L lines,Néel-and bubble-type optical skyrmions,and optical lattices,to name a few.We demonstrate that the topological invariants associated with optical singularities are protected by the symmetries of the microstructure.Lastly,based on symmetry arguments,we formulate a so-called symmetry matching condition to clarify the excitation of a specific type of optical singularity.Our work establishes a unified theoretical framework to explore optical singularities in photonic microstructures with symmetries,shedding light on the symmetry origin of multidimensional and multiplexed optical singularities and providing a symmetry perspective for exploring many singularity-related effects in optics and photonics.展开更多
Phase singularities(PSs)in topological darkness-based sensors have received significant attention in optical sensing due to their rapid,ultra-sensitive,and label-free detection capabilities.Here,we present both experi...Phase singularities(PSs)in topological darkness-based sensors have received significant attention in optical sensing due to their rapid,ultra-sensitive,and label-free detection capabilities.Here,we present both experimental and theoretical investigations of an ultrasensitive and multiplexed phase-sensitive sensor utilizing dual topological PSs in the visible and near-infrared regions.This sensor uses a simple structure,which consists of an ultra-thin highly absorbing film deposited on a metal substrate.We demonstrate the achievement of dual-polarization darkness points for s-and p-polarizations at different incident angles.Furthermore,we theoretically explain the double topological PSs accompanied by a perfect±π-jump near a zero-reflection point,based on the temporal coupled-mode formalism.To validate its multifunctional capabilities,humidity sensing tests were carried out.The results demonstrate that the sensor has a detection limit reaching the level of 0.12‰.These findings go beyond the scope of conventional interference optical coatings and highlight the potential applications of this technology in gas sensing and biosensing domains.展开更多
The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent ...The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.展开更多
针对特高压接入的输电网网架错综复杂、远景适应性差,甚至出现网架规划与开环分区决策相互独立导致资源浪费等问题,该文引入奇异值分解(singular value decomposition,SVD)和特征索引技术,提出了一种考虑电磁环网开环分区和500/220kV典...针对特高压接入的输电网网架错综复杂、远景适应性差,甚至出现网架规划与开环分区决策相互独立导致资源浪费等问题,该文引入奇异值分解(singular value decomposition,SVD)和特征索引技术,提出了一种考虑电磁环网开环分区和500/220kV典型供电结构的输电网多阶段规划方法。首先,提取典型供电结构的路径特征,制定了一种基于标签路径特征的典型供电结构索引策略;然后,构建了一种基于SVD的典型供电结构相似度指标,基于此,以全局典型供电结构相似程度最大为目标,建立了相似度识别规划模型;最后,提出了一种反馈调节机制及求解方法,统筹协调各阶段网架规划和开环分区之间的决策信息。与传统规划方法相比,该文方法不仅能够避免不同阶段开环分区决策导致的资源浪费,还可以减少复杂的规划评估指标计算,构建供电可靠性高、运行方式灵活、远景适应性强的网架结构。基于湖南某地区实际电网算例验证了该文方法的准确性和有效性。展开更多
为解决石油行业大数据高效安全传输难题,将图像转化为三通道矩阵数据并对矩阵进行奇异值分解,综合考虑Laplace算子、灰度方差函数、离散余弦变换系数、图像相关系数、熵函数、图像结构相似度和图像信噪比等7个评价因素,利用熵权逼近理...为解决石油行业大数据高效安全传输难题,将图像转化为三通道矩阵数据并对矩阵进行奇异值分解,综合考虑Laplace算子、灰度方差函数、离散余弦变换系数、图像相关系数、熵函数、图像结构相似度和图像信噪比等7个评价因素,利用熵权逼近理想解排序(technique for order preference by similarity to an ideal solution,TOPSIS)法对分解后的奇异值进行优选,在确保数据真实性的前提下用少量奇异值表征原始图像,进行图像压缩,降低数据大小,提高传输效率;提出多通道猫脸分割加密方法,分别对每个颜色通道的图像进行随机分割、随机加密和随机排序,解决了传统猫脸加密算法颜色通道线性相关度高,整体置乱度低的问题.结果表明:改进奇异值压缩技术在保证图像清晰的情况下仅利用15%的奇异值数据完成对图像的压缩,最大图像压缩比可达4.43,平均压缩后所占用的存储空间仅为原空间的26.29%,数据传输控制协议通信平均传输效率提高86.39%.在加密图像达到0相关的前提下,多通道猫脸分割加密算法加密图像在像素点处三通道颜色值完全不同,新方法颜色通道相关系数分别为0.20、0.22和0.25,对比传统猫脸加密方法,分别降低0.78、0.75和0.71.新方法加密效果好、难破解,可为石油行业数字化转型提供理论和技术支撑.展开更多
针对滚动轴承因长期处于强噪声工作环境而故障频发,且早期故障信息微弱难以提取等问题,提出了一种基于奇异值分解(singular value decomposition,SVD)与参数优化变分模态分解(variational mode decomposition,VMD)的联合降噪方法。首先...针对滚动轴承因长期处于强噪声工作环境而故障频发,且早期故障信息微弱难以提取等问题,提出了一种基于奇异值分解(singular value decomposition,SVD)与参数优化变分模态分解(variational mode decomposition,VMD)的联合降噪方法。首先,对轴承振动信号进行了SVD,依据奇异值差分谱理论确定了有效奇异值的阶数并进行了叠加重构,经过矩阵逆变换得到了初步降噪信号;然后,运用灰狼优化算法对VMD的模态个数K和惩罚因子α两参数寻优后进一步分解了初步降噪信号,同时基于峭度和相关系数复合指标选取模态分量;最后,对筛选信号进行了重构,并包络解调分析了降噪前后的故障特征频率。仿真数据和实验数据分析表明:所提方法在强噪声背景下或故障特征信息极其微弱时,都能够有效抑制噪声并提取有效故障信息。展开更多
文摘By introducing noncanonical vortex pairs to partially coherent beams, spatial correlation singularity (SCS) and orbital angular momenta (OAM) of the resulting beams are studied using the Fraunhofer diffraction integral. The effect of noncanonical strength, off-axis distance and vortex sign on spatial correlation singularities in far field is stressed. Furthermore, far-field OAM spectra and densities are also investigated, and the OAM detection and crosstalk probabilities are discussed. The results show that the number of dislocations of SCS always equals the sum of absolute values of topological charges for canonical or noncanonical vortex pairs. Although the sum of the product of each OAM mode and its power weight equals the algebraic sum of topological charges for canonical vortex pairs, the relationship no longer holds in the noncanonical case except for opposite-charge vortex pairs. The changes of off-axis distance, noncanonical strength or coherence length can lead to a more dominant power in adjacent mode than that in center detection mode, which also indicates that crosstalk probabilities of adjacent modes exceed the center detection probability. This work may provide potential applications in OAM-based optical communication, imaging, sensing and computing.
基金supported by the National Natural Science Foundation of China(11931009,12271495,11971450,and 12071449)Anhui Initiative in Quantum Information Technologies(AHY150200)the Project of Stable Support for Youth Team in Basic Research Field,Chinese Academy of Sciences(YSBR-001).
文摘On a compact Riemann surface with finite punctures P_(1),…P_(k),we define toric curves as multivalued,totallyunramified holomorphic maps to P^(n)with monodromy in a maximal torus of PSU(n+1).Toric solutions to SU(n+1)Todasystems on X\{P_(1);…;P_(k)}are recognized by the associated toric curves in.We introduce character n-ensembles as-tuples of meromorphic one-forms with simple poles and purely imaginary periods,generating toric curves on minus finitelymany points.On X,we establish a correspondence between character-ensembles and toric solutions to the SU(n+1)system with finitely many cone singularities.Our approach not only broadens seminal solutions with two conesingularities on the Riemann sphere,as classified by Jost-Wang(Int.Math.Res.Not.,2002,(6):277-290)andLin-Wei-Ye(Invent.Math.,2012,190(1):169-207),but also advances beyond the limits of Lin-Yang-Zhong’s existencetheorems(J.Differential Geom.,2020,114(2):337-391)by introducing a new solution class.
基金supported by the National Natural Science Foun-dation of China(62301596 and 62288101)Shaanxi Provincial Science and Technology Innovation Team(23-CX-TD-48)+4 种基金the KU Leuven internal funds:the C1 Project(C14/19/083)the Interdisciplinary Network Project(IDN/20/014)the Small Infrastructure Grant(KA/20/019)the Research Foundation of Flanders(FWO)Project(G090017N,G088822N,and V408823N)the Danish National Research Foundation(DNRF165).
文摘Optical singularities are topological defects of electromagnetic fields;they include phase singularity in scalar fields,polarization singularity in vector fields,and three-dimensional(3D)singularities such as optical skyrmions.The exploitation of photonic microstructures to generate and manipulate optical singularities has attracted wide research interest in recent years,with many photonic microstructures having been devised to this end.Accompanying these designs,scattered phenomenological theories have been proposed to expound the working mechanisms behind individual designs.In this work,instead of focusing on a specific type of microstructure,we concentrate on the most common geometric features of these microstructures—namely,symmetries—and revisit the process of generating optical singularities in microstructures from a symmetry viewpoint.By systematically employing the projection operator technique in group theory,we develop a widely applicable theoretical scheme to explore optical singularities in microstructures with rosette(i.e.,rotational and reflection)symmetries.Our scheme agrees well with previously reported works and further reveals that the eigenmodes of a symmetric microstructure can support multiplexed phase singularities in different components,such as out-of-plane,radial,azimuthal,and left-and right-handed circular components.Based on these phase singularities,more complicated optical singularities may be synthesized,including C points,V points,L lines,Néel-and bubble-type optical skyrmions,and optical lattices,to name a few.We demonstrate that the topological invariants associated with optical singularities are protected by the symmetries of the microstructure.Lastly,based on symmetry arguments,we formulate a so-called symmetry matching condition to clarify the excitation of a specific type of optical singularity.Our work establishes a unified theoretical framework to explore optical singularities in photonic microstructures with symmetries,shedding light on the symmetry origin of multidimensional and multiplexed optical singularities and providing a symmetry perspective for exploring many singularity-related effects in optics and photonics.
基金supported by the National Key R&D Program of China(2022YFA1404701)Program of Shanghai Academic Research Leader under Grant(22XD1422100)+4 种基金National Natural Science Foundation of China(62075231,12141303,12073018)Shanghai Science and Technology Committee(20JC1414603,23dz2260100)Shanghai Pujiang Program(21PJ1411400)China Postdoctoral Science Foundation(2021M703335)Young Elite Scientists Sponsorship Program by CAST(YESS20220355).
文摘Phase singularities(PSs)in topological darkness-based sensors have received significant attention in optical sensing due to their rapid,ultra-sensitive,and label-free detection capabilities.Here,we present both experimental and theoretical investigations of an ultrasensitive and multiplexed phase-sensitive sensor utilizing dual topological PSs in the visible and near-infrared regions.This sensor uses a simple structure,which consists of an ultra-thin highly absorbing film deposited on a metal substrate.We demonstrate the achievement of dual-polarization darkness points for s-and p-polarizations at different incident angles.Furthermore,we theoretically explain the double topological PSs accompanied by a perfect±π-jump near a zero-reflection point,based on the temporal coupled-mode formalism.To validate its multifunctional capabilities,humidity sensing tests were carried out.The results demonstrate that the sensor has a detection limit reaching the level of 0.12‰.These findings go beyond the scope of conventional interference optical coatings and highlight the potential applications of this technology in gas sensing and biosensing domains.
文摘The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.
文摘针对特高压接入的输电网网架错综复杂、远景适应性差,甚至出现网架规划与开环分区决策相互独立导致资源浪费等问题,该文引入奇异值分解(singular value decomposition,SVD)和特征索引技术,提出了一种考虑电磁环网开环分区和500/220kV典型供电结构的输电网多阶段规划方法。首先,提取典型供电结构的路径特征,制定了一种基于标签路径特征的典型供电结构索引策略;然后,构建了一种基于SVD的典型供电结构相似度指标,基于此,以全局典型供电结构相似程度最大为目标,建立了相似度识别规划模型;最后,提出了一种反馈调节机制及求解方法,统筹协调各阶段网架规划和开环分区之间的决策信息。与传统规划方法相比,该文方法不仅能够避免不同阶段开环分区决策导致的资源浪费,还可以减少复杂的规划评估指标计算,构建供电可靠性高、运行方式灵活、远景适应性强的网架结构。基于湖南某地区实际电网算例验证了该文方法的准确性和有效性。
文摘为解决石油行业大数据高效安全传输难题,将图像转化为三通道矩阵数据并对矩阵进行奇异值分解,综合考虑Laplace算子、灰度方差函数、离散余弦变换系数、图像相关系数、熵函数、图像结构相似度和图像信噪比等7个评价因素,利用熵权逼近理想解排序(technique for order preference by similarity to an ideal solution,TOPSIS)法对分解后的奇异值进行优选,在确保数据真实性的前提下用少量奇异值表征原始图像,进行图像压缩,降低数据大小,提高传输效率;提出多通道猫脸分割加密方法,分别对每个颜色通道的图像进行随机分割、随机加密和随机排序,解决了传统猫脸加密算法颜色通道线性相关度高,整体置乱度低的问题.结果表明:改进奇异值压缩技术在保证图像清晰的情况下仅利用15%的奇异值数据完成对图像的压缩,最大图像压缩比可达4.43,平均压缩后所占用的存储空间仅为原空间的26.29%,数据传输控制协议通信平均传输效率提高86.39%.在加密图像达到0相关的前提下,多通道猫脸分割加密算法加密图像在像素点处三通道颜色值完全不同,新方法颜色通道相关系数分别为0.20、0.22和0.25,对比传统猫脸加密方法,分别降低0.78、0.75和0.71.新方法加密效果好、难破解,可为石油行业数字化转型提供理论和技术支撑.
文摘针对滚动轴承因长期处于强噪声工作环境而故障频发,且早期故障信息微弱难以提取等问题,提出了一种基于奇异值分解(singular value decomposition,SVD)与参数优化变分模态分解(variational mode decomposition,VMD)的联合降噪方法。首先,对轴承振动信号进行了SVD,依据奇异值差分谱理论确定了有效奇异值的阶数并进行了叠加重构,经过矩阵逆变换得到了初步降噪信号;然后,运用灰狼优化算法对VMD的模态个数K和惩罚因子α两参数寻优后进一步分解了初步降噪信号,同时基于峭度和相关系数复合指标选取模态分量;最后,对筛选信号进行了重构,并包络解调分析了降噪前后的故障特征频率。仿真数据和实验数据分析表明:所提方法在强噪声背景下或故障特征信息极其微弱时,都能够有效抑制噪声并提取有效故障信息。
