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
Singularities are the positions at which a physical quantity becomes not well-behaved or undefined.In the context of optics,singularities can manifest in various forms,including amplitude,phase,and polarization singul...Singularities are the positions at which a physical quantity becomes not well-behaved or undefined.In the context of optics,singularities can manifest in various forms,including amplitude,phase,and polarization singularities.Among these,polarization singularities are typically classified into V-points,C-points,and L-lines.展开更多
As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimat...As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.展开更多
Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior i...Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier-Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence-divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.展开更多
In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc t-t0/a along closed smooth contours restricted i...In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc t-t0/a along closed smooth contours restricted in the strip 0 〈 Rez 〈 aπ is discussed. Finally, the solutions with singularities of order one for the above two problems are discussed.展开更多
A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transforma...A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.展开更多
We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with sol...We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by this article contain special cases discussed before.展开更多
This paper deals with the time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise. The dimension of the Fokker Planck equation is reduced by the linea...This paper deals with the time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise. The dimension of the Fokker Planck equation is reduced by the linear transfor- mation. The exact expression of the time dependence of information entropy is obtained based on the definition of Shannon＇s information entropy. The relationships between the properties of dissipative parameters, system singularity strength parameter, quasimonochromatic noise, and their effects on information entropy are discussed.展开更多
Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior i...Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, only of late has there been much in the way of corresponding identifications of flow-induced stress singularities in fluid mechanics. These recent asymptotic identifications are for a single incompressible viscous fluid： Here the asymptotic approach is extended to apply to a configuration entailing two such fluids, For this configuration, various specifications leading to power or log singularities are determined. These results demonstrate that flow-induced stress singularities can occur in a structural container at a location where no singularities are identified within solid mechanics alone.展开更多
Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations wi...Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter.展开更多
Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory. It is shown that there exist C-points and L-lines, which depend...Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory. It is shown that there exist C-points and L-lines, which depend on off-axis displacement parameters along the x and y directions, waist width, wavelength, and topological charge of the diffracted Gaussian vortex beam, as well as on propagation distance. The results are illustrated by numerical calculations.展开更多
A Van Hove singularity(VHS) is a singularity in the phonon or electronic density of states of a crystalline solid. When the Fermi energy is close to the VHS, instabilities will occur, which can give rise to new phases...A Van Hove singularity(VHS) is a singularity in the phonon or electronic density of states of a crystalline solid. When the Fermi energy is close to the VHS, instabilities will occur, which can give rise to new phases of matter with desirable properties. However, the position of the VHS in the band structure cannot be changed in most materials. In this work, we demonstrate that the carrier densities required to approach the VHS are reached by gating in a suspended carbon nanotube Schottky barrier transistor. Critical saddle points were observed in regions of both positive and negative gate voltage, and the conductance flattened out when the gate voltage exceeded the critical value. These novel physical phenomena were evident when the temperature is below 100 K. Further, the temperature dependence of the electrical characteristics was also investigated in this type of Schottky barrier transistor.展开更多
Parallel manipulator is associated with a set of functions defined by its closure constraints. In this paper, using Lie algebra method, we provide a study on the singularities of parallel manipulators, their relations...Parallel manipulator is associated with a set of functions defined by its closure constraints. In this paper, using Lie algebra method, we provide a study on the singularities of parallel manipulators, their relations with the second order of the closure functions, and the tangent space of the configuration space of the manipulator. The transverse condition criterion is applied to analyze the behavior of the singularities. This gives a downright explication why the 6R paradoxical mechanisms work in their singular configurations, and allows to gain insight on configuration space singularities and to choose the adequate design parameters for the parallel manipulator.展开更多
The evolution of polarization singularities supported in a one-dimensional periodic plasmonic system is studied.The lateral inversion symmetry of the system,which breaks the in-plane inversion symmetry and up-down mir...The evolution of polarization singularities supported in a one-dimensional periodic plasmonic system is studied.The lateral inversion symmetry of the system,which breaks the in-plane inversion symmetry and up-down mirror symmetry simultaneously,yields abundant polarization states.A complete evolution process with geometry for the polarization states is traced.In the evolution,circularly polarized points(C points)can stem from 3 different processes.In addition to the previously reported processes occurring in an isolated band,a new type of C point appearing in two bands simultaneously due to the avoided band crossing,is observed.Unlike the dielectric system with a similar structure which only supports at-Γbound states in the continuum(BICs),accidental BICs off theΓpoint are realized in this plasmonic system.This work provides a new scheme of polarization manipulation for the plasmonic systems.展开更多
In this paper, the relation between the spectral degree of coherence and degree of polarization of random electromagnetic beams is derived by the Stokes parameters. And the concept of polarization singularity is exten...In this paper, the relation between the spectral degree of coherence and degree of polarization of random electromagnetic beams is derived by the Stokes parameters. And the concept of polarization singularity is extended from spatially fully coherent beams to partially coherent electromagnetic beams. Theoretical analysis shows that correlation vortices are linearly polarized singularities. The results are illustrated by numerical examples.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Singularities are the positions at which a physical quantity becomes not well-behaved or undefined.In the context of optics,singularities can manifest in various forms,including amplitude,phase,and polarization singularities.Among these,polarization singularities are typically classified into V-points,C-points,and L-lines.
文摘As an important type of polynomial approximation, approximation of functions by Bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by Bernstein operators. The main results are the Jackson＇s estimates of functions f∈ （Wwλ）2 andre Cw, which extends the result of （Della Vecchia et al., 2004）.
文摘Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier-Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence-divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.
基金Supported by the National Natural Science Foundation of China (19971064)
文摘In this article, periodic Riemann boundary value problem with period 2aπ along closed smooth contours is discussed, and then singular integral equation with kernel csc t-t0/a along closed smooth contours restricted in the strip 0 〈 Rez 〈 aπ is discussed. Finally, the solutions with singularities of order one for the above two problems are discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.
基金Supported by the NNSF of China (10471107)RFDP of Higher Education of China (20060486001)
文摘We transform the singular integral equations with solutions simultaneously having singularities of higher order at infinite point and at several finite points on the real axis into ones along a closed contour with solutions having singularities of higher order, and for the former obtain the extended Neother theorem of complete equation as well as the solutions and the solvable conditions of characteristic equation from the latter. The conclusions drawn by this article contain special cases discussed before.
基金Project supported by the National Natural Science Foundation of China(Grant No.11102132)
文摘This paper deals with the time evolution of information entropy for a stochastic system with double singularities driven by quasimonochromatic noise. The dimension of the Fokker Planck equation is reduced by the linear transfor- mation. The exact expression of the time dependence of information entropy is obtained based on the definition of Shannon＇s information entropy. The relationships between the properties of dissipative parameters, system singularity strength parameter, quasimonochromatic noise, and their effects on information entropy are discussed.
文摘Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, only of late has there been much in the way of corresponding identifications of flow-induced stress singularities in fluid mechanics. These recent asymptotic identifications are for a single incompressible viscous fluid： Here the asymptotic approach is extended to apply to a configuration entailing two such fluids, For this configuration, various specifications leading to power or log singularities are determined. These results demonstrate that flow-induced stress singularities can occur in a structural container at a location where no singularities are identified within solid mechanics alone.
基金Supported by the National Natural Science Foundation of China (10471107)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20060486001)
文摘Under the appropriate hypotheses subject to the unknown function and the free term, by means of our Lemma, we prove the rationality of order at x = ∞ on two sides for the characteristic singular integral equations with solutions having singularities of higher order on the real axis X. We transform the equations into solving equivalent Riemann boundary value problems with solutions having singularities of higher order and with additional conditions on X. The solutions and the solvable conditions for the former are obtained from the latter.
基金Project supported by the China Postdoctoral Science Foundation (Grant No. 2009450159)the Foundation of the State Key Laboratory of Optical Technologies for Micro-Frabrication and Micro-Engineering,Chinese Academy of Sciences (Grant No. KF001)
文摘Polarization singularities in the near-field of Gaussian vortex beams diffracted by a circular aperture are studied by a rigorous electromagnetic theory. It is shown that there exist C-points and L-lines, which depend on off-axis displacement parameters along the x and y directions, waist width, wavelength, and topological charge of the diffracted Gaussian vortex beam, as well as on propagation distance. The results are illustrated by numerical calculations.
基金supported by National Science Foundation of China (Grant No. 51472057)the Major Nanoprojects of Ministry of Science and Technology of China (2016YFA0200403)
文摘A Van Hove singularity(VHS) is a singularity in the phonon or electronic density of states of a crystalline solid. When the Fermi energy is close to the VHS, instabilities will occur, which can give rise to new phases of matter with desirable properties. However, the position of the VHS in the band structure cannot be changed in most materials. In this work, we demonstrate that the carrier densities required to approach the VHS are reached by gating in a suspended carbon nanotube Schottky barrier transistor. Critical saddle points were observed in regions of both positive and negative gate voltage, and the conductance flattened out when the gate voltage exceeded the critical value. These novel physical phenomena were evident when the temperature is below 100 K. Further, the temperature dependence of the electrical characteristics was also investigated in this type of Schottky barrier transistor.
基金Supported in part by the Key Project of the National Nature Science Foundation of China (No.60534020)the National Nature Science Foundation of China (No.60474037)the National 863 Plan of China (No.2002AA755026)
文摘Parallel manipulator is associated with a set of functions defined by its closure constraints. In this paper, using Lie algebra method, we provide a study on the singularities of parallel manipulators, their relations with the second order of the closure functions, and the tangent space of the configuration space of the manipulator. The transverse condition criterion is applied to analyze the behavior of the singularities. This gives a downright explication why the 6R paradoxical mechanisms work in their singular configurations, and allows to gain insight on configuration space singularities and to choose the adequate design parameters for the parallel manipulator.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12074049 and 12047564)the Fundamental Research Funds for the Central Universities,China (Grant Nos.2020CDJQY-Z006 and 2020CDJQYZ003)the Research Foundation of SWUST (Grant No.21zx7141)。
文摘The evolution of polarization singularities supported in a one-dimensional periodic plasmonic system is studied.The lateral inversion symmetry of the system,which breaks the in-plane inversion symmetry and up-down mirror symmetry simultaneously,yields abundant polarization states.A complete evolution process with geometry for the polarization states is traced.In the evolution,circularly polarized points(C points)can stem from 3 different processes.In addition to the previously reported processes occurring in an isolated band,a new type of C point appearing in two bands simultaneously due to the avoided band crossing,is observed.Unlike the dielectric system with a similar structure which only supports at-Γbound states in the continuum(BICs),accidental BICs off theΓpoint are realized in this plasmonic system.This work provides a new scheme of polarization manipulation for the plasmonic systems.
基金Project support by the Open Foundation of the Sate Key Laboratory of Optical Technologies for Micro-Fabrication & Micro-Engineering,Chinese Academy of Sciences,and China Postdoctoral Science Foundation (CPSF) (Grant No. 2009450159)
文摘In this paper, the relation between the spectral degree of coherence and degree of polarization of random electromagnetic beams is derived by the Stokes parameters. And the concept of polarization singularity is extended from spatially fully coherent beams to partially coherent electromagnetic beams. Theoretical analysis shows that correlation vortices are linearly polarized singularities. The results are illustrated by numerical examples.
