To explore the effect of non-uniform polarization on orbital angular momentum(OAM) in anisotropic medium, in this work investigated are the evolution of the spiral spectra and OAM densities of non-uniformly polarized ...To explore the effect of non-uniform polarization on orbital angular momentum(OAM) in anisotropic medium, in this work investigated are the evolution of the spiral spectra and OAM densities of non-uniformly polarized vortex(NUPV)beams in uniaxial crystals propagating orthogonal to the optical axis, and also the case of uniformly polarized vortex(UPV)beams with left-handed elliptical polarization. In the input plane, the NUPV beams present their spiral spectra of m-mode concentrated at m = l ± 1 modes rather than m = l mode, and reveal the relation among topological charge l, mode of spiral spectra m and the power weight value Rmexpressed by l=∑^(∞)_(m)=-∞Rm. is still satisfied for UPV beams in uniaxially anisotropic crystals, whereas for NUPV beams their relations are no longer valid owing to non-uniform polarization. Furthermore, the analysis indicates that the asymmetrical distribution of power weight of spiral spectra and the non-zero value in the sum of longitudinal OAM densities originate from the initial non-uniform polarization and anisotropy in uniaxial crystals rather than topological charges. In addition, the relation between spiral spectrum and longitudinal OAM density is numerically discussed. This work may provide an avenue for OAM-based communications,optical metrology, and imaging by varying the initial non-uniform polarization.展开更多
We investigate the dynamic quantities:momentum,spin and orbital angular momenta(SAM and OAM),and their conversion relationship in the structured optical fields at subwavelength scales,where the spin–orbit interaction...We investigate the dynamic quantities:momentum,spin and orbital angular momenta(SAM and OAM),and their conversion relationship in the structured optical fields at subwavelength scales,where the spin–orbit interaction(SOI)plays a key role and determines the behaviors of light.Specifically,we examine a nanostructure of a Ag nanoparticle(Ag NP)attached on a cylindrical Ag nanowire(Ag NW)under illumination of elliptically polarized light.These dynamic quantities obey the Noether theorem,i.e.,for the Ag nanoparticle with spherical symmetry,the total angular momentum consisting of SAM and OAM conserves;for the Ag NW with translational symmetry,the orbital momentum conserves.Meanwhile,the spin-to-orbital angular momentum conversion is mediated by SOI arising from the spatial variation of the optical potential.In this nanostructure,the conservation of momentum imposes a strict restriction on the propagation direction of the surface plasmon polaritons along the Ag NW.Meanwhile,the orbital momentum is determined by the polarized properties of the excitation light and the topography of the Ag NP.Our work offers insights to comprehend the light behaviors in the structured optical fields in terms of the dynamic quantities and benefits to the design of optical nano-devices based on interactions between spin and orbital degrees of freedom.展开更多
The magnetic charge concept is further developed to define the vibrational motion of a charged particle moving in the ether/dark matter. The angular momentum of the resulting motion is derived to be ħ/2 at all velocit...The magnetic charge concept is further developed to define the vibrational motion of a charged particle moving in the ether/dark matter. The angular momentum of the resulting motion is derived to be ħ/2 at all velocities. The vibrational motion also provides additional justification for the Coulomb and gravitational forces not having a singularity. Additional insights into antimatter composition and annihilation are also developed.展开更多
Mahto et al. have shown δS≥0 and M2=a*J by using the first law of the black hole mechanics in the vacuum and Einstein mass-energy equivalence relation specially for spinning black holes. In the presen...Mahto et al. have shown δS≥0 and M2=a*J by using the first law of the black hole mechanics in the vacuum and Einstein mass-energy equivalence relation specially for spinning black holes. In the present paper, this work is extended to propose a model for the change in mass of the spinning black holes due to corresponding change in the angular momentum for maximum & half spin parameter of black holes (a* = 1 & 1/2) and calculated their values for different test black holes in XRBs and AGN. We have also shown that the change in mass of the spinning black holes due to corresponding change in the angular momentum for maximum spinning rate of black holes (a* = 1) is double to that of the spinning black holes having spinning parameter (a* = 1/2).展开更多
In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter canno...In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work, we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrödinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.展开更多
As an inherent degree of freedom,total angular momentum(TAM)of photons consisting of spin angular momentum and orbital angular momentum has inspired many advanced applications and attracted much attention in recent ye...As an inherent degree of freedom,total angular momentum(TAM)of photons consisting of spin angular momentum and orbital angular momentum has inspired many advanced applications and attracted much attention in recent years.Probing TAM and tailoring beam’s TAM spectrum on demand are of great significance for TAM-based scenarios.We propose both theoretically and experimentally a TAM processor enabling tunable TAM manipulation.Such a processor consists of a set of quasi-symmetric units,and each unit is composed of a couple of diffraction optical elements fabricated through polymerized liquid crystals.Forty-two single TAM states are experimentally employed to prove the concept.The favorable results illustrate good TAM state selection performance,which makes it particularly attractive for high-speed large-capacity data transmission,optical computing,and high-security photon encryption systems.展开更多
The present paper gives a theoretical model for the change in entropy of spinning black holes due to change in mass to use the first law of black hole mechanics for unit spinning parameter and angular momentum in XRBs...The present paper gives a theoretical model for the change in entropy of spinning black holes due to change in mass to use the first law of black hole mechanics for unit spinning parameter and angular momentum in XRBs. This shows that the entropy change with respect to the mass of uncharged spinning black holes is essentially the function of mass and their surface gravity are lesser than to that of the non-spinning black holes.展开更多
Spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. It is wildly believed that spin is a purely quantum mechanical concept and has no classical analog...Spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. It is wildly believed that spin is a purely quantum mechanical concept and has no classical analogue. In fact, elementary particles are conceived as point objects which have no axis to “spin” around. Therefore, there is no explaining how spin arises at the fundamental level, why particles have the values they do, and what underpins the Pauli Exclusion principle and Bose-Einstein behavior. However, spin is like a vector quantity;it has a definite magnitude, and it has a “direction”, in order to spin should be composite. In this paper we propose a physical explanation for spin of the electron at the sub-particle level, relying on the vortex model of the electron. The electron is described as a superfluid frictionless vortex which has a mass, angular momentum and spin to provide a complete explanation of all properties of the electron: it composite, spinning around its own axis, produces a tiny magnetic fields independent of those from its orbital motions. The classical hydrodynamic laws are used to describe the quantum properties of the electron, such as spin, angular momentum, magnetic momentum and a magnetic dipole. The circulation in the vortex is constant, and the angular momentum of the vortex is conserved and has the same value of Planck constant. The direction of the angular momentum of a spinning electron vortex is along the axis of rotation and determined by the direction of spin. The spin quantum number 1/2 has a fixed value which represents the gap between the circulation rate of the core of the vortex and the boundaries of the vortex. The changeable values +1/2 “spin-up” or -1/2 “spin-down” indicate the direction of the magnetic dipole of the vortex. The relation between spin and Planck constant is discussed and the origin h/4pi angular momentum units are revealed.展开更多
We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin(LS)eigenspaces within the n-fold antisymmetrized tensor product∧^(n)V_(u),where n is the number of electrons and ...We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin(LS)eigenspaces within the n-fold antisymmetrized tensor product∧^(n)V_(u),where n is the number of electrons and u=s,p,d,…denotes the atomic subshell.This is an essential step for dimension reduction in configurationinteraction(CI)methods applied to atomic many-electron quantum systems.The algorithm relies on the observation that each Lz eigenstate with maximal eigenvalue is also an L2 eigenstate(equivalently for Sz and S2),as well as the traversal of LS eigenstates using the lowering operators L−and S−.Iterative application to the remaining states in∧^(n)V_(u)leads to an implicit simultaneous diagonalization.A detailed complexity analysis for fixed n and increasing subshell number u yields run time O(u^(3n−2)).A symbolic computer algebra implementation is available online.展开更多
基金supported by the Science and Technology Program of Sichuan Province, China (Grant No. 23NSFSC1097)。
文摘To explore the effect of non-uniform polarization on orbital angular momentum(OAM) in anisotropic medium, in this work investigated are the evolution of the spiral spectra and OAM densities of non-uniformly polarized vortex(NUPV)beams in uniaxial crystals propagating orthogonal to the optical axis, and also the case of uniformly polarized vortex(UPV)beams with left-handed elliptical polarization. In the input plane, the NUPV beams present their spiral spectra of m-mode concentrated at m = l ± 1 modes rather than m = l mode, and reveal the relation among topological charge l, mode of spiral spectra m and the power weight value Rmexpressed by l=∑^(∞)_(m)=-∞Rm. is still satisfied for UPV beams in uniaxially anisotropic crystals, whereas for NUPV beams their relations are no longer valid owing to non-uniform polarization. Furthermore, the analysis indicates that the asymmetrical distribution of power weight of spiral spectra and the non-zero value in the sum of longitudinal OAM densities originate from the initial non-uniform polarization and anisotropy in uniaxial crystals rather than topological charges. In addition, the relation between spiral spectrum and longitudinal OAM density is numerically discussed. This work may provide an avenue for OAM-based communications,optical metrology, and imaging by varying the initial non-uniform polarization.
基金National Key R&D Program of China(Grant Nos.2017YFA0205700,2015CB932403,and 2017YFA0206000)the National Natural Science Foundation of China(Grant Nos.21790364,11374023,61422501,11674012,61176120,61378059,6097701,and 61521004).
文摘We investigate the dynamic quantities:momentum,spin and orbital angular momenta(SAM and OAM),and their conversion relationship in the structured optical fields at subwavelength scales,where the spin–orbit interaction(SOI)plays a key role and determines the behaviors of light.Specifically,we examine a nanostructure of a Ag nanoparticle(Ag NP)attached on a cylindrical Ag nanowire(Ag NW)under illumination of elliptically polarized light.These dynamic quantities obey the Noether theorem,i.e.,for the Ag nanoparticle with spherical symmetry,the total angular momentum consisting of SAM and OAM conserves;for the Ag NW with translational symmetry,the orbital momentum conserves.Meanwhile,the spin-to-orbital angular momentum conversion is mediated by SOI arising from the spatial variation of the optical potential.In this nanostructure,the conservation of momentum imposes a strict restriction on the propagation direction of the surface plasmon polaritons along the Ag NW.Meanwhile,the orbital momentum is determined by the polarized properties of the excitation light and the topography of the Ag NP.Our work offers insights to comprehend the light behaviors in the structured optical fields in terms of the dynamic quantities and benefits to the design of optical nano-devices based on interactions between spin and orbital degrees of freedom.
文摘The magnetic charge concept is further developed to define the vibrational motion of a charged particle moving in the ether/dark matter. The angular momentum of the resulting motion is derived to be ħ/2 at all velocities. The vibrational motion also provides additional justification for the Coulomb and gravitational forces not having a singularity. Additional insights into antimatter composition and annihilation are also developed.
文摘Mahto et al. have shown δS≥0 and M2=a*J by using the first law of the black hole mechanics in the vacuum and Einstein mass-energy equivalence relation specially for spinning black holes. In the present paper, this work is extended to propose a model for the change in mass of the spinning black holes due to corresponding change in the angular momentum for maximum & half spin parameter of black holes (a* = 1 & 1/2) and calculated their values for different test black holes in XRBs and AGN. We have also shown that the change in mass of the spinning black holes due to corresponding change in the angular momentum for maximum spinning rate of black holes (a* = 1) is double to that of the spinning black holes having spinning parameter (a* = 1/2).
文摘In quantum mechanics, there is a profound distinction between orbital angular momentum and spin angular momentum in which the former can be associated with the motion of a physical object in space but the latter cannot. The difference leads to a radical deviation in the formulation of their corresponding dynamics in which an orbital angular momentum can be described by using a coordinate system but a spin angular momentum cannot. In this work, we show that it is possible to treat spin angular momentum in the same manner as orbital angular momentum by formulating spin dynamics using Schrödinger equation in an intrinsic coordinate system. As an illustration, we apply the formulation to the dynamics of a hydrogen atom and show that the intrinsic spin angular momentum of the electron can take half-integral values and, in particular, the intrinsic mass of the electron can take negative values. We also consider a further extension by generalising the formulation so that it can be used to describe other intrinsic dynamics that may associate with a quantum particle, for example, when a hydrogen atom radiates a photon, the photon associated with the electron may also possess an intrinsic dynamics that can be described by an intrinsic wave equation that has a similar form to that for the electron.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFB3607700)the National Natural Science Foundation of China(Grant Nos.11834001 and 61905012)+3 种基金the National Defense Basic Scientific Research Program of China(Grant No.JCKY2020602C007)the Beijing Natural Science Foundation(Grant No.1232031)the Special Fund for Basic Scientific Research of Central Universities of China(Grant No.2022CX11006)the National Postdoctoral Program for Innovative Talents(Grant No.BX20190036).
文摘As an inherent degree of freedom,total angular momentum(TAM)of photons consisting of spin angular momentum and orbital angular momentum has inspired many advanced applications and attracted much attention in recent years.Probing TAM and tailoring beam’s TAM spectrum on demand are of great significance for TAM-based scenarios.We propose both theoretically and experimentally a TAM processor enabling tunable TAM manipulation.Such a processor consists of a set of quasi-symmetric units,and each unit is composed of a couple of diffraction optical elements fabricated through polymerized liquid crystals.Forty-two single TAM states are experimentally employed to prove the concept.The favorable results illustrate good TAM state selection performance,which makes it particularly attractive for high-speed large-capacity data transmission,optical computing,and high-security photon encryption systems.
文摘The present paper gives a theoretical model for the change in entropy of spinning black holes due to change in mass to use the first law of black hole mechanics for unit spinning parameter and angular momentum in XRBs. This shows that the entropy change with respect to the mass of uncharged spinning black holes is essentially the function of mass and their surface gravity are lesser than to that of the non-spinning black holes.
文摘Spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. It is wildly believed that spin is a purely quantum mechanical concept and has no classical analogue. In fact, elementary particles are conceived as point objects which have no axis to “spin” around. Therefore, there is no explaining how spin arises at the fundamental level, why particles have the values they do, and what underpins the Pauli Exclusion principle and Bose-Einstein behavior. However, spin is like a vector quantity;it has a definite magnitude, and it has a “direction”, in order to spin should be composite. In this paper we propose a physical explanation for spin of the electron at the sub-particle level, relying on the vortex model of the electron. The electron is described as a superfluid frictionless vortex which has a mass, angular momentum and spin to provide a complete explanation of all properties of the electron: it composite, spinning around its own axis, produces a tiny magnetic fields independent of those from its orbital motions. The classical hydrodynamic laws are used to describe the quantum properties of the electron, such as spin, angular momentum, magnetic momentum and a magnetic dipole. The circulation in the vortex is constant, and the angular momentum of the vortex is conserved and has the same value of Planck constant. The direction of the angular momentum of a spinning electron vortex is along the axis of rotation and determined by the direction of spin. The spin quantum number 1/2 has a fixed value which represents the gap between the circulation rate of the core of the vortex and the boundaries of the vortex. The changeable values +1/2 “spin-up” or -1/2 “spin-down” indicate the direction of the magnetic dipole of the vortex. The relation between spin and Planck constant is discussed and the origin h/4pi angular momentum units are revealed.
基金The author would like to thank Gero Friesecke for many helpful discussions,and DFG for financial support under project FR 1275/3-1.
文摘We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin(LS)eigenspaces within the n-fold antisymmetrized tensor product∧^(n)V_(u),where n is the number of electrons and u=s,p,d,…denotes the atomic subshell.This is an essential step for dimension reduction in configurationinteraction(CI)methods applied to atomic many-electron quantum systems.The algorithm relies on the observation that each Lz eigenstate with maximal eigenvalue is also an L2 eigenstate(equivalently for Sz and S2),as well as the traversal of LS eigenstates using the lowering operators L−and S−.Iterative application to the remaining states in∧^(n)V_(u)leads to an implicit simultaneous diagonalization.A detailed complexity analysis for fixed n and increasing subshell number u yields run time O(u^(3n−2)).A symbolic computer algebra implementation is available online.
