Hopfions are three-dimensional(3D)topological states discovered in field theory,magnetics,and hydrodynamics that resemble particle-like objects in physical space.Hopfions inherit the topological features of the Hopf f...Hopfions are three-dimensional(3D)topological states discovered in field theory,magnetics,and hydrodynamics that resemble particle-like objects in physical space.Hopfions inherit the topological features of the Hopf fibration,a homotopic mapping from unit sphere in 4D space to unit sphere in 3D space.Here we design and demonstrate dynamic scalar optical hopfions in the shape of a toroidal vortex and expressed as an approximate solution to Maxwell’s equations.Equiphase lines correspond to disjoint and interlinked loops forming complete ring tori in 3D space.The Hopf invariant,product of two winding numbers,is determined by the topological charge of the poloidal spatiotemporal vortices and toroidal spatial vortices in toroidal coordinates.Optical hopfions provide a photonic testbed for studying topological states and may be utilized as high-dimensional information carriers.展开更多
Abstract Experiments were conducted in a water tunnel by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The Reynolds number Reo is 2 460 on the base of momentum thickness. According to the physic...Abstract Experiments were conducted in a water tunnel by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The Reynolds number Reo is 2 460 on the base of momentum thickness. According to the physical mechanism of the stretch and compression of multi-scale vortex structures in the wall-bounded turbulence, the topological characteristics of turbulence statistics in logarithmic layer were illustrated by local-averaged velocity structure function. During coherent structures bursting, results reveal that the topological structures of velocity gradients, velocity strain rates and vorticities behave as antisymmetric quadrupole modes. A three-layer antisymmetric quadrupole vortex packet confirms that there is a tight relationship between the outer layer and the near-wall layer.展开更多
基金We acknowledge the support from the National Natural Science Foundation of China(NSFC)(92050202(Q.Z.),61875245(C.W.)),Shanghai Science and Technology Committee(19060502500(Q.Z.)),and Wuhan Science and Technology Bureau(2020010601012169(C.W.)).
文摘Hopfions are three-dimensional(3D)topological states discovered in field theory,magnetics,and hydrodynamics that resemble particle-like objects in physical space.Hopfions inherit the topological features of the Hopf fibration,a homotopic mapping from unit sphere in 4D space to unit sphere in 3D space.Here we design and demonstrate dynamic scalar optical hopfions in the shape of a toroidal vortex and expressed as an approximate solution to Maxwell’s equations.Equiphase lines correspond to disjoint and interlinked loops forming complete ring tori in 3D space.The Hopf invariant,product of two winding numbers,is determined by the topological charge of the poloidal spatiotemporal vortices and toroidal spatial vortices in toroidal coordinates.Optical hopfions provide a photonic testbed for studying topological states and may be utilized as high-dimensional information carriers.
基金supported by the National Natural Science Fundation of China (11272233)National Basic Research Program (973 Program) (2012CB720101)2013 Opening Fund of LNM,Institute of Mechanics,Chinese Academy of Sciences
文摘Abstract Experiments were conducted in a water tunnel by tomographic time-resolved particle image velocimetry （Tomo-TRPIV）. The Reynolds number Reo is 2 460 on the base of momentum thickness. According to the physical mechanism of the stretch and compression of multi-scale vortex structures in the wall-bounded turbulence, the topological characteristics of turbulence statistics in logarithmic layer were illustrated by local-averaged velocity structure function. During coherent structures bursting, results reveal that the topological structures of velocity gradients, velocity strain rates and vorticities behave as antisymmetric quadrupole modes. A three-layer antisymmetric quadrupole vortex packet confirms that there is a tight relationship between the outer layer and the near-wall layer.
