Topology is the study of geometrical properties and spatial relations unaffected by continuous changes and has become an important tool for understanding complex physical systems.Although recent optical experiments ha...Topology is the study of geometrical properties and spatial relations unaffected by continuous changes and has become an important tool for understanding complex physical systems.Although recent optical experiments have inferred the existence of vector fields with the topologies of merons,the inability to extract the full three-dimensional vectors misses a richer set of topologies that have not yet been fully explored.We extend the study of the topology of electromagnetic fields on surfaces to a spin quasi-particle with the topology of a meron pair,formed by interfering surface plasmon polaritons(SPPs),and show that the in-plane vectors are constrained by the embedding topology of the space as dictated by the Poincaré–Hopf theorem.In addition,we explore the time evolution of the three-dimensional topology of the spin field formed by femtosecond laser pulses.These experiments are possible using our here-developed method called polarimetric photo-emission electron microscopy(polarimetric PEEM),which combines an optical pump–probe technique and polarimetry with PEEM.This method allows for the accurate generation of SPP fields and their subsequent measurement,revealing both the spatial distribution of the full three-dimensional electromagnetic fields at deep subwavelength resolution and their time evolution.展开更多
基金support from the ERC(Complexplas,3DPrintedoptics),DFG(SPP1391“Ultrafast Nanooptics,”CRC 1242“Non-Equilibrium Dynamics of Condensed Matter in the Time Domain”Grant Nos.278162697-SFB 1242 and GRK2642“Photonic Quantum Engineers”),BMBF(Printoptics),BW Stiftung(Spitzenforschung,Opterial),Carl-Zeiss Stiftungsupport from the MPI vip Professorship Program and from the DFG(Grant No.GRK2642“Photonic Quantum Engineers”)for a Mercator Fellowship.
文摘Topology is the study of geometrical properties and spatial relations unaffected by continuous changes and has become an important tool for understanding complex physical systems.Although recent optical experiments have inferred the existence of vector fields with the topologies of merons,the inability to extract the full three-dimensional vectors misses a richer set of topologies that have not yet been fully explored.We extend the study of the topology of electromagnetic fields on surfaces to a spin quasi-particle with the topology of a meron pair,formed by interfering surface plasmon polaritons(SPPs),and show that the in-plane vectors are constrained by the embedding topology of the space as dictated by the Poincaré–Hopf theorem.In addition,we explore the time evolution of the three-dimensional topology of the spin field formed by femtosecond laser pulses.These experiments are possible using our here-developed method called polarimetric photo-emission electron microscopy(polarimetric PEEM),which combines an optical pump–probe technique and polarimetry with PEEM.This method allows for the accurate generation of SPP fields and their subsequent measurement,revealing both the spatial distribution of the full three-dimensional electromagnetic fields at deep subwavelength resolution and their time evolution.
