We present Floquet fractal topological insulators:photonic topological insulators in a fractal-dimensional lattice consisting of helical waveguides.The helical modulation induces an artificial gauge field and leads to...We present Floquet fractal topological insulators:photonic topological insulators in a fractal-dimensional lattice consisting of helical waveguides.The helical modulation induces an artificial gauge field and leads to a trivial-totopological phase transition.The quasi-energy spectrum shows the existence of topological edge states corresponding to real-space Chern number 1.We study the propagation of light along the outer edges of the fractal lattice and find that wavepackets move along the edges without penetrating into the bulk or backscattering even in the presence of disorder.In a similar vein,we find that the inner edges of the fractal lattice also exhibit robust transport when the fractal is of sufficiently high generation.Finally,we find topological edge states that span the circumference of a hybrid half-fractal,half-honeycomb lattice,passing from the edge of the honeycomb lattice to the edge of the fractal structure virtually without scattering,despite the transition from two dimensions to a fractal dimension.Our system offers a realizable experimental platform to study topological fractals and provides new directions for exploring topological physics.展开更多
Artificial gauge fields the control over the dynamics of uncharged particles by engineering the potential landscape such that the particles behave as if effective external fields are acting on them.Recent years have w...Artificial gauge fields the control over the dynamics of uncharged particles by engineering the potential landscape such that the particles behave as if effective external fields are acting on them.Recent years have witnessed a growing interest in artificial gauge fields generated either by the geometry or by time-dependent modulation,as they have been enablers of topological phenomena and synthetic dimensions in many physical settings,e.g.,photonics,cold atoms,and acoustic waves.Here,we formulate and experimentally demonstrate the generalized laws of refraction and reflection at an interface between two regions with different artificial gauge fields.We use the symmetries in the system to obtain the generalized Snell law for such a gauge interface and solve for reflection and transmission.We identify total internal reflection(TIR)and complete transmission and demonstrate the concept in experiments.In addition,we calculate the artificial magnetic flux at the interface of two regions with different artificial gauge fields and present a method to concatenate several gauge interfaces.As an example,we propose a scheme to make a gauge imaging system-a device that can reconstruct(image)the shape of an arbitrary wavepacket launched from a certain position to a predesigned location.展开更多
基金sponsored by the Israel Science Foundationby the US Air Force Office of Scientific Research(AFOSR)by an Advanced Grant from the European Research Council.
文摘We present Floquet fractal topological insulators:photonic topological insulators in a fractal-dimensional lattice consisting of helical waveguides.The helical modulation induces an artificial gauge field and leads to a trivial-totopological phase transition.The quasi-energy spectrum shows the existence of topological edge states corresponding to real-space Chern number 1.We study the propagation of light along the outer edges of the fractal lattice and find that wavepackets move along the edges without penetrating into the bulk or backscattering even in the presence of disorder.In a similar vein,we find that the inner edges of the fractal lattice also exhibit robust transport when the fractal is of sufficiently high generation.Finally,we find topological edge states that span the circumference of a hybrid half-fractal,half-honeycomb lattice,passing from the edge of the honeycomb lattice to the edge of the fractal structure virtually without scattering,despite the transition from two dimensions to a fractal dimension.Our system offers a realizable experimental platform to study topological fractals and provides new directions for exploring topological physics.
基金support by the Deutsche Forschungsgemeinschaft through CRC/Transregio 185 OSCAR(project No.277625399)support by an ERC Advanced Grant,by the Israel Science Foundationby the German-Israel DIP project.
文摘Artificial gauge fields the control over the dynamics of uncharged particles by engineering the potential landscape such that the particles behave as if effective external fields are acting on them.Recent years have witnessed a growing interest in artificial gauge fields generated either by the geometry or by time-dependent modulation,as they have been enablers of topological phenomena and synthetic dimensions in many physical settings,e.g.,photonics,cold atoms,and acoustic waves.Here,we formulate and experimentally demonstrate the generalized laws of refraction and reflection at an interface between two regions with different artificial gauge fields.We use the symmetries in the system to obtain the generalized Snell law for such a gauge interface and solve for reflection and transmission.We identify total internal reflection(TIR)and complete transmission and demonstrate the concept in experiments.In addition,we calculate the artificial magnetic flux at the interface of two regions with different artificial gauge fields and present a method to concatenate several gauge interfaces.As an example,we propose a scheme to make a gauge imaging system-a device that can reconstruct(image)the shape of an arbitrary wavepacket launched from a certain position to a predesigned location.
