Field distribution of the Z_(2)topological edge state revealed by cathodoluminescence nanoscopy

Photonic topological insulators with robust boundary states can enable great applications for optical communication and quantum emission,such as unidirectional waveguide and single-mode laser.However,because of the diffraction limit of light,the physical insight of topological resonance remains unexplored in detail,like the dark line that exists with the crys-talline symmetry-protected topological edge state.Here,we experimentally observe the dark line of the Z_(2)photonic topo-logical insulator in the visible range by photoluminescence and specify its location by cathodoluminescence characteriza-tion,and elucidate its mechanism with the p-d orbital electromagnetic field distribution which calculated by numerical sim-ulation.Our investigation provides a deeper understanding of Z_(2)topological edge states and may have great signific-ance to the design of future on-chip topological devices.

Nonlinear topological valley Hall edge states arising from type-Ⅱ Dirac cones

A Dirac point is a linear band crossing point originally used to describe unusual transport properties of materials like graphene.In recent years,there has been a surge of exploration of type-II Dirac/Weyl points using various engineered platforms including photonic crystals,waveguide arrays,metasurfaces,magnetized plasma and polariton micropillars,aiming toward relativistic quantum emulation and understanding of exotic topological phenomena.Such endeavors,however,have focused mainly on linear topological states in real or synthetic Dirac/Weyl materials.We propose and demonstrate nonlinear valley Hall edge(VHE)states in laserwritten anisotropic photonic lattices hosting innately the type-Ⅱ Dirac points.These self-trapped VHE states,manifested as topological gap quasi-solitons that can move along a domain wall unidirectionally without changing their profiles,are independent of external magnetic fields or complex longitudinal modulations,and thus are superior in comparison with previously reported topological edge solitons.Our finding may provide a route for understanding nonlinear phenomena in systems with type-Ⅱ Dirac points that violate the Lorentz invariance and may bring about possibilities for subsequent technological development in light field manipulation and photonic devices.

Vector valley Hall edge solitons in the photonic lattice with type-Ⅱ Dirac cones

Topological edge solitons represent a significant research topic in the nonlinear topological photonics.They maintain their profiles during propagation,due to the joint action of lattice potential and nonlinearity,and at the same time are immune to defects or disorders,thanks to the topological protection.In the past few years topological edge solitons were reported in systems composed of helical waveguide arrays,in which the time-reversal symmetry is effectively broken.Very recently,topological valley Hall edge solitons have been demonstrated in straight waveguide arrays with the time-reversal symmetry preserved.However,these were scalar solitary structures.Here,for the first time,we report vector valley Hall edge solitons in straight waveguide arrays arranged according to the photonic lattice with innate type-II Dirac cones,which is different from the traditional photonic lattices with type-I Dirac cones such as honeycomb lattice.This comes about because the valley Hall edge state can possess both negative and positive dispersions,which allows the mixing of two different edge states into a vector soliton.Our results not only provide a novel avenue for manipulating topological edge states in the nonlinear regime,but also enlighten relevant research based on the lattices with type-II Dirac cones.

Floquet spectrum and optical behaviors in dynamic Su–Schrieffer–Heeger modeled waveguide array

Floquet topological insulators(FTIs) have been used to study the topological features of a dynamic quantum system within the band structure. However, it is difficult to directly observe the dynamic modulation of band structures in FTIs. Here, we implement the dynamic Su–Schrieffer–Heeger model in periodically curved waveguides to explore new behaviors in FTIs using light field evolutions. Changing the driving frequency produces near-field evolutions of light in the high-frequency curved waveguide array that are equivalent to the behaviors in straight arrays. Furthermore, at modest driving frequencies,the field evolutions in the system show boundary propagation, which are related to topological edge modes. Finally, we believe curved waveguides enable profound possibilities for the further development of Floquet engineering in periodically driven systems, which ranges from condensed matter physics to photonics.