Photonic Higher-order Topological Insulator And Weyl Semimetal Phase Based On Artificially Periodic Structures

Photonic crystals and metamaterials are periodic artificial crystal structures,which present novel optical phenomena and realize the manipulation of electromagnetic waves through modifying the photonic dispersion relation via band engineering.In recent years,with the emergence of topological quantum materials and the development of energy band theory,photonic crystals and metamaterials have become ideal platforms for the research of topological photonics in various spatial dimensions.Based on the existence of band gap,this thesis mainly studies photonic topological insulators and photonic topological semimetals,which consists of the following four parts:Part Ⅰ:Higher-order topological corner states in the twisted photonic crystalQuadrupole topological insulators were recently discovered in flux-threading lattices as higher-order topological insulators which give access to topological wave trapping at both the edges and corners.Photonic crystals,lying at the boundary between continuous media and discrete lattices,however,are incompatible with the present quadrupole topological theory.Here,we unveil quadrupole topological photonic crystals triggered by a twisting degree of freedom.Using a topologically trivial 2D dielectric photonic crystal as the motherboard,we show that twisting induces quadrupole topology without flux threading.The twisting-induced crystalline symmetry enriches the edge polarization structure,leading to anomalous quadrupole topology.Versatile edge and corner phenomena are observed by tuning the twisting angle which controls simultaneously the photonic band gap and the Wannier gap.Our study paves the way toward topological twist-photonics and sheds light on quadrupole topology in the quasi-continuum regime for phonons,electrons,and polaritons.Part Ⅱ:Topological rainbow in Kagome latticeKagome lattice is another 2D lattice used to study higher-order topological physics,and its higher-order topological states appear in supercell structures composed of Kagome photonic crystals with different topological phases caused by the change of intra-unit-cell atoms.Using the dielectric cylinders,we construct the triangle,rectangle,and hexagon photonic crystal supercell,and find that different morphologies of corners have different mode frequencies.In particular,we design a polygon supercell that has topological corner states at four corners,and remarkably the order of the frequencies of these states are synchronized to the spatial order(clockwise or counterclockwise)of the corners in the polygon.Being different from the traditional rainbow trapping design,our work presents a new scheme which is based on topological corner states and might find potential applications in future integrated photonics.Part Ⅲ:Frequency-split Weyl points in Weyl metamaterialsWeyl point is the two-fold degenerate point where two energy bands cross linearly in three-dimensional momentum space.It can be described by the Weyl equation in relativistic quantum mechanics,and exhibits the physical properties,such as chirality,of Weyl fermions.Recently,it has been observed that two pairs of Weyl points take place in the photonic metamaterials based on a saddle-shaped metallic meta-atom.However,the total chirality of the Weyl metamaterials is zero because the Weyl points appear at the same frequency.By breaking the mirror symmetry of the saddle-shaped meta-atom structure,we theoretically investigate the chirality-dependent split in the frequencies of the Weyl points:the Weyl points of positive chirality redshift and those of negative chirality blueshift.Our experimental results reveal that the frequency-split Weyl points constitute an ideal system which exhibits a non-zero response of total chirality and is used to study the relativistic chiral physics.Part Ⅳ:Chiral magnetic transport phenomenon in Weyl metamaterialsThe Weyl points with different frequency for different chirality provide a material platform for research of imbalanced chirality physics.On the other hand,the intra-cell rotation of the saddle-shaped meta-atom structure in the Weyl metamaterial causes Weyl points to translate in momentum space,and this momentum displacement can be equivalent to the magnetic vector potential.Furthermore,a pseudo-magnetic field is generated through spatial non-uniform distribution of the rotation angle.In this part,we design a uniform pseudo-magnetic field using the rotation scheme in the Weyl metamaterials with mirror symmetry breaking,i.e.frequency-split Weyl points,and observe the Landau zero-mode response with non-zero total chirality.The imbalanced chiral species and the magnetic field are two key factors to realize the chiral magnetic effect that is a novel effect for Weyl fermions.Our synergistic realization of these two factors in spatially inhomogeneous Weyl metamaterials makes it possible to study chiral magnetic effects in photonic systems.Combine the characteristics of photonic band,we research the higher order topological corner states and the chiral phenomena of Weyl semimetals in photonic materials.These results are expected to be widely used in construction of optical manipulation devices,low power devices and nano-photonic devices.