Studies On The Topological Invariants And Interface States In One-dimensional Photonic Crystals

Topological insulators and topological semimetals are one of the hot topics in condense matter,the associated phenomenon,such as one-way robust transport,chiral anomaly and so on,have a grate application potential.Recently,the concept is also introduced into photonic systems,to realize some novel effects,including photonic quantum Hall effect,photonic quantum spin Hall effect,photonic valley Hall effect and so on.The Weyl points which defined in three dimensional space have also been proposed both in theories and experiments in last several years.In this thesis,we probe the topological invariants in one-dimensional photonic crystals.Furthermore,the interface states protected by topological invariants of photonic crystals have also been studied.The main content include:1.1.A brief introduction is taken on the topological invariants in various photonic systems,including Zak phase in one-dimensional systems,the topological insulators in two-dimensional systems(topological Chem insulators,topological Z2 insulators and topological crystalline insulators),and "topological semimetal" in three-dimensional systems(Dirac semimetals,Weyl semimetals and Nodal Line semimetals).The interface states,which were protected the topological invariants,have many novel phenomenon,and hence have great application potentials.2.The dispersion and eignfunction were deduced by transformation matrix.According to the bulk-edge correspondence,the reflection phase of the truncated photonic crystals was determined by the Zak phase of the photonic crystals.By introducing the interface states between metal films and photonic crystals,the Zak phases were measured in experiment.if replacing the metal films with metasurface,the interface states can be flexibly manipulated.3.We studied the dispersion of one-dimensional photonic crystals in a generalized three-dimensional space.Combining two geometric parameters of the photonic crystals with the Bloch momentum,a three-dimensional space can be constructed,and the Weyl points were observed there.The reflection phase of the truncated photonic crystals exhibits vortex in parameter space,which is protected by the Weyl points,and carries the same charge as the Weyl points.The vortex of reflection phase guarantee the existence of interface states between photonic crystals and any arbitrary reflecting medium.4.Topological phase transition has been observed in the one-dimensional photonic crystals in a four-dimensional space.Due to the dimension of a parameter space is not limited in three-dimensional,we introduce three geometric parameter,and construct a four-dimensional space together with the Bloch momentum.In the generalized space,the topological phase transition has been observed,while at the transition point,the dispersion behaves like the Nodal Line Semimetals in electric system.At these transition point,the photonic crystals will give a perfect transmission.