Research On Coupled Topological States And Their Applications In C₄ Symmetric Photonic Crystals

After the quantum Hall effect was discovered,topology as a branch of mathematics was introduced into condensed matter physics.A lot of topology-related theories and phenomena such as the quantum anomalous Hall effect,and quantum spin Hall effects are successively proposed and revealed,and topological state as a new state of matter has attracted a lot of attention.With the study of topological phase of matter from condensed matter physics to photon system,topological photonics has become one of the hot topics in the field of optics.At present,photonic quantum Hall effect,photonic quantum spin Hall effect and valley Hall effect have been found in photon system.Topological states in optics have strong application prospects,and their edge states are protected by topological properties,so they have good robustness and unique backscattering suppression.In addition,higher-order topological insulators recently found in electronic systems have also been introduced into photon system.Their lower-dimensional topological photonic states provide a new idea for multi-dimensional manipulation of light and device design based on topological photon.Therefore,this paper also study some topological phenomena in photon system,and put forward some related applications.Firstly,based on the two-dimensional photonic crystal with C₄ symmetric lattice,we propose a second-order photonic topological insulator.This paper can achieve the topological phase transition,by changing the distance of the dielectric cylinders.In the photonic topological insulator,this paper find an edge state and two corner states.The types of the two corner states are different,one is topological corner state and the other is trivial corner state.Our findings provide an evolution of bulk-corner-edge-corner-bulk in a hierarchy of dimensions,which enriches the study of corner states in photonic systems.In addition,by comparing the robustness and mode area to distinguish two corner states in this paper.And then by simulations,we find and verify the topological corner state can form a bound state in continuum,but trivial corner state cannot.Then,a sandwiched structure composed of ordinary-topological-ordinary photonic crystal slabs is proposed,resulting in two coupled edge states because of the coupling between topological edge states,which have high-capacity transport characteristics.Besides,a band gap is found between the two CESs when the coupling reached the strongest,and get two coupled corner states in the band gap by using a bend metastructure.We experimentally observe the various states:coupled edge states,coupled and topological corner states by using near-field scanning technology,which enables more flexible in the manipulation of the light field.This paper also compare the differences of the three corner states by calculating mode area,robustness.Finally,Based on C₄ symmetric two-dimensional topological photonic crystal,we realize topological rainbow capture in a structure with parameter gradient composed of ordinary-topological-ordinary sandwiched structure.In the proposed sandwiched structure,the two coupled topological edge states with different frequencies are separated and trapped in different positions,due to group velocity of near to zero.This paper have realized the dual-mode of topological rainbow in a structure,and the dual-mode of topological rainbow capture under single-mode excitation is also verified by using a simple bend design.Our work provides new ideas for guiding and localizing optical flow,while providing some practical cases for the coupling of topological states in photonic system.In addition,it can provide reference for other systems and has a wide application prospect.