The Study Of Higher-order Topological Photonic Crystals Based On Kagome Lattice

Benefiting from the rapid development of topological insulators,their analogs in optical systems,photonic topological insulators,have received more and more attention.Due to the unidirectionality and robustness of the edge states of photonic topological insulators,they have important applications in the fields of optical communication,optical information processing,and optical quantum computing.In recent years,research on photonic topological insulators has expanded from conventional topological states to higher-order topological states.Conventional topological insulators focus on topological states that are one dimension lower than the bulk dimension,while higher-order topological insulators focus on topological states that are more than two dimensions lower than the bulk dimension,and have a bulk-edge-corner correspondence that exceeds the traditional bulk-edge correspondence.Higher-order topological insulators can be divided into quadrupole topological insulators and Wannier-type topological insulators.Among them,Wannier-type topological insulators have been widely studied due to their clear concept and simple structure.Kagome lattice photonic topological insulators,like typical Wannier-type topological insulators,are an important platform to study higher-order topological phases and their phase transitions.At present,the research on higher-order topological insulators mostly focuses on the phase transition between trivial phases and higher-order topological phases,but the phase transitions between different higher-order topological phases are still rarely reported,and the application cases of higher-order topological insulators in photonic devices are insufficient.In response to these two problems,this paper is based on the kagome photonic crystals,and the following research results are obtained:1.We realize multiple higher-order topological phase transitions during periodic geometric deformation of kagome photonic crystals.The study found that the periodic geometric deformation between the kagome lattice and the triangular lattice can be achieved by changing only one geometric parameter.During this process,the system undergoes continuous phase transitions between three distinct topological phases,which are distinguished by bulk polarization and higher-order topological indices.By changing the geometric parameters and observing the changes in the supercell corner and edge states,we find that the corner and edge states only appear at the junction of different topological structures,and the frequency is regulated by the geometric parameters.Finally,we calculate the fractional charge values of the triangular supercells for different topological properties,revealing the higher-order topological properties of the bands.2.We realize topological rainbow trapping by exploiting higher-order topological corner states in kagome photonic crystals.Three higher-order topological phases exist in Kagome photonic crystals and can undergo phase transitions by expanding or rotation.The computational results show that the higher-order topological corner states exist only at the corners composed of different topological photonic crystals and the frequency is related to the geometric configuration of the corners.Based on this feature,we design a polygonal supercell containing various corner configurations.The simulation results show that the higher-order topological corner states are sequentially excited at the corners of the supercell in an anticlockwise(clockwise)direction with increasing frequency.Finally,we experimentally realized topological rainbow trapping based on a microwave band using the all-dielectric kagome photonic crystals platform.