Design And Research Of Topological Lasers Based On Two-Dimensional Valley Photonic Crystals

Photonic crystals are a periodic structural with great potential for light manipulation.However,photonic devices based on photonic crystals inevitably have disorders and defects during processing,which leads to scattering losses.What’s more,the loss will increase as the device size becomes smaller,which severely limits the development of miniaturization of photonic devices.The emergence of optical topological states that are immune to defects and have backscatter suppression can pave a new way for designing and realizing the low-loss photonic integrated chips and optical communication devices,revolutionizing the development of optical communication.Various photonic topological insulators and topologically protected photonic states were realized either by breaking time-reversal symmetry with applied magnetic fields,construction of pseudospin states protected by time-reversal symmetry or spatial inversion symmetry breaking.In particular,richer fundamental physics can be achieved by employing nonlinear light-matter interactions in active topological photonic systems,thus opening up new prospects for applications such as topological lasers.In this thesis,we design an all-dielectric valley photonic crystal based on the honeycomb lattice in the telecommunication region by means of the quantum valley Hall effect,and study the unidirectional and anti-scattering transmission characteristics of the topological edge states.On this basis,we propose the triangular resonant cavity based on the valley photonic crystal and analyze the resonance characteristics of the resonant cavity in detail.In addition,topological laser structure based on the valley photonic crystal cavities is designed.The proposed topological laser with a small footprint and low loss provides a novel strategy for realizing the ultra-small light sources.The main works are as follows:(1)Summarize the development process and research situation of two-dimensional photonic topological insulator,topological valley photonics and topological insulator lasers.Compared the advantages and disadvantages of the main implementation schemes.(2)Introduce the concepts of topological invariance and Berry curvature,and calculated the topological invariant in quantum Hall systems,quantum spin Hall systems and quantum valley Hall systems.Discuss numerical calculation methods for photonic crystals and deduce the tight-binding approximation and Finite-Difference Time-Domain.Briefly introduce the performance evaluation index of photonic crystal nanocavities and derive in detail the rate equation of four-level two-electron model for modeling lasers.(3)We propose a valley photonic crystal,which introduces the valley degrees of freedom by adjusting the spatial structure of the photonic crystal.Valley edge states with the unidirectionality and robustness appear in the domain walls of photonic crystal structures with different topological properties Topological corner states arise at the structure with zigzag interface,which can exist stably because the frequency of corner states different from that of the edge states.(4)We design a topological resonant cavity based on the valley photonic crystal,and study the performance of the resonant cavity with bearded interface.On this basis,we explore the lasing actions of the topological laser based on the bearded interface resonant cavity by a fourlevel two-electron model.Moreover,the lasing actions of all topological states in the optical frequency range can exist in the zigzag interface resonant cavity structure,i.e.,multihierarchical laser in two-dimensional bulk,one-dimensional edge,and zero-dimensional corner states.