Study On Edge States And Topological Edge States In Moiré Photonic Lattices

Photonic lattice is a coupled waveguide array modulated by refractive index change in photonic crystal.The wave equation in the photonic lattice and the Schr?dinger equation in the evolution of the wave function in the quantum system have the same mathematical form,and the spatial evolution of light in the photonic lattice can be likened to the time evolution of the wave function in the quantum system.Therefore,photonic lattice is an effective optical platform to study some physical phenomena in quantum mechanical systems and condensed matter physics.In addition,photonic lattice provides an important platform for the study of optical solitons,topological edge states,flat band local states and non-Hermitic optics.The moiré lattice is composed of the coherent superposition of two sublattices of the same periodic structure with relative rotation angles,and has a unique physical structure.In optics,moiré photonic lattices are used to probe a variety of fundamental phenomena,including light localization,optical solitons and edge states.Due to the diversity of coupled moiré lattice structures,it provides a new research platform for exploring edge states and topological physics of complex lattices.Edge states exist at the boundaries of two-dimensional systems.This is an interesting physical phenomenon in solid-state physics that plays an important role in transmission and brings broad prospects for the development of future electronic or optoelectronic devices.The topological edge state is a new state of matter with the properties of topologically protected transport and resistance to defect disorder.Topological edge states are the basis for exploring some physical phenomena and have become one of the main frontiers of condensed matter physics.Subsequently,topological concepts have appeared in various fields of physics,including photonics,acoustics,microwaves and atomics.Especially in the field of photonics,topological optical insulators have attracted increasing attention and have developed into one of the frontier fields of optics and photonics.Photonic lattices provide an important platform for research and development in the field of topological photonics,such as Floquet topological photonic insulators,topological edge solitons,nonlinear induced topological phase transitions and non-Hermitian topological states.In this thesis,our research work uses graphenelike moiré photonic lattice and square-octagonal moiré photonic lattice as experimental models to study edge states and topological edge states.First,we study the edge states of a graphenelike moiré photonic lattice,which is composed of two triangular sublattices of the same period with opposite and specific twist angles superimposed,and has a complex hexagonal structure.When the graphenelike moiré lattice is truncated into three types of edges similar to the graphene lattice,zigzag,bearded and armchair edges.By calculating the band structure,we found that only the zigzag edge supports edge states,while the other two edges do not support edge states.Using continuous laser direct writing technology,a zigzag edge graphenelike moiré photonic lattice was prepared.At the zigzag edge under linear and nonlinear conditions,we observed different edge states and angle states of the moiré photonic lattice under different excitations.Under linear conditions,esge states and corner states excitations couple into the nearest neighbor waveguide contained by the edge mode,whereas under nonlinear conditions,the detection light energy is localized in the initially excited waveguide.These findings contribute to the understanding of topological edge states and nonlinear edge solitons in moiré photonic lattices.In addition,following the discovery of the fourth type of edge in graphene lattice ——twig edge,we also studied the twig edge similar to graphene moiré lattice.By using the tightbinding approximation model,the energy band structure of the twig edge is calculated.The energy band structure shows that the twig edge also supports edge states,and its edge state mode distribution is calculated.Using laser writing technology,a graphene-like Moiré photonic lattice with twig edge was prepared,and a twig edge state was observed.Next,we studied the edge states in the square-octagonal moiré lattice.This moiré lattice is formed by the anti-phase superposition of two identical periodic square sublattices with opposite phases and specific twist angles.Five different edges were explored,namely type-Ⅰ zigzag edge,type-Ⅱ zigzag edge,type-Ⅰ bearded edge,type-Ⅱ bearded edge and armchair edge.Based on the idea of nearest-neighbor coupling in tight-binding approximation models,we calculated the band structures of five types of edges,and all five types of edges support edge states.We theoretically analyzed the edge states mode distribution corresponding to the eigenstates and eigenvalues of the edge state bands.The edge state mode distribution shows that in the band of the armchair edge and the type-Ⅱ bearded edge,multiple edge state bands support the same edge state.In the experiment,we used continuous wave laser direct writing technology to establish a square octagonal moiréphotonic lattice with five edges.We observed different edge states under different edge excitations and further verified the existence of five edge states.We find that the edge states supported by type-Ⅰ zigzag edge are topologically nontrivial,and the corresponding topological invariants are characterized by nonzero two-dimensional polarization.By simulating the dynamic evolution of edge states,the characteristics of topologically protected transport are demonstrated.Finally,we propose and demonstrate topological edge states of a graphenelike moiré lattice composed of helical waveguides.Longitudinal helical modulation generates an artificial gauge field that breaks the time-reversal symmetry of the graphenelike moiré photonic lattice system and forms a topological edge state.We calculated the Berry curvature and Chern number of all bulk bands to further verify the topological phase transition.We calculated the band structure of the helical waveguide-type graphenelike moiré lattice with zigzag edge and twig edge.The band structure shows that the bandgap opens and the Dirac point disappears,and the degenerate edge state is in the Floquet lattice transformed into a crossed one-way edge state,transformed into a topological edge state.We studied the propagation dynamics evolution of zigzag edge and twig edge topological edge states in graphenelike moiré lattice helical waveguide arrays,and found that the detection beam propagates unidirectionally along the edge,even in the presence of defective lattice points at the edge,does not couple within the lattice or backscatter,and has the capability of topologically protected transport.The research results of this thesis broaden people’s understanding of the edge states of coupled moiré photonic lattices.The moiré photonic lattice provides a new platform for exploring topological physics and has potential application prospects in the development of optical devices.