Research On Light Propagation In Asymmetrically Coupled Few-layered Photonic Lattices

As one of the essential means of spatial light control,the discrete transmission of light waves is mainly realized by the combined action of the trapping of weak waveguides and the cou-pling of evanescent waves between adjacent waveguides.Many discrete optical systems,such as gratings and photonic crystals,are widely used to realize discrete light control due to their excellent device integration performance and significant research value and application prospects in optical communication,optical interconnection,photonic devices,and photonic integration.In practice,considering the boundary of the system,the research on the edge state of the optical system has always been one of the critical topics in the regulation of light transmission.And the previous research on the optical edge state mainly focuses on the ideal symmetric coupled optical system,that is,the energy exchange between adjacent waveguides is symmetrical.However,in reality,many optical systems have asymmetric couplings of en-ergy between adjacent waveguides,but related research is scarce.In this paper,the asymmet-ric coupled photonic lattice is used as the research platform,combined with coupled-mode theory,Bloch theorem,and other theories,to systematically study the propagation of light waves in bulk and at the boundary,focusing on the topological edge states and energy bands of the finite system.The inversion phenomenon aims to reveal the regulation law of light transmission in asymmetric coupling optical systems and provide theoretical and experimen-tal guidance for designing new photonic devices in the future.The specific research contents are as follows:The first chapter introduces the basic concepts of photonic lattices and the progress in the study of edge states of light waves,the concept of asymmetric coupled photonic lattices,and the advancement of light transmission in asymmetric coupled photonic lattices.In the second chapter,firstly,a physical model of an asymmetric coupled photonic lattice is constructed using the perturbation theory.Secondly,based on the knowledge of coupled-mode theory and quantum mechanics,the Hamiltonian and dispersion relation of the system is analytically solved.Then,combined with topological physics,the topological properties of the system are studied,the existence conditions of topological edge states are analyzed,and an equal light intensity mode with the undefined winding number in a non-Hermitian pho-tonic lattice is discovered for the first time.Finally,the edge state transmission of Gaussian light under topological conditions and the equal intensity transmission under topologically undefined states are deeply studied by simulation.And the defect method verifies the robust-ness of topological and topologically undefined states.This research provides a new way to control light transmission and realize the design of new photonics splitting devices,which are expected to be applied in new lasers and photonic integrated devices.In the third chapter,firstly,the effective magnetic field of photons is generated by in-troducing phase asymmetric coupling in a quasi-one-dimensional rhombus lattice.Then,the dispersion distribution function of the system is analyzed analytically,and it is found that the system has the phenomenon of band inversion.Further research found that the local oscil-lation of the edge state of the light and the forked transmission of the body state can both be realized by adjusting the intra-layer and inter-layer coupling coefficients κ_i and phase fac-torΦ.This research enriches the physical connotation of Hermitian photonics,provides a new idea for using the Hermitian photonics system to control light transmission,and is of great significance in optical communication.The fourth chapter is the conclusion and prospect of this thesis.We summarize the main work of the postgraduate stage,describe the innovation of the work,and then look forward to the future research direction and method based on the current work.