Studies On The Light Bifurcation And Topological Interface State In Non-hermitian Photonic Lattice

The controlling of the transmission and evolution of light waves is a topic of considerable interest in the field of optics,which mainly refers to modulating the field's amplitude,frequency,polarization,dispersion of the light pulses and spatial distribution through typically optical effects,including electro-optic effect,acoustic-optics effect,and magneto-optics effect.With the development of quantum mechanics and condensed matter physics,the typical effects,such as the PT symmetry,non-Hermiticity,and topology are introduced into the field of photonics to modulate light waves and a large number of new phenomena emerged,which significantly promote the development of photonics.Based on the classical electromagnetic field theory and quantum theory,the thesis studies the non-Hermitian light waves' dynamics and the topologically protected edge state in open photonic lattice and investigates the modulation mechanism of non-Hermiticity and topology effects systematically on the spatial distribution and dispersion of light waves,aiming to explore new theories and methods for light wave controlling.The main research results are as following:In the first chapter,the basic concepts of non-Hermitian photonics and topological photonics are introduced,and corresponding phenomena are also included.Besides,the non-Hermitian topological photonics is briefly generalized.Finally,the main research contents of this thesis are summarized.In the second chapter,we introduce the basic theories about photonic lattice and gauge potential first.Then,we propose a one-dimensional PT-symmetric compound photonic lattice and construct the dynamic equation of light waves.Moreover,we study the effects of coupling and Peierls phase on bandstructure,group velocity,and the group velocity dispersion of the light waves.Next,we study the diffractionless light bifurcation phenomenon by numerical simulation and further study the effect of next-nearest neighbor coupling on the power ratio of two branches by fitting.The result provides a novel idea for optical switches and future all-optical paths.In chapter three,we construct a quasi-one-dimensional PT-symmetric photonic lattice.Based on the topological photonics and quantum theories,we compute the topological invariants of the lattice and realize the quantized Berry phase under PT symmetry.Then we study the influence of the non-Hermiticity on topological edge states by analyzing the energy spectrum and mode distribution.Finally,we further propose a combined PT-symmetric lattice and study the system's topological properties to realize stable topological states.The results provide a new idea for realizing the stable diffractionless transmission of light waves and have potential application in topological photonic devices.In chapter four,the conclusion and prospect of the thesis are presented.We summarized the principal results and innovation points in the thesis.Lastly,the outlook for further study are proposed.