Topological And Non-Hermitian Properties Of One-Dimensional Periodic Optical Structures

One of the mainstreams in optics and photonics research is to explore novel optical phenomena and effects,the underlying principle of which are further used to realize the manipulation of light flow and light field in various photonic structures.In recent years,the concepts of quantum systems or condensed matter physics,topology and non-Hermitian,have been extended to optical systems,leading to the generation of more bizarre phenomena.In analogy to the band theory in solid state physics,the band in periodic optical structures also can present a non-trivial topological phase,which leads to non-trivial topology of the photonic wave function on the whole band.The field of topological photonics,which uses its unique topological characteristics to control the behavior of light,provides a novel method to control light flow.At the same time,parity-time(PT)symmetric systems are also interesting yet extotic physitic system.The PT system can have real spectrum,and contains exceptional points,where eigenvalues and eigenvectors are identical.In periodic optical systems,and non-trivial topological phases can be obtained by adjusting their material and structure parameters.In order to further understand the topological and non-Hermitian properties of optical structures,it is necessary to analyze and understand the underlying principles behind the physical phenomena,and realize the functional photonic devices and possible applications with theoretical analysis.In this thesis,the one-dimensional periodic optical structure is used as the research platform.Starting from the symmetry of optical systems,we study the manifestation of optical modes in optical topological structures under Hermitian and non-Hermitian conditions,then elaborates and analyzes the topological and non-Hermitian optical phenomena with the help of numerical simulation,analytic calculation and machine learning.The main novel results contain the following three parts:Firstly,by researching a PT symmetric waveguide array with gain and loss,it is found that the edge states are isolated from the bulk states when the non-Hermitian is weak.However,the edge states and the bulk states are strongly hybridized with the increase of non-Hermitian.The strong mode hybridization is further verified by a non-Hermitian coupled mode theory developed from reaction conservation and phenomenological models.The study of the relationship between edge states and bulk states extends the understanding of topological optical properties under non-Hermitian conditions and contributes to realizing the optical applications of specific mode transformation.Secondly,based on the definition of scalar inner,which can restore the complete orthogonality of the modes in the non-Hermitian structures,the non-Hermitian port boundary condition are redefined with the finite element algorithm and is applied on a periodic PT planar waveguide array model.Comparing to Hermitian port,non-Hermitian port can realize no reflection transmission in the Hermitian and non-Hermitian system,as well as the evolution between PT exact phase and PT broken phase.At same time,by extracting and analyzing S parameters and calculating the quasi-energy conservation,the validity of the non-Hermitian port is further verified.Thirdly,the neural network algorithm can be used to calculate efficiently the topological phase of optical structures,which is the basis of constructing the edge states of optical topologies.By putting forward the concept of mapping physical parameter space with physical laws to operator parameter space,the physical adaptation network is constructed to improve the prediction ability(extrapolation ability)beyond the parameter range of the training set,which provides a new manner for the construction of optical topological structures.Taking the periodic double-layer plate-like optical structure as an example,considering different datasets,the physical adaptation network can accurately predict the topological phase transition outside the training set,even if the transition is not clearly given in the training dataset.