Study On Stable Optical Propagation Mode Based On Topological Singularity And Patity-Time Symmetry

Symmetry is the key to the nature.Simultaneously,it can be found everywhere in nature and implied the features of various matter and phenomena,so it is ofen regarded as the most fundamental and significant concept in physics.In both classical mechanics and quantum mechanics,symmetries of a system allow one to make general statements about the system’s behaviors.Based on the mathematical analogies between electrodynamics and quantum mechanics,the symmetry in quantum mechanics is helpful to understand phenomena in the electromagnetic systems.On the condition that inversion symmetry is broken,the interactions between light and matter undergo fundamental changes and produce more abundant physical phenomena.This thesis mainly aims to realize stable optical mode transmission in optical waveguide systems based on topological singularity and parity-time(PT)symmetry.In addition to frequency,wavevector,polarization,and phase,nontrivial topology serves as a critical property of matarial,which is used to characterize global behavior of the wave function in the whole Brillouin zone.As such,it becomes an indispensable degree of freedom,and paves the way to find new physical phenemena.Due to the flexibility and diversity of the photonic systems,this category also opens up new opportunities for implementing intriguing topological models and exploring topological effects in new ways.Besides,PT symmetry occures in non-Hermiitan,which is invriant under the simultaneous parity(P)and time-reversal(T)symmetry operations.The spectra of PT symmetry can be real and have an degeneracy known as exceptional points(EPs).While this PT-symmetry induced degeneracy cannot be diagonizable.This thesis focuses on stable optical mode transmission in waveguides systems with structural defects or intrinsic loss of material.Along the line of Dirac point,Weyl point and topological protection interface states and the PT symmetry induced phase transition and loss induced transmission,this thesis performs the following studies:The existence of topological protected interface states in one-dimensional plasmonic and dielectric waveguides systems with inversion-symmetry breaking is explored.In topology,inversion symmetry or time-reversal symmetry breaking protected Weyl point behaves as a “magnetic monopole” in three-dimensional reciprocal space.Furthermore,the higher dimensional physics can be studied in lower dimenional structure.In order to simplify the structure,it is possible to study higher-dimensional Weyl physics in a low-dimensional space with synthetic space.If two energy bands of the one-dimensional inversion symmetry system are linearly intersected,and the eigenstates are exchanged when the wave vector passes through this point.Then the Dirac point can be transformed into the Weyl point in the three-dimensional synthetic space.Through the combination of transfer matrix method(TMM)and finite element numerical simulation,the interface states localized between the structural array and the trivial plasmonic or dielectric material in the geometric dimension space are investigated.The formation of interface states between two arrays with different inversion symmetry breaking types is studied.Dirac point in inversion symmetry acts as an intermediate transition point where the imaginary part of the surface impedance at the band gap becomes opposite.If the inversion symmetry is broken,the degenerate point is lifted,and the surface impedance is closly related to the type and degree of inversion symmetry breaking.As such,the connection between different inversion symmetry broken lattices determines the characteristics of the interface state.The effects of gain and loss on the real and imaginary parts of the propagation mode,and the resulting PT symmetry,quasi-PT symmetry and stable propagation modes in two dimensional waveguides system are studied.The formation of PT symmetry is not only required by the distribution of refractive index,but also depends on the symmetry of the decoupled modes.At the same time,the dispersion of the same modes and different modes coupling under uniform and nonuniform gain and loss distributions,and the resulting stable optical mode transmission are studied.Extended to two-dimensional photonic crystals,the interactions among multiple bands are explored when the gain and loss are turned on.Different spatial distributions of gain and loss lead to a thresholdless PT symmetric phase transition and the exceptional ring arising from the center or boundary of the Brillouin zone.Lastly,the non-Hermitian Su-Schrieffer-Heeger(SSH)model with PT symmetry is applied to study the edge states.If the Hamiltonian of this SSH model commutes with PT symmetric operator,there exist edge states of gain and loss in the band gap of the PT symmetric dispersion,and they are locally localized at the edges with smaller coupling coefficients.If topological defect is introduced in a finite lattices,the interface state with real eigenvalue exists at the defect point.In conclusion,topological photonics and PT symmetry greatly enrich the optical phenomena in the waveguide system,and have important significance for the lossless transport of optical modes and the application of interface transmission in on-chip system.The research in this thesis provides a flexible solution for the loss-induced transmission and the construction of topological protection interface states.At the same time,the results of the study are helpful in understanding the original quantum effects and can be applied in other classical wave systems such as acoustic waves and elastic waves.Furthermore,the research of this thesis can be naturally extended to the study of PT symmetry in the topological system.