Study On Topological Mode Switch And Edge Mode In Optical Waveguides Based On Third-order Exceptional Point

Exceptional points(EP) are singular points where two or more eigenvalues and their corresponding eigenvectors coalesce in parameter space of the system.In physical system,the behavior of the mathematical model at this point is quite different from that of the neighboring points.This special degenerate point mainly exists in the non-Hermitian system which energy exchanges with the surrounding environment.In the past two decades,people have been paid more and more attention on non-Hermitian system,especially the systems related to the concept of parity-time symmetry.In recent years,non-Hermitian system has attracted great attention in optics.Gain and loss in optical system can be flexibly adjusted with the progress of processing technology.As a result,the photonic system can be utilized to examine the concept of non-Hermitian physics.Furthermore,novel artificial materials and structures with new optical properties can be designed and produced based on nonHermitian concept.The third-order EP emerges when the three eigenvalues and their corresponding eigenvectors coalesce at the same time.Previous studies have shown that the performance of optical sensors can be greatly improved near the third-order EP.However,its topological characteristics have not been well studied.For the third-order EP,the research of this paper is mainly divided into the following two aspects:In this paper,we first introduce a non-Hermitian three-waveguide structure which can effectively generate the third-order EP.We comprehensively study the topological response of the eigenmode near the third-order EP.A third-order EP point is obtained by reasonably setting the waveguide parameters.By suitably changing the loss variable,the third-order EP point gradually splits into two second-order EP points,which are separated further and further in the Riemannian surface.All EPs have very good topological response to the transformation of eigenmodes.The transformation path of the eigenmode can be clearly reflected on the Riemannian surface by encircling the EP.Similar to the mode conversion in the two-waveguide system,the conversion between the eigenmodes also has the chiral and non-chiral behavior by different starting points in the same path when the third-order EP is dynamically encircled in the three-waveguide system.There are more EP in the threewaveguide structure and thus more plentiful topological response are discovered.The new physical phenomena revealed in the three waveguide system can be utilized to design novel optical devices in the multimode system.We also simulated the non-Hermitian Aharonov-Bohm cage in waveguide array arranged in a diamond lattice,and studied its optical propagation characteristics.In particular,we introduce imaginary coupling coupling into the system,which is realized by introducing auxiliary waveguide into the optical waveguide and adding gain and loss.By properly setting the real and imaginary coupling of the system,the mode field between adjacent elements can effectively generate a magnetic flux of ?,forming an Aharonov-Bohm cage.The results show that the system can support the gapped topological edge modes even when the bulk band structure coalesces into third-order EP over the whole Brillion zone.By mapping the Hamiltonian of the system to the square root of the anti-PT symmetric system,the topological characteristics of the system are revealed.In addition,the optical wave dynamics of bulk and edge modes are studied by simulation.They show complete localization and diffraction free propagation.In addition,under the local excitation,according to the different boundary points of the initial excitation,the power of the bulk mode increases linearly,and the propagation of the edge mode may be conservative or exponentially amplified.This study provides an effective scheme for the realization of robust optical propagation.