| Non-Hermitian systems are considered to be a class of open systems governed by non-Hermitian Hamiltonians which extend the Hermiticity postulate and break conservation of energy induced by gain and loss,or are described as nonreciprocal systems with asymmetric coupling strength,exhibit distinctive energy degeneracy singularities that are called exceptional points(EPs),where the eigenvalues and the corresponding eigenvectors coalesce simultaneously.EPs are ubiquitous in nonHermitian systems,and relevant implementations have been realized in myriad platforms,especially in optical and photonic systems.The remarkable response of EPs to perturbations can enhance the sensitivity of sensing and detection systems,as well as the properties of EPs and their associated parity-time symmetric phase transition can enable considerable optical applications such as unidirectional invisibility,single-mode laser output,and coherent perfect absorption.An interesting feature of the non-Hermitian system is its topological structure,which is defined as the intersecting eigenvalue surfaces around the EPs.One of the most appealing phenomena is the asymmetric state conversion when dynamically encircling rather than parametrically encircling an EP in the parameter space,exhibiting a chiral transmission behavior,which can be attributed to the nonadiabatic transition between nonorthogonal eigenstates.Although the comprehensive theoretical explanation for the underlying mechanisms of nonadiabatic transitions is still ambiguous,some theoretical studies have provided insights,such as analyses using time evolution operators in the instantaneous eigenbasis,and analytical solutions in terms of special functions in twolevel non-Hermitian systems,etc.Furthermore,even if the parameters of system vary sufficiently and slowly during the encircling process,the non-Hermiticity will spoils the adiabatic theorem,leading to the irreversible nonadiabatic transitions.Both experimental and theoretical investigations have confirmed that this chiral behavior is protected by the topological structure of eigenvalue surfaces near the EPs,making it robust against certain parameter perturbations.The key to the chiral transmission characteristics lies in the self-intersecting lowest-loss eigenvalue surface of pairwise bifurcation topology shared by both sides around an EP.This raises the question on what the dynamics would be in non-Hermitian systems possessing multiple degenerate lowest-loss energy levels.Additionally,the prerequisite of traits that the conventional dynamical encirclement of enclosing an EP is broken when only encircling its proximity,preserving a still chiral switching.Previous literatures have explored the theory and experiments of encircling the vicinity of EPs to verify chiral transmission,however,the research on the proximity-encirclement is deficient in multistate systems.This thesis begins by providing a brief introduction to the concepts and applications of non-Hermitian EPs.It reviews the theoretical and experimental investigations on encircling EPs and summarizes some research methods and existing results related to the dynamical encirclement of EPs.Analyzing and discussing the aforementioned questions,the achievements of this research are obtained as follows:Theoretical study on the nonchiral transmission caused by dynamically encircling EPs in non-Hermitian systems with quasidegenerate energy levels.The investigation is addressed by studying a photonic-waveguide-array non-Hermitian system where two EPs are encircled dynamically.The system possesses four quasidegenerate lowest-loss eigenvalue surfaces and such topological structure results in an exotic nonchiral behavior for switching eigenstates,such that the final state is always a superposition of the four lowest-loss eigenstates.The robustness of this transmission behavior to perturbations in the length of the waveguide device and the form of the trajectories around encircling EPs is discussed,and it is demonstrated that once the quasidegenerate energy levels are broken and the related degeneracies are lifted,the system will restore the chiral transmission behavior.Moreover,by analyzing the evolution during the dynamically encircling EPs as the length of the waveguide array increases within a certain range,it is found that the location in parameter space where nonadiabatic transitions occur shifts,indicating that the nonadiabatic transitions occur earlier at a relative length of the device.Theoretical study on the proximity encirclement of multiple EPs in non-Hermitian systems.Another non-Hermitian system model based on photonic-waveguide-array was proposed to investigate the dynamics by encircling two EPs or their proximity.A series of encircling trajectories defined by the parametric equations are designed to steer the evolution of photonic modes in waveguides.The propagation of light along the waveguides is also simulated as wave scatterings to intuitively capture this nonHermitian physics and compare it to manifest the differences between dynamical proximity and conventional EP encirclement.It is found that the system will evolve to a stable final state earlier as a symbol of the possible occurrence of the nonadiabatic transition,if two EPs are sufficiently encircled,by solving a collection of dominant instantaneous real eigenstates during the overall evolution.Also,precise calculations of the encircling radius parameter within a fine range revealed a critical transmission behavior of the state conversion from nonchiral to chiral.As the encircling radius parameter increased start with small values that the encircling loop is far away from enclosing EPs to approach their proximity,and the critical radius parameter is unequal for each input mode or encircling direction.The study on the model evolution of dynamically encircling EPs in multilevel nonHermitian systems in this thesis can enrich the understanding of the dynamically encircling EPs,and may proffer some ideas for developing novel non-Hermitian photonic devices with anti-interference and robustness. |
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