Novel Light Transfer Behaviors Based On SU(2) Symmetry And Fractional Topology In Non-hermitian Optical Systems

This thesis mainly focuses on the 1D non-Hermitian optical systems.The non-Hermitian system is a special open system,which possessing independence and maneuverability.It is usually complicated and difficult to describe an open system,but a non-Hermitian system can be discussed by a non-Hermitian Hamiltonian and the corresponding von Neumann equation,that leads to great simplification in the study process.In recent years,the study of non-Hermitian system attracts much attention,for one thing,it extends the research scope of quantum mechanics to open systems,and for another thing,the special properties of non-Hermitian Hamiltonian may lead to a series of physical phenomena which are significantly different from that in the typical Hermitian systems.On another front,owing to the formal equivalence between the paraxial wave equation and the Schrodinger equation,the non-Hermitian description may also be applied to a variety of nonconservative classical optical systems.In this thesis we construct a series of 1D non-Hermitian optical systems,combine Them with the SU(2)symmetry(Chapters Ⅲ and Ⅳ)and chiral symmetry(ChapterⅤ),and the corresponding novel optical phenomena are discussed.First,we study the 1D systems with limited lattices and use SU(2)symmetry to construct higher-order EP points.Utilizing ring resonator array(Chapter Ⅲ)or waveguide array(Chapter Ⅳ)as physical models,the optical phenomena near EP points are studied.Then on this basis,in Chapter V we extend the research object to 1D system with infinite lattices and use chiral symmetry to make the system have fractional topological order related to EP points,and then the regulating effect of the synthetic gauge field is discussed.The details are listed as follows:Chapters Ⅰ and Ⅱ are the introductions of research background and relevant theoretical bases.In Chapter Ⅲ,we construct a parity-time(PT)symmetric 1D multi-mode ring resonator array and adjust the parameter setting such that the array possesses underlying symmetry given by SU(2)group.Following a Gilmore-Perelomov coherent state approach,the eigenvalue problem of the evolution matrix can be simplified greatly,and the distribution of high-order exceptional points(EPs)that attributes to SU(2)symmetry is discussed.It can be found that the transmission spectrum especially the pattern of transmission peaks undergoes a dramatic change around the high-order EPs.As a comparison,we then adjust the coupling coefficients so that the SU(2)symmetry is no longer held.The high-order EPs break up into a series of low order EPs,and the original clear boundary between the PT unbroken and broken regions is replaced by a transition region,and interesting phenomena happen in this region,such as the coexistence of divergent and non-divergent peaks and multi-number of Breit-Wigner peaks.Compared to earlier studies,this diversity of transmission spectrum may provide new ideas for the construction of optical system.In Chapter Ⅳ,we turn our attention to non-Hermitian SU(2)symmetric waveguide arrays.Compared with the ring resonator arrays,since the Schrodinger-like equation that describes the waveguide array takes the partial derivative of propagation distance z rather than time t,thus we can intuitively observe the evolution process from the light intensity distribution.In the beginning,we study the PT symmetric array and explore the evolution progress following the Schrodinger-like equation utilizing the intensity distribution graphic along the propagating direction,and we found that the evolutionary behavior changes dramatically near the high-order EP.Then we build a mode-coupling matrix of antiPT symmetry,and using assistant waveguides and adiabatic approximation approach,we construct the equivalent imaginary coupling coefficient,thus the antiPT symmetric mode-coupling matrix may correspond to an N modes waveguide array that supports another transition between distinct light transfer behaviors around one N th-order EP.The extension of the waveguide array from PT symmetry to anti-PT symmetry not only gives full play to the advantage of the typical anti-PT symmetric systems in integrated optics,but also has enriched the evolution picture of the waveguide system especially for the oscillating behavior.In Chapter V,we study the generalized Aubry-Andre-Harpe(AAH)model which is a non-Hermitian topological insulator constructed by a 1D trimerized lattice of PT symmetry.We utilize the feature of convenience of optical systems to introduce a complex next-nearest-neighbor(NNN)coupling in each cell as well as the Peierls phase which is the usual approach of constructing a synthetic gauge field.Firstly,we investigate the relationship between the edge states and the fractional topological order and found that the number of edge states has a one-to-one correspondence with the total Zak phase.Then on this basis,we investigate influential role of synthetic gauge field on this model.As the Peierls phase increasing,the topological regions for one pair of edge states are extended and their localization strengths of photon distributions reinforced,and the other pair of edge states have the opposite trend.The newly induced influential progress is much like a magnetic field.Considering the typical AAH model is widely used in the study of localization phase transition,the introduction of synthetic gauge field not only provides a new degree of freedom for regulating quasi-periodic topological insulators,but also further enriches the theory of localization phase transition and has a positive effect on the study of non-Hermitian topological insulators.