Research Of Topological Photonics In Low-dimensional Systems With Modulation

The topological phase,appearing together with topological phase transition,is a kind of special phases of matters.They are described by the new parameter,i.e.,topological order.Topological phase transition is different from traditional phase transition due to symmetry unchanged during phase transition.The first example of topological phenomenon is the integral quantum Hall effect.After that,a series of topology related phenomena have been found.The discovery of topological insulator based on spin-orbit coupling triggered a wave research for topological matters.Under this background,the research about finding possible topological phenomena in photonic system have been unfolded.In optical micro-and nano-structures,for example,photonic crystal and metamaterials,using special optical materials plus external magnetic field or designing the structure of system,the topological phenomena similar with that of electronic materials have been produced and confirmed.The edge states,which are protected by topology and propagate along the boundary of system,have been found too.Due to the robust of the edge states,topological study is potential for application in photonics.Thus the research about topological photonics are paid attention more and more.The thesis focuses on hot topics of present research in topological photonics.We focus on on-chip integrated one dimensional and two dimensional optical structures with micrometer and nanometer scale,including one dimensional coupled waveguide arrays,two dimensional disk optical resonators lattices and two dimensional lattice consisted of rotated microring resonators.We study systematically the topological phenomena in these systems,especially,the edge states protected by topology.It should be noted that the researches in this thesis all have been done with the help of modulation with periodicity.In fact,the methods have become a branch of topological physics,that is using Floquet-Bloch Theorem to dynamically produce topological states.So far the Floquet topological insulator and photonic Floquet topological insulator have been proposed and realized by this method.Here we propose some schemes to produce photonic topological phenomena in low-dimensional integrated optical structures via an external periodic modulation combined with design of the lattice structure.We think these results are significance to theoretical and experimental studies on topological photonics and applications in integrated optical devices.Three results for this thesis are as follow:1.Based on breaking the inversion symmetry and inducing artificial gauge field,we propose two models to produce Weyl points in two dimensional disk micro-resonators arrays via the modulation of frequency and phase of the external optical field.We demonstrate that there are Weyl points and related Fermi arcs in both two models as long as the frequency and phase of modulation,materials and radii of resonators satisfy certain conditions.We find the optical edge sates protected by topology in the two models.And we illustrate the two models are both realizable in current technique.2.We propose a curved nonparallel coupled waveguide arrays.By using Floquet-Bloch Theorem we find the dispersion is different from the parallel coupled waveguide arrays.Simulation is performed to illustrate the propagation properties of light.Furthermore,We study the relation between the arrays and Su-Schrieffer-Heeger(SSH)model,and point out the effect of dynamic modulation of coupling coefficients on Z2 topological order in the system.We show the evidence of edge modes existing in boundary and the propagation of the edge modes.3.Due to the optical Sagnac effect in a rotated micro-ring resonator the two counter-propagating cavity modes form a pair of non-degenerate pseudo-spin.Here we mimic the Zeeman effect of electron in magnetic field in this system via the artificial magnetic field induced by rotation and find the one-way coupling of the single rotated micro-ring resonator.By arranging the resonators in a two-dimensional hexagonal lattice and using the artificial magnetic field together with the nearest-neighbor coupling we realize the photonic topological effect.The result indicates that the topological and one-way transmission properties of the edge sates exist in the system.We discuss the relationship between topological insulator and the system.