Study On Topological Edge States Of Photonic/Phononic Crystals

Over the past decades,the study of the family of quantum Hall effects has spawned a new paradigm that is so called topological materials.The Hall conductance of twodimensional electron gas under extra-low temperature and strong external magnetic field has a quantized value,which is insensitive to continuous changes of material parameters and structures.In physics,it is originated from a kind of new order,i.e.,topological invariant(Chern number in quantum Hall case).Recently,this concept of topology has been extended to photonic and phononic systems due to their similar band structures of artificially periodic geometries for photons or phonons,leading to a new and prosperous research field — topological photonics and phononics.The robust feature of topology can facilitate a robust way to control photons/phonons in the sense that the photons/phonons can propagate along the edge in a one-way fashion with completely backscattering-immune propagation or spin-momentum locking behaviors.Since it was born in 2005,topological photonics and phononics have attracted intense attention due to the robust one-way propagation of topological edge states.The study of these novel edge states can not only deepen our understanding of classical-wave topological physics,but also improve our manipulating capability of wave propagation,showing great application potentials in future practical devices.My thesis focused on the study of topological features of edge states in two elaborately designed photonic and phononic crystals,and made preliminary explorations on the realization of new topological phase and optical application devices.Here,we,for the first time,design and realize three-dimensional acoustic topological insulators based on several three-dimensional honeycomb phononic crystals with chiral structures.The acoustic pseudospin can be constructed based on spatial symmetry,as well as spin-orbit interaction which plays a key role in topological phases.We experimentally observed the two-dimensional gapless Dirac surface states via acoustic field scanning and Fourier transform technology,matching well with our theoretical predictions.Moreover,we can further break the symmetry of the twodimensional surface Dirac cone to obtain a pair of one-dimensional gapless hinge state,deemed as the three-dimension 2nd-order topological insulators.According to bulksurface-edge correspondence,a remarkable property of topological insulators,both the two-dimensional surface states and one-dimensional hinge states could be well characterized by their bulk topology.To achieve it,the Wilson loop,nested Wilson loop and surface spin-Chern number approaches were used to calculate the topological invariants of our acoustic systems.On the other hand,we propose a kind of topological boundary constructed by two adjacent two-dimensional magneto-optical photonic crystals with opposite magnetic biases.Due to the opposite signs of the nontrivial Chern numbers at each side,two topological edge states,i.e.,symmetrical and anti-symmetrical states,can be found.Interestingly,these two topological edge states possess the same direction of energy propagation but opposite directions of phase propagation.With oblique incidence,one specific topological edge state can be selectively excited and coupled out in a compact structure(as small as four layers),leading to fascinating transportation features such as one-way negative refractions.Moreover,we can utilize various phase delays of two sources to design an all-photonic tunable splitter based on the hybridization of two topological edge states.