Research On Topological States And Functional Devices In Acoustics

Topology is a mathematical concept describing the properties of space that are pre-served under continuous deformations.By analyzing the concepts of space,dimension and transformation,topology has become an important branch of mathematics.It has gradually been extended to other areas,such as biology,computer science and physics.The discoveries of the quantum Hall effect,quantum spin Hall effect and topological insulators have revolutionized our understanding of condensed matter physics and have also stimulated researches on the topological properties in the classical wave systems.In optics,topological phase transitions have been achieved in two-dimensional?2D?systems using gyromagnetic photonic crystal,bi-anisotropic metamaterials and cou-pled optical waveguides.Due to the similarity between acoustic wave equations and Maxwell equations,topological protected wave engineering in acoustics is at the fron-tier of ongoing metamaterials research.Based on the non-backscattering topological protected transmission and the strong robustness against the defects,topological bound-ary states may have great application prospects in acoustic communications,noise con-trol and electro-acoustics integration.Against this background,this thesis focuses on the study of the topological boundary states and related functional devices in acoustic systems.The contents are as follows.In the 1st chapter,starting from topological phase transition and topological insu-lators,the origin of topological boundary states is summarized.The topological insula-tors in optics are reviewed and the recent works on the topological acoustics are briefly introduced.In the 2nd chapter,the subwavelength one-dimensional?1D?multiple topological interface states are achieved through merging the acoustic metamaterials and the sonic crystals.A double-channel Mie resonator based on the cylindrical labyrinthine acous-tic metamaterials is designed.The 1D sonic crystal composed of the periodically ar-rayed metamolecules containing two double-channel Mie resonators is embedded in 1D waveguide.The band gap can be opened through changing the interval among neigh-boring cells and the topological Zak phase transition can be obtained.The multiple topological interface states in band gaps are clearly observed at the interface between two kinds of sonic crystals with different Zak phases and show good robustness against several defects.In the 3rd chapter,based on the honeycomb sonic crystals,two ways to build the acoustic pseudospin multipoles and topological edge states are proposed.The first one is to utilize acoustic soft cylinders whose effective refractive index is higher than that of air.The primitive cell is enlarged three times and the Dirac cones at the boundary of the 1st Brillouin zone can be folded to the center using band-folding mechanism.As a result,a quadruple degenerated double Dirac cone is obtained.By shrinking or expand-ing the metamolecule,the degeneracy can be lifted and two double degenerated states can be formed.The direction of sound propagation within each metamolecule plays the role of pseudospin dipolar modes or quadruple modes.The contraction or expansion of a metamolecule produces the topological phase transition from trivial state to non-trivial one.There will be a topological edge state transmitting along the interface of sonic crystals with different topological phases.Such boundary state is robust against defects such as cavity,disorders and bending.The second way is to construct a hon-eycomb lattice with three-legged scatterers.Simply rotating the three-legged scatterers induces the topological transition between different phases.Furthermore,the proposed edge states are similar to the pseudospin-orbit coupling existing on the boundary be-tween the trivial and nontrivial sonic crystals.Finally,the existence of topological edge states and its robustness against defects are observed in experiments.In the 4th chapter,the topological valley-projected edge states and the related a-coustic functional devices are studied.By breaking the mirror symmetry in the prim-itive cell of the honeycomb lattice or breaking the C_3vsymmetry in the triangular lat-tice,the Dirac cone can be lifted to obtain a band gap.The corresponding valley states present the valley pseudospins with different chiralities.Different symmetry-broken ways introduce the different topological valley phases.According to the bulk-boundary correspondence,there will be valley-projected edge state on the interface between the structures with different valley phases.The formation of Bessel beams and topological valley-projected transport in honeycomb sonic crystals composed of soft materials are discussed in detail.The experimental implementation of the subwavelength topolog-ical valley-projected edge states in honeycomb sonic crystals composed of soda cans is proposed.The topological boundary state formed by breaking the C_3vsymmetry in the triangular lattice is used to experimentally demonstrate a topological acoustic delay line and a directional acoustic duplex antenna.In the 5th chapter,second-order topological insulator in acoustic Hermitian and non-Hermitian systems and the related applications are proposed.Based on the 2D SSH model and the hierarchal bulk-edge-corner correspondence,2D Zak phase transitions in a square lattice are realized.Topological corner states are observed.The non-Hermitian characteristics of topological corner states are studied after introducing acoustic gain and loss part into the system.The attenuation or enhancement of acoustic energy at corners can be tuned by changing the non-Hermitian parameter.Finally,based on the perforated acoustic metamaterials,a second-order acoustic topological insulator with a deep subwavelength scale is successfully constructed.The multiple corner states existing in three frequency bands are experimentally observed and an acoustic imaging device is proposed based on this structure.In the last chapter,the paper is summarized and the future development is prospected.