Topological Interface States In Classical Wave Systems

The topological physics is growing rapidly in condensed matter physics,as the counterpart of electrons,the conception of topology is induced into photonics,this is where the topological photonics originate from.In photonics,band structures emerging when electromagnetic waves propagate through periodic structures,analogous to that electrons in a system with periodic potential,the topological properties of band structures in photonics can be characterized by quantized topological invariants.The topological surface states emerge when two insulators with different topological phases are connected,and they are robust against some local defects and immune from the back-scattering.In light of these advantages,we have constructed and measured topological interface states in various physical branches,including photonics and phononics.The details of this article are listed as follows:First,we will introduce the method of modulating the dispersion relation and band structures of electromagnetic waves via varying the geometric parameters of the structure.Specifically,we design a kind of structure consisting of a metallic film coated by dielectric grating on both sides,surface plasmon polartions(SPPs)emerge on the surface of the planar metallic film.It is found that the SPP modes can be efficiently tuned by the relative shift or the filling ratio of the gratings on both sides.The coupling strength between SPP modes can be tailored via varying the relative shift of the gratings on both sides,which can suppress or enhance the absorption of the system.In addition,the coupled mode theory(CMT)is utilized to evaluate the coupling efficiency and further reproduce the absorption spectra.The conclusion drawn from CMT is corroborated by the full wave simulations.Second,we design a kind of spoof SPP(SSPP)crystals in microwave regime based on SPPs.In the second part we propose a spoof-insulator-spoof(SIS)structure,which can serve as a waveguide for spoof SPP modes.If a periodic geometry modulation in the wavelength scale is introduced to the SIS waveguide,this multiscale SIS(MSIS)waveguide possesses band gaps for spoof SPPs analogous to the band gaps in a photonic crystal.Inspired by the topological interface states found in photonic crystals,here we construct interface states by connecting two MSIS waveguides with different topological properties(inverted Zak phases of bulk bands).The topological interface states in the MSIS waveguides are observed experimentally,and the measured results agree excellently with the numerical ones.Based on the platform of the SSPPs system,we extend the system from onedimensional(1D)periodic structures to two-dimensional(2D)periodic structures.The extensive researches of two-dimensional layered materials have revealed that valleys,as energy extrema in momentum space,can offer a new degree of freedom for carrying information.Based on this concept,we demonstrate a designer surface plasmon crystal comprising metallic patterns deposited on a dielectric substrate,which can become a valley-Hall photonic topological insulator by exploiting the mirror-symmetry-breaking mechanism.Topological edge states with valley-dependent transport are directly visualized in the microwave regime.The experimental results verify the one-way propagation of the valley-polarized edge states,and demonstrate the robustness against sharp corners is and perturbations.The observed edge states are confirmed to be fully valley-polarized through spatial Fourier transforms.Topological interface states are also realized in acoustic systems based on the full phase diagrams.Zak phases can define the topological property of bulk bands of 1D periodic systems and determine the existence of topological interface states at the junction of two semi-infinite structures.Here,we propose a scheme based on the full phase diagrams of bandgaps to control the existence of topological interface states within any specified bandgaps.As an example,two connected one-dimensional phononic crystals are considered,and the interface states within any specific bandgap or their combinations can be achieved.The appearance of interface states in a single bandgap,in all odd bandgaps,in all even bandgaps,or in all bandgaps,is observed in both simulations and experiments.This scheme of full phase diagrams can be extended to design topological interface states in other kinds of periodic systems,such as photonic crystals and designer plasmonic crystals.At last,we probe the topological protection of the topological interface states in 1D system with inversion symmetry.The topological interface states in 1D PCs with inversion symmetry are protected by inversion symmetry and are robust against perturbations.However,once the inversion symmetry is broken,the interface states are destroyed and even vanished.The above conclusions are analytically verified based on the plane wave expansion(PWE)method,and are demonstrated by the simulated results in spoof SPPs system.In this paper,to design the interface states in classical wave systems,we induce the conception of topological invariants to the classical wave systems.In the platform of artificial crystals,the topological phase for each band can be tailored by geometric parameters.Topological interface states emerge when two insulators with different topological phases are connected.These topological interface states are pretected by certain kinds of sysmmtry,so they are robust against the perturbations that preserve corresponding symmetry,and can support one-way surface states.The conception in this paper can be extended to other Bloch classical wave systems(e.g.,acoustic waves,electromagnetic waves,elastic waves),and may have potential applications in information propagation,quantum computing,photonic devices,optical isolators and topological lasers.