Research On Zero Refractive Index And Topological Property Of Acoustic Waves And Surface Water Waves

Recently,artificial metamaterial has made great advancement whether on theoretical research or experimental applications.Artificial metamaterial is periodic structure designed for tailoring electromagnetic wave,sonic wave and surface water waves.It includes photonic/phononic crystals,metasurface and metamaterial depending on the relation of lattice constant and wave length at specific frequency.Researchers have achieved many exotic phenomena which are lack in natural material such as negative refraction effect,tunneling effect,collimation effect,super lenses effect and so on.Band theory can be used to depict the wave transmission behavior in periodic structure according to the Bloch theory.At low frequency,the effective parameters of the periodic structure can be retrieved by effective medium theory.Therefore,it is an important approach to study artificial metamaterial by tailoring dispersion relation.The dissertation mainly designs exotic points in the band structure(Dirac-like point and double Dirac point)and explores their fantastic transmission properties using effective medium theory,such as wave-front shaping,focusing,redirecting,cloaking and so on.Besides,we also study topological effect by constructing spin in the classical wave system and achieve some novel topological transmission phenomena just as those in electronic systems,such directional transmission associated with pseudospin and topological transmission immune to defects for example.Our research work enriches the transmission features of classical waves and plays great inspiring role for further research.Related research work is as follows:1.In acoustic crystal,we exploit coating constituent as element to arrange in square lattice,and flat bands emerge due to local resonance.In fact,there is a Dirac-like point at the center of the Brillouin zone center after enlarging the frequency range near the degenerate flat band.The dispersion relation attained by(?) perturbation method is consistent with that by finite element method near the Dirac-like point.For further describe the property of the system,effective medium theory was utilized to get the effective parameter of the acoustic crystal at the Dirac-like point frequency.Near zero refractive index verifies that our system is an index near zero system.Infinite phase velocity and zero phase accumulation of zero-refractive-index material inspire perfect transmission,wave-front shaping,focusing,cloaking and other applications,which were verified by finite element method.2.By modulating the topological structure of the water channel,we can make two Dirac Cone overlap at the center of the Brillouin zone in the water wave system.Near the double Dirac point,water wave system shows many interesting properties such as selective transmission for incident waves with various incident angles,splitting,tunneling,cloaking and so on,which are unique to zero refractive index material.All of these have potential applications for extracting and guiding water wave device.3.By modulating the topological structure of the water channel,we can make two double degenerate states interchange each other.Quantum spin-Hall effect was emulated in our system by utilizing the spatial symmetry of the unit cell.The mathematical formalism of the Hamiltonian in the water wave system is the same as that of BHZ theory in condensed matter physics.Chern number can be achieved from the Hamiltonian and topological phase of the system then be identified.There are two intersecting edge states at the interface formed by two periodic structures with different topological phases.At different edge states,water wave system has various transmission orientations associated with the pseudospin,which attributes to spin splitter device.As protected by time reversal symmetry,the edge states confined at the interface in our system also own directional transmission immune to backscattering.4.We consider phononic crystal which is composed of a honeycomb array of iron cylinder embedded in air.Each unit cell contains two iron cylinders with different radius.The Dirac points at non-equivalent corners k and k' of the Brillouin zone was broken and band gap appears as inversion asymmetry is formed.The orientations of orbital angular momentum are opposite at the upper and lower band edges of the band gap.Protected by time reversal symmetry,the orbital angular momentum orientations are also reversed at different valley states with the same frequency level.Unidirectional transmission character at the topological edge state confined to the interface composed of different topological periodic structures could be achieved.Different valley states stimulation may result in diverse topological transmission phenomena.The valley contrasting physics strengthen our understanding to the concept of topology.