Research On The Effective Zero-refractive Index And Schoch Effect Of Acoustic Crystal Near The Dirac Point

As a kind of new artificial periodic material,more and more scholars have paid their attention on the phononic crystal over the two decades.Phononic crystals is a periodic composite materials or structures with acoustic or elastic wave band.When the periodic scale of phononic crystals is on an order of magnitude with sound or elastic waves and acoustic wave or elastic wave propagating in the periodic elastic medium structure is prevent,it will form the phononic band gap.Acoustic wave or elastic wave is not allowed to pass when the frequency within the range of the band gap,but waves with passband can be propagated without loss whithin other frequency range under the effect of dispersion relations.We can control the propagation of classical waves by selecting different arrangements of crystal lattices,scatterer shapes,and materials with different parameters to change the frequency of classical waves.Phononic crystals have shown many exotic physical characters,such as sound focus,collimation and perfect lens effect.At the center of the Brillouin zone of the phononic crystal,the Dirac cone dispersion relationship caused by accidental degeneracy has important application prospects in classical wave manipulation.In this dissertation,the relation of the Dirac-cone dispersions to zero-index refracrion of phononic crystals are studied systematically by effective medium theory and finite element method.The Schoch displacement near the Dirac point are also carefully investigated,and the forward and backward Schoch effects on the phononic crystal with zero refractive index are observed and simulated.First of all,we introduce the related concepts and important characteristics of phononic crystals,and expound the research progress of phononic crystals in the world for more than a decade,and review its future research and development direction.Then,the concept and basic characteristics of acoustic metamaterials are introduced,and the research status of acoustic metamaterials both at home and abroad is discussed.Secondly,a method for mapping phononic crystals with Dirac-cone dispersion to zero-index acoustic metamaterials is introduced detailedly.Using the introduce theory and method,we studied two-dimensional square and triangular lattice phononic crystals with Dirac-cone dispersion in the Brillouinzone and calculated their effective parameters.We have obtain a very important conclusion:only when the Dirac-cone dispersion of the phononic crystal are obtained by the coupling of the monopole state and the dipole state and the Dirac point frequency is a low frequency,and there is only one extended state,the acoustic crystal can be mapped to zero refractive index acoustic metamaterial.Finally,the Schoch effect of zero-index acoustic metamaterials was studied.The reflection on the interface between half infinite phononic and water are simulated using the finite element method.It is found that there exists forward and backward Schoch effects and the Schoch displacement is intimately related to the incident angle and incident wave length.The above results are very valuable for design the acoustic devices in the future.