Study On The Propagation Features Of Acoustic Waves Near The Dirac Cones In Phononic Crystals

In recent years,the phononic crystal has bee a hot research topic.It is an artificial composite with periodic spatial structure and band gap structure.Researchers are not confined to the band gap itself,mainly to study the unique characteristics of the band gap.Such as Dirac points,Dirac-like points,semi-Dirac points and double Dirac points formed by conical dispersion relations.The Dirac cone demonstrates many intriguing physical properties,including pseudo-diffusion transport,edge state,and Zitterbewegung oscillations.The Dirac-like cone also has demonstrated some novel wave propagation behaviors like acoustic cloaking,tailoring of the wave front,and perfect lens,which are related to a zero effective refractive index(the effective mass density and the reciprocal of the effective bulk modulus equal to zero).It will also promote the innovation and application of acoustic components.In this paper,the singular transmission characteristics of Dirac-like points and Dirac points in phononic crystals are studied from two aspects of sound waves normal incidence and oblique incidence.The specific contents of this thesis are as follows:(1)We demonstrate how to achieve angular control for oblique incident acoustic waves for both total transmission and reversed reflection in phononic crystals.The phononic crystals consist of rectangular rubber rods arranged in square lattice structure and triangular lattice structure in water background.A Dirac point is found at the Brillouin zone boundary along XM direction in these structure.By changing the length-width ratio of the rubber rods,the Dirac point is found to move along the XM direction,which makes the unity transmission angle selectable,not for normal incident wave,but for oblique incident wave.Different from Brewster's angle mechanism,the functionality of angular control does not rely on the refraction indices of the background medium.At the frequency of the Dirac point,the total transmission phenomenon is observed at a particular incident angle related to the Dirac point,irrespective of the thickness of the phononic crystals.However,the transmission will gradually become weak unto zero when deviating from particular angle as a result ofthe band gap.Interestingly,at that particular incident angle,the transmitted acoustic wave takes 0 or ? phase shifting through even or odd number phononic crystal layers.Unlike the photonic crystal systems,the systems in this study merely require two components(rubber and water)to achieve phase shifting.Finally,by establishing a new acoustic meta-surface with a ?/2 phase change on the surface of the phononic crystal,angular control can be achieved in the reflection domain.(2)The properties of Dirac-like point are also studied by using two-dimensional phononic crystals composed of rubber and water.Firstly,we take the two-dimensional square lattice structure of the rubber cylindrical rods embedded in the water and the triangular lattice structure of the rectangular rubber rods embedded in the water.It is found that there exists a triple degenerate Dirac-like point in the Brillouin zone(38)point.The results of eigenstates analysis show that these triple degenerate Dirac-like points are obtained by the coupling of the monopole state and the dipole state.Secondly,based on the frequency of the Dirac-like point,we get the phase reconstruction property by sound waves normal incidence.The total transmission phenomenon is also observed near the Dirac-like point.Finally,using the phase characteristics of Dirac-like points,we study the applications related to Dirac-like points,such as acoustic cloaking,tailoring of the wave front.It is proved that these properties can be realized only if the frequency of the Dirac-like point,and the other frequencies can not be obtained.