Complete band gaps in two-dimensional phononic crystal slabs

© 2006 American Physical Society. The electronic version of this article is the complete one and can be found online at: http://link.aps.org/doi/10.1103/PhysRevE.74.046610DOI: .1103/PhysRevE.74.046610The propagation of acoustic waves in a phononic crystal slab consisting of piezoelectric inclusions placed periodically in an isotropic host material is analyzed. Numerical examples are obtained for a square lattice of quartz cylinders embedded in an epoxy matrix. It is found that several complete band gaps with a variable bandwidth exist for elastic waves of any polarization and incidence. In addition to the filling fraction, it is found that a key parameter for the existence and the width of these complete band gaps is the ratio of the slab thickness, d, to the lattice period, a. Especially, we have explored how these absolute band gaps close up as the parameter d∕a increases. Significantly, it is observed that the band gaps of a phononic crystal slab are distinct from those of bulk acoustic waves propagating in the plane of an infinite two-dimensional phononic crystal with the same composition. The band gaps of the slab are strongly affected by the presence of cutoff frequency modes that cannot be excited in infinite media

Acoustic confinement and waveguiding with a line-defect structure in phononic crystal slabs

© 2010 American Institute of Physics. The electronic version of this article is the complete one and can be found at: http://dx.doi.org/10.1063/1.3500226DOI: 10.1063/1.3500226We present a new way of forming phononic crystal waveguides by coupling a series of line-defect resonators. The dispersion proprieties of these coupled resonator acoustic waveguides CRAW can be engineered by using their geometrical parameters.We show that single-mode guiding over a large bandwidth is possible in CRAW formed in a honeycomb-lattice phononic crystal slab of holes in zinc oxide. In addition, a finite length of CRAW structure acts as an efficient selective acoustic filter for Lamb waves

In-plane confinement and waveguiding of surface acoustic waves through line defects in pillars-based phononic crystal

International audienceWe present a theoretical analysis of an in-plane confinement and a waveguiding of surface acoustic waves in pillars-based phononic crystal. The artificial crystal is made up of cylindrical pillars placed on a semi-infinite medium and arranged in a square array. With a well-chosen of the geometrical parameters, this pillars-based system can display two kinds of complete band gaps for guided waves propagating near the surface, a low frequency gap based on locally resonant mode of pillars as well as a higher frequency gap appearing at Bragg scattering regime. In addition, we demonstrate a waveguiding of surface acoustic wave inside an extended linear defect created by removing rows of pillars in the perfect crystal.We discuss the transmission and the polarization of such confined mode appearing in the higher frequency band gap. We highlight the strong similarity of such defect mode and the Rayleigh wave of free surface medium. An efficient finite element analysis is used to simulate the propagation of guided waves through silicon pillars on a silicon substrate

Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface

International audienceWe investigate theoretically the propagation of acoustic waves in a two-dimensional array of cylindrical pillars on the surface of a semi-infinite substrate. Through the computation of the band structure of the periodic array and of the transmission of waves through a finite length array, we show that the phononic crystal can support a number of surface propagating modes in the nonradiative region of the substrate, or sound cone, as limited by the slowest bulk acoustic wave. The modal shape and the polarization of these guided modes are more complex than those of classical surface waves propagating on a homogeneous surface. Significantly, an in-plane polarized wave and a transverse wave with sagittal polarization appear that are not supported by the free surface. In the band structure, guided modes define band gaps that appear at frequencies markedly lower than those expected from the Bragg interference condition. We identify them as originating from local resonances of the individual cylindrical pillars and show their dependence on the geometrical parameters, in particular with the height of the pillars. The transmission of surface acoustic waves across a finite array of pillars shows the signature of the locally resonant band gaps for surface modes and their dependence on the symmetry of the source and its polarization. Numerical simulations are performed by using the finite element method and considering silicon pillars on a silicon substrate

Band structure of evanescent waves in phononic crystals

International audienceEvanescent waves must be considered in propagation problems whenever scattering, diffusion, or diffraction by a finite object are investigated. In the context of phononic crystals, they appear very naturally within frequency band gaps. Since no waves can propagate within a band gap, only evanescent waves are left to explain the exponentially-decreasing transmission of acoustic waves. We have extended the classical plane wave expansion (PWE) method so that it includes complex wave vectors in the direction of propagation. To do so, it is necessary to consider a fixed frequency and to solve for the wave vector, in contrast to the traditional way of obtaining band structures by considering any Bloch wave vector within the first Brillouin zone and solving for the frequency of allowed modes. The new complex PWE method has been used to generate band structures for two-dimensional silicon - void phononic crystals. Both propagative and evanescent solutions are found at once. The decay constants within band gaps are thus found and shown to depend on the wave polarization. The consideration of complex wave vectors also allows us to identify clearly the different branch systems in the band structure and to connect bands below and above band gaps. Furthermore, the distribution of the acoustic fields of evanescent modes can be computed. Their transformation from below to above a band gap as well as within the band gap itself is shown

Evanescent Bloch waves in phononic crystals

International audiencePhononic crystals are two- or three-dimensional periodic structures that are composed with two or more materials with different elastic constants, giving rise to complete band gaps under specific conditions. Band structures are usually employed to describe infinite phononic crystals, as they provide one with all propagative waves in the periodic medium, or Bloch waves. It is however well known that evanescent waves must be considered in propagation problems whenever scattering, diffusion, or diffraction by a finite object are involved. We have extended the classical plane wave expansion (PWE) method so that it includes complex wave vectors in the direction of propagation at a fixed frequency. The new complex PWE method has been used to generate complex band structures for two-dimensional phononic crystals. Both propagative and evanescent solutions are found at once. This method of analysis is expected to become the basic building block to solve scattering problems in phononic crystals, yielding naturally diffraction efficiencies, as is illustrated with an example. In addition, it directly gives the eigenfrequency contours that are required to understand refraction (positive or negative) in phononic crystals

Ultrasonic and hypersonic phononic crystals

International audienceWe report on the experimental and theoretical investigation two kinds of acoustic waves in two dimensional phononic crystal: bulk acoustic waves and surface acoustic waves. For bulk acoustic waves, the work focuses on the experimental observation of full acoustic band gaps in a two-dimensional lattice of steel cylinders immersed in water as well as deaf bands that cause strong attenuation in the transmission for honeycomb and triangular lattices. For surface acoustic waves, complete acoustic band gaps found experimentally in a two-dimensional square-lattice piezoelectric phononic crystal etched in lithium niobate will be presented. Propagation in the phononic crystal is studied by direct generation and detection of surface waves using interdigital transducers. The complete band gap extends from 203 to 226 MHz, in good agreement with theoretical predictions. Near the upper edge of the complete band gap, it is observed that radiation to the bulk of the substrate dominates. This observation is explained by introducing the concept of sound line