Two-dimensional phononic crystals: surface acoustic waves (original) (raw)
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Surface acoustic waves in two-dimensional periodic elastic structures
Physical Review B, 1998
Acoustic waves localized at the surface of two-dimensional ͑2D͒ periodic elastic structures, or 2D phononic crystals, are studied theoretically by taking account of the elastic anisotropy of constituent materials. The surface considered is perpendicular to the axis of a periodic array of cylinders embedded in a background material. The dispersion relations of the surface modes are calculated for circular cylinders of AlAs which form a square lattice in a GaAs matrix. The folding and anisotropy of the surface wave branches, as well as the existence of pseudosurface waves, are found. The stop band distributions of the surface, pseudosurface, and bulk waves are plotted in a form relevant for comparison with ultrasound imaging experiments. ͓S0163-1829͑98͒00336-1͔
Surface guided waves in two-dimensional phononic crystals
Wave Motion, 2007
With FDTD (finite-difference time-domain) calculations we study the acoustic waves propagating in a semi-infinite, two-dimensional (2D) periodic elastic structure, i.e., a 2D phononic crystal, with a flat surface together with a line defect. Specifically we search for the acoustic modes localized near the surface and at the same time confined inside the straight line defect, i.e., the surface guided waves. The surface assumed is perpendicular to the axis of circular cylinders (steel) embedded periodically in a background material (polymer). These surface guided waves found are unstable in general due to the interaction with bulk acoustic waves but can propagate the distances over several hundreds of lattice constants for a certain range of frequencies.
Journal of Applied Physics, 2016
In this paper, we report a theoretical investigation of surface acoustic waves propagating in onedimensional phononic crystal. Using finite element method eigenfrequency and frequency response studies, we develop two model geometries suitable to distinguish true and pseudo (or leaky) surface acoustic waves and determine their propagation through finite size phononic crystals, respectively. The novelty of the first model comes from the application of a surface-like criterion and, additionally, functional damping domain. Exemplary calculated band diagrams show sorted branches of true and pseudo surface acoustic waves and their quantified surface confinement. The second model gives a complementary study of transmission, reflection, and surface-to-bulk losses of Rayleigh surface waves in the case of a phononic crystal with a finite number of periods. Here, we demonstrate that a non-zero transmission within non-radiative band gaps can be carried via leaky modes originating from the coupling of local resonances with propagating waves in the substrate. Finally, we show that the transmission, reflection, and surface-to-bulk losses can be effectively optimised by tuning the geometrical properties of a stripe. V
Acoustic Phononic Crystals with Square-Shaped Scatterers for Two-Dimensional Structures
International Symposium Innovative Technologies Engineering and Science, 2017
Metamaterials are artificial materials that possess unusual physical properties that are not usually found in natural materials. Phononic crystals (PnC) can be constructed by periodic distribution of inclusions embedded in a matrix with high contrast in mechanical properties. They can forbid the propagations of acoustic waves in certain frequencies by creating band gaps. Such band gaps may be independent of the direction of propagation of the incident wave. In present work the acoustic band structure of a two-dimensional phononic crystal consisting of square-shaped rods embedded in air matrix are studied to find the existence of stop bands for the waves of certain energy. The wave band structures of acoustic waves in 2D air/solid phononic structure are investigated theoretically by Finite Element (FE) simulations. A time harmonic analysis of the acoustic wave propagation is performed using the acoustics package of the FE software Comsol Multiphysics v5.3. Phononic band diagrams ω=ω(k) for a 2D PnC were plotted versus the wavevector k along the M-Г-X-M path in the first Brillouin zone. The calculated phonon dispersion results indicate the existence of full acoustic modes in the proposed structure along the high symmetry points.
Frequency degeneracy of acoustic waves in two-dimensional phononic crystals
Journal of Physics: Conference Series, 2007
Degeneracies of acoustic wave spectra in 2D phononic crystals (PC) and PC slabs are studied. A PC structure is constituted of parallel steel rods immersed into water and forming the quadratic lattice. Given the projection kz of the wave vector on the direction of rods, the bulk wave spectrum of the infinite PC is a set of frequency surfaces fi(kx, ky), i = 1, 2,. .. , where kx,y are the components of the wave vector in the plane perpendicular to the rods. An investigation is performed of the shape of frequency surfaces in the vicinity of points (k dx , k dy), where these surfaces fall into contact. In addition, the evolution of the degeneracy with changing rod radius and cross-section shape is examined. Degeneracy in the spectrum of leaky modes propagating along a single waveguide in a PC slab is also investigated.
Physical Review B, 1999
Spatial and frequency distributions of forbidden bands of both surface and bulk acoustic waves are studied theoretically for two-dimensional ͑2D͒ periodic elastic structures consisting of aluminum and polymer. The surface is perpendicular to the 2D periodic arrays of circular cylinders embedded in a background material. The dispersion relations of the surface and bulk modes with wave vectors parallel to the surface are calculated for triangular lattices, and the stop band distributions are plotted in a form relevant to the comparison with ultrasound imaging experiments. ͓S0163-1829͑99͒03043-X͔
Pseudosurface acoustic waves in hypersonic surface phononic crystals
Physical Review B, 2009
We present a theoretical framework allowing to properly address the nature of surface-like eigenmodes in a hypersonic surface phononic crystal, a composite structure made of periodic metal stripes of nanometer size and periodicity of 1 µm, deposited over a semi-infinite silicon substrate. In surface-based phononic crystals there is no distinction between the eigenmodes of the periodically nanostructured overlayer and the surface acoustic modes of the semi-infinite substrate, the solution of the elastic equation being a pseudo-surface acoustic wave partially localized on the nanostructures and radiating energy into the bulk. This problem is particularly severe in the hypersonic frequency range, where semi-infinite substrate's surface acoustic modes strongly couple to the periodic overlayer, thus preventing any perturbative approach. We solve the problem introducing a surface-likeness coefficient as a tool allowing to find pseudo-surface acoustic waves and to calculate their line shapes. Having accessed the pseudo-surface modes of the composite structure, the same theoretical frame allows reporting on the gap opening in the now well-defined pseudo-SAW frequency spectrum. We show how the filling fraction, mass loading and geometric factors affect both the frequency gap, and how the mechanical energy is scattered out of the surface waveguiding modes.
Physical Review Letters, 2001
Experimental measurements of acoustic transmission through a solid-solid two-dimensional binarycomposite medium constituted of a triangular array of parallel circular steel cylinders in an epoxy matrix are reported. Attention is restricted to propagation of elastic waves perpendicular to the cylinders. Measured transmitted spectra demonstrate the existence of absolute stop bands, i.e., band gaps independent of the direction of propagation in the plane perpendicular to the cylinders. Theoretical calculations of the band structure and transmission spectra using the plane wave expansion and the finite difference time domain methods support unambiguously the absolute nature of the observed band gaps.
Physical Review B, 2012
The square symmetry of the equifrequency contour of longitudinal waves in a solid/solid two-dimensional phononic crystal (PC) is shown through numerical calculations and experiments to lead to peculiar propagation phenomena. A slab of steel/epoxy PC immersed in water refracts incident longitudinal waves by an angle of zero degrees. The waves propagate along the shortest path between the slab faces. This characteristic enables the superposition within the same volume of the PC of waves with different incidence angles. Two incident waves with symmetrical incident angles can interfere constructively or destructively inside the PC depending on their initial phase difference. This phase difference is shown to enable control of wave propagation through the PC.