Surface acoustic waves in two-dimensional periodic elastic structures

Abstract

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.

Phonon dispersion in hypersonic two-dimensional phononic crystal membranes

“…Therefore, such structures have become attractive for optomechanics, radio frequency (RF), and thermoelectric applications [17,22,23]. Various one-, two-, three-dimensional PnCs designed to tune the propagation of bulk [2][3][4][13][14][15]24], surface (Rayleigh, Sezawa) [6,[25][26][27], and plate (Lamb) waves [5,16,18,28] have been investigated both theoretically and experimentally in a wide range of sizes and frequencies. However, the direct measurements of the hypersonic phonon dispersion were performed mostly for bulk [2][3][4]24,29,30] and surface PnCs [6,[31][32][33], while the influence of the phononic patterning in thin membranes was studied theoretically and experimentally by means of transmission measurements, where the acoustic waves are generated and detected electrically [5,18,34,35] or optically [28] in the kHz-MHz range.…”

Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch

“…So far, several authors have calculated acoustic band structures of 2D phononic crystals for both the bulk 3-6 and surface 13,14 vibrations with a plane-wave-expansion ͑PWE͒ method. This simple method usually works very well.…”

Tuning of a hypersonic surface phononic band gap using a nanoscale two-dimensional lattice of pillars

“…A two-dimensional periodic nanostructure in the form of pillars deposited on such a substrate, or holes (inclusions) made in the substrate, enables the control of heat flow 13 and propagation of hypersonic surface acoustic waves (SAWs). [17][18][19][20] In the surface phononics, the frequency band gap can be controlled by the filling factor, spacing, the elastic properties of the pillars/inclusions, and also the height of the pillar, which is considered in this paper. This paper presents experimental results obtained by surface Brillouin light scattering spectroscopy (SBLS) [23][24][25] supported by theoretical modeling by the finite-element method (FEM) 26 for a 2D aluminum hypersonic phononic structure on silicon substrate.…”

“…Such composite structures comprise photonic crystals made of components of different permittivity, [1][2][3][4] magnonic crystals that are ferromagnetics of different permeability, 5,6 and phononic crystals. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] In phononic crystals of a heterogeneous one-dimensional (1D), 2D, or 3D structure, the elastic (acoustic) waves propagating in the medium are not simple plane waves that can be classified as transverse and longitudinal (or quasitransverse and quasilongitudinal). With a proper choice of material parameters and modulation spacing, it is possible to induce a complete band gap for which propagation of acoustic waves of arbitrary polarization and wave vector is forbidden.…”

“…Contrary to the linear dispersion relation in the long-wavelength limit, a mechanical wave of a wavelength comparable to the spacing may undergo multiple scattering at the interfaces of different elastic media, which leads to destructive interference and to the appearance of bands of forbidden frequencies at which propagation of mechanical waves is not allowed. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] A huge part of the advanced technological solutions in electronic devices is implemented on silicon substrates. A two-dimensional periodic nanostructure in the form of pillars deposited on such a substrate, or holes (inclusions) made in the substrate, enables the control of heat flow 13 and propagation of hypersonic surface acoustic waves (SAWs).…”