Fundamental Properties of Phononic Crystal

Abstract

The control and manipulation of acoustic/elastic waves is a fundamental problem with many potential applications, especially in the field of information and communication technologies. For instance, confinement, guiding, and filtering phenomena at the scale of the wavelength are useful for signal processing, advanced nanoscale sensors, and acousto-optic on-chip devices; acoustic metamaterials, working in particular in the sub-wavelength regime can be used for efficient and broadband sound isolation as well as for imaging and super-resolution.Phononic crystals, which are artificial materials constituted by a periodic repetition of inclusions in a matrix, are proposed to achieve these objectives via the possibility of engineering their band structures. The elastic properties, shape, and arrangement of the scatterers modify strongly the propagation of the acoustic/elastic waves in the structure. The phononic band structure and dispersion curves can then be tailored with appropriate choices of materials, crystal lattices, and topology of inclusions.Similarly to any periodic structure, the propagation of acoustic waves in a phononic crystal is governed by the Bloch [1] or Floquet theorem from which one can derive the band structure in the corresponding Brillouin zone. The periodicity of the structures, that defines the Brillouin zone, may be in one (1D), two (2D), or three dimensions (3D). The propagation of acoustic waves in layered periodic materials or superlattices which are now being considered as 1D phononic crystals has been extensively studied [2] since the early paper of Rytov [3]. However, the

Mechanical low-frequency filter via modes separation in 3D periodic structures

“…[8][9][10][11][12] Among others, the bandgap (i.e., the frequency range of prevented wave transmission) is one of the most investigated properties: a wide and complete bandgap is generally beneficial to guarantee robust wave attenuation around a certain frequency. 4,13 In many cases, a complete bandgap is obtained by a periodic arrangement of two or more materials, 4,14 but significant results can also be achieved for a single material, [15][16][17] among which the one endowed with a very large complete bandgap that the authors show in a previous paper. 18 In general, periodic structures endowed with bandgaps exhibit attenuation in the transmission spectrum of the finite structure in correspondence of the bandgap frequency range.…”

Additive Manufacture of Small-Scale Metamaterial Structures for Acoustic and Ultrasonic Applications

“…The effect that causes this transmission loss is also apparent in the high pressures inside the resonating inclusions. In a phononic crystal (and other lattice types) the band gap is caused by Bragg scattering, whereby waves of a particular wavelength (determined by the lattice constant) are scattered from the inclusions and interfere destructively [60]. Acoustic meta-atoms that are smaller than the acoustic wavelength utilise gaps due to resonance effects [24].…”

Analysis and Design of High-Frequency 1-D CMUT Imaging Arrays in Noncollapsed Mode

“…Bragg's resonance arises as a result of scattering caused by the periodic discontinuity of acoustic propagation between membranes. Destructive interference of the scattered waves forms a band gap at the frequency c 0 /d, where c 0 is the speed of sound of the medium [46]. This resonance acts as a limiting factor to the frequency response of the CMUTs, both in single element and imaging array element, with smaller pitches resulting in higher limits.…”