Phase-controlling phononic crystal

Abstract

We report on a phononic crystal ͑PC͒ consisting of a square array of cylindrical polyvinylchloride inclusions in air that can be used to control the relative phase of two incident acoustic waves with different incident angles. The phase shift between waves propagating through the crystal depends on the angle of incidence of the incoming waves and the PC length. The behavior of the PC is analyzed using the finite-difference-time-domain method. The band structure and equifrequency contours calculated via the plane wave expansion method show that the distinctive phase controlling properties are attributed to noncollinear wave and group velocity vectors in the PC as well as the degree of refraction.Phononic crystals ͑PCs͒ are composite materials which derive their spectral ͑-space͒ and wave vector ͑k-space͒ properties from the scattering of elastic waves by periodic arrays of elastic inclusions embedded in an elastic matrix. Bulk or defected PCs have been shown to exhibit numerous useful spectral capabilities including transmission band gaps, local modes for guiding, filtering, and multiplexing. 1-15 k-space properties result from features in the band structure that impact refraction. 16-28 These properties parallel many of those found in photonic crystals. 29,30 The -space and k-space properties are directly related to the size, geometry, scale, and composition of the constitutive materials of the PC.In the present letter, we demonstrate that the band structure of a two-dimensional PC constituted of a square array of cylindrical polyvinylchloride ͑PVC͒ inclusions in an air matrix can be used to control the relative phase of elastic waves. Phase control is due to the propagation of elastic waves in the PC with wave vectors that are not collinear with their group velocity vectors. This condition implies that excited Bloch waves travel at different phase velocities in the direction of their group velocity. Additionally, this crystal shows near zero-angle refraction permitting wave collimation as well as enabling the superposition of beams with different wave vectors in the same volume of crystal. Phase manipulation of these superposed waves can result in constructive or destructive interferences between noncollinear incident beams. Finally, there are operating frequencies for which the circular equifrequency contour ͑EFC͒ in air is larger than the first Brillouin zone of the PC, allowing several Bloch modes to exit the crystal, leading to the phenomenon of beam splitting. The work presented in this letter constitutes a significant move toward broadening the range of properties and applications of PCs beyond their more common spectral and wave number properties.The PVC-air system parameters are: PVC = 1364 kg/ m 3 , c t,PVC = 1000 m / s, c l,PVC = 2230 m / s, AIR = 1.3 kg/ m 3 , c t,AIR =0 m/ s, and c l,AIR = 340 m / s, where is density, c t is transverse speed of sound, and c l is longitudinal speed of sound. The inclusion radius is 12.9 mm and the lattice parameter is 27 mm. The plane wave expansion ͑PWE͒ method was e...

Optically tunable acoustic wave band-pass filter

“…In their history, phononic structures have been engineered with phonon dispersion curves showing frequency band-gaps (Bragg gaps) for longitudinal and shear waves [1][2][3][4] as well as passing bands with unique refractive properties such as negative refraction [5][6][7][8][9][10][11] and zero-angle refraction. [12][13][14] Several useful applications have been suggested from these spectral (ω-space) and wave vector (k-space) properties, such as (1) materials to isolate vibrations, 15,16 (2) composites to guide acoustic and elastic waves [17][18][19][20][21] and (3) devices to focus/collimate phonons. [22][23][24] Similar functionalities have been demonstrated for semi-infinite systems.…”

Analysis of the wave propagation properties of a periodic array of rigid cylinders perpendicular to a finite impedance surface

“…Exhaustive studies have been performed in order to know the underlying physics in their main control properties of sonic and elastic waves. Refraction, [3][4][5] invisibility, 6 bandgaps, 7,8 or recently, control of phase properties, 9 are some topics related with the exploitation of the wave propagation properties of PC.…”

Inverted bi-prism phononic crystals for one-sided elastic wave transmission applications

“…Nevertheless, there is only one intersecting point between the dotted purple lines and the SH0 mode EFC of the uniform plate, marked by Arrow 3. Calculating the phase velocities at the interface, the angle of refraction of the transmitted wave is shown to be 37 and no bi-refraction 5,6,21 is shown to occur in this case. The same phenomena occur for the case of wave incidence from the uniform plate towards the upper prism.…”

“…3. The refraction into multiple waves 5,6,21 of the uniform plate from the inverted bi-prism PC should be avoided when an SH0 wave is incident from the right; this will ensure concentrated transmission power only along one direction. There may be a few different configurations that may satisfy the three requirements, but we consider two symmetrically placed 45 PC prisms of which the unit cell is shown in Fig.…”