Negative refraction of phonons and acoustic lensing effect of a crystalline slab

Imamura, Koki; Tamura, Shin–ichiro

doi:10.1103/physrevb.70.174308

Cited by 41 publications

(26 citation statements)

References 20 publications

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“…Negative refraction can arise from one of two mechanisms. Systems can either consist of locally resonant structures which exhibit a negative effective mass and negative bulk modulus [2,3], or by a Phononic Crystal (PC), consisting of a periodic array of inclusions in a physically dissimilar matrix [4][5][6][7][8][9]. In the latter case, Bragg scattering leads to dispersive behavior with some pass bands exhibiting a negative group velocity.…”

Section: Introductionmentioning

confidence: 99%

Resolution limit of a phononic crystal superlens

et al. 2011

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We report on the subwavelength imaging capabilities of a Phononic Crystal (PC) flat lens consisting of a triangular array of steel cylinders in methanol, all surrounded by water. The image resolution of the PC flat lens beats the Rayleigh diffraction limit because bound modes in the lens can be excited by evanescent waves emitted by the source. These are modes that only propagate in the direction parallel to the water/lens interface. These modes resonantly amplify evanescent waves that contribute to the reconstruction of an image. By employing the Finite Difference Time Domain (FDTD) method and ultrasonic experiments, we also explore the effect on the image resolution and focal point on various structural and operational parameters such as source frequency, geometry of the lens, source position and time. The mechanisms by which these factors affect resolution are discussed in terms of the competition between the contribution of propagative modes to focusing and the ability of the source to excite bound modes of the PC lens.

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Section: Introductionmentioning

confidence: 99%

Resolution limit of a phononic crystal superlens

et al. 2011

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“…1-15 k-space properties result from features in the band structure that impact refraction. [16][17][18][19][20][21][22][23][24][25][26][27][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.…”

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confidence: 85%

Phase-controlling phononic crystal

Swinteck

Robillard

Bringuier

et al. 2011

Applied Physics Letters

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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...

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“…Besides the topics related to the existence of absolute band gaps, there is a continuous growing interest on refractive properties of phononic crystals, in particular: negative refraction phenomena and their applications in imaging and sub-wavelength focusing in phononic crystals [87][88][89][90][91], self-collimation and beam-splitting in relation with the shape of the equifrequency surfaces [92], control of the sound propagation with metamaterials with emphasis on cloaking and hyperlens phenomena.…”

Section: Concluding Remarks and Further Developments In The Field Of mentioning

confidence: 99%

Fundamental Properties of Phononic Crystal

Pennec

Djafari‐Rouhani

2016

Phononic Crystals

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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

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Negative refraction of phonons and acoustic lensing effect of a crystalline slab

Cited by 41 publications

References 20 publications

Resolution limit of a phononic crystal superlens

Resolution limit of a phononic crystal superlens

Phase-controlling phononic crystal

Fundamental Properties of Phononic Crystal

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