Internal diffraction of ultrasound in crystals: Phonon focusing at long wavelengths

Hauser, Matt R.; Weaver, Richard L.; Wolfe, J. P.

doi:10.1103/physrevlett.68.2604

Cited by 73 publications

(23 citation statements)

References 8 publications

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“…This boundary condition should approximately be applicable, for instance, to the excitation of surface waves by a focused ultrasound beam emitted from an immersion transducer. 5 The solution of Eq. (1) takes the form …”

Section: Formulationmentioning

confidence: 99%

“…Recently, experiments on the bulk-wave propagation and the related focusing with ultrasound beams have been made by several groupS.4,5 Specifically, utilizing the ultrasonic imaging technique, Hauser, Weaver, and Wolfe 5 have observed very clearly the finite-wavelength effect on the phonon focusing, that is, the fringe patterns of acoustic intensity have been seen in the expected focusing regions. These patterns arise from the interfer-0163-1829/94/49(24)/17378(7)/$06.00 49 ence between waves with different wave vectors but with group velocities pointing in the same direction.…”

Section: Introductionmentioning

confidence: 99%

“…This effect is called "internal diffraction" of acoustic waves in crystals. 5 The focusing effect is also expected to occur for phonons propagating along crystal surfaces, i.e., surface phonons or surface acoustic waves. Theoretically, the focusing of Rayleigh surface waves (RSW) on the (100), (110), and (111) faces of GaAs and in several other crystals with lower symmetries has been studied by Tamura and Honjo.…”

Section: Introductionmentioning

confidence: 99%

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Finite-wavelength effect on the ballistic propagation of surface acoustic waves

Tamura

Yagi

1994

Phys. Rev. B

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We study the phonon-focusing effects of the Rayleigh and pseudosurface waves propagating ballistically on the (100) surface of cubic crystals. Specifically, solving the wave equations for lattice displacements, we consider the finite-wavelength effect at the MHz-frequency range and for 1-cm propagation distance. The amplitude and polarization of lattice displacements at the surface associated with surface waves are sensitive to the propagation direction. Owing to this characteristic of surface waves, the focusing factor defined in the ray picture does not necessarily describe correctly the intensity of surface waves excited from a point source. The angular dependences of the calculated displacement amplitudes explain an important feature of the recent focusing experiment of Rayleigh waves, which the simple theory based on the focusing factor fails to predict.

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Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite-wavelength effect on the ballistic propagation of surface acoustic waves

Tamura

Yagi

1994

Phys. Rev. B

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“…This behaviour in the geometric shadow has been predicted by Maris in 1983 [1], by applying to phonons analysis the pioneerly work performed by Pearcey in electromagnetism [2]. It has been experimentally observed at ultrasonic frequencies by making use of quasi-monochromatic sources [3][4][5]. This phenomenom of diffraction at an edge, which is observed although no actual screen spatially limits the radiation, is called internal diffraction or diffraction at the cusp edge.…”

Section: Introductionmentioning

confidence: 98%

“…The relation given by Eq. (27) depends on x 3 . To obtain an invariant energy relation, let us integrate this relation along the depth.…”

Section: Energy Relationmentioning

confidence: 99%

Complex surface rays associated with inhomogeneous skimming and Rayleigh waves

Deschamps¹,

Huet²

2009

International Journal of Non-Linear Mechanics

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The Rayleigh wave, that propagates at the free surface of semi-infinite anisotropic medium, is composed of three inhomogeneous partial waves, each propagating along the surface with a different attenuation along the depth. Since this wave does not exhibit an attenuation on the surface, let us call it the homogeneous Rayleigh wave. The associated slowness corresponds to the real solution of the Rayleigh dispersion equation. Besides this classical solution, an infinite number of complex solutions of the Rayleigh dispersion equation exits. For such particular Rayleigh waves, the slowness vector, i.e. the identical component on the surface of the slowness of each partial waves, is taken to be complex. Thus, these Rayleigh waves are attenuated on the surface and as shown here, their attenuation is normal to the ray direction (or the energy velocity direction). Similarly to the infinite inhomogeneous plane waves which can be associated with complex rays, we call these waves, inhomogeneous Rayleigh waves. We use the inhomogeneous skimming waves, which are inhomogeneous plane waves, and the inhomogeneous Rayleigh waves to explain differently the usual diffraction phenomena on the free surface which cannot be explained by the real ray theory. For example, the arrival time of the wave packet observed beyond the cusp is in perfect accordance with the arrival time of some specific inhomogeneous Rayleigh waves. We show that these results are in agreement with the computation of the Green function. They apply to the theory of surface waves in linear elastodynamics with intrinsic anisotropy as well as to the theory of surface waves in linearized (incremental) elastodynamics with strain- A c c e p t e d m a n u s c r i p tPage 2 induced anisotropy (also known as small-amplitude waves superimposed on the large static homogeneous deformation of a nonlinear solid).

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References

2008

Acoustic Microscopy

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Internal diffraction of ultrasound in crystals: Phonon focusing at long wavelengths

Cited by 73 publications

References 8 publications

Finite-wavelength effect on the ballistic propagation of surface acoustic waves

Finite-wavelength effect on the ballistic propagation of surface acoustic waves

Complex surface rays associated with inhomogeneous skimming and Rayleigh waves

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