Direct access to the dispersion relations of multiple anisotropic surface acoustic modes by Fourier image analysis

Abstract

We present a method based on a combination of temporal and spatial Fourier image analysis, involving the incorporation of a time-reversed acoustic propagation component, that can be used to obtain the angular dispersion or general dispersion relations of multiple surface acoustic modes excited by a localized pulsed source. The method is applied to the study of acoustic propagation at the surface of the highly anisotropic single-crystal TeO 2 coated with a thin gold film. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1602151͔ Surface acoustic wave propagation on bulk materials and thin film structures has proved of fundamental and practical interest for studying anisotropy and measuring film thicknesses or elastic properties. 1-6 A common method for such investigations is to use plane acoustic wave fronts, and to repeat the experiment for each propagation direction sequentially. However, the imaging of acoustic waves emanating from a point source is very useful for materials characterization because phenomena dependent on propagation direction, such as surface phonon focusing, can be effectively and immediately recorded with an omnidirectional acoustic wave vector distribution. [7][8][9][10][11] For surface acoustic imaging with impulsive point sources, the group velocity is readily measured from the wave front shape. However, it is the phase velocity-or its reciprocal, the slowness-that is more directly related to material elastic properties. 12 Impulsive point-source acoustic excitation of anisotropic samples by nature involves the generation of several surface and bulk acoustic modes that can produce complex overlapping wave fronts; no general method for the direct and automatic extraction of the individual dispersion relations ͑and hence the phase velocities͒ from such experimental images involving multiple propagating modes traveling parallel to the surface has been proposed. Previous methods can only be applied to images where only one acoustic mode propagates in any particular direction. 9 In this letter we present a general technique for analysis in time-resolved acoustic imaging at surfaces in the two lateral spatial dimensions that allows the extraction of the full set of dispersion relations for all excited modes simultaneously.We demonstrate the method with experiments on the transparent tetragonal crystal TeO 2 cut in the ͑001͒ orientation and coated with a thin polycrystalline gold film of thickness ͑40 nm͒ small enough to avoid significant thin film dispersion here and thus simplify comparison with theory. This crystal is strongly anisotropic in this cut and results in a complex phonon focusing pattern, ideal for evaluating techniques for acoustic mode analysis. 9, 13 We use an ultrafast optical pump and probe technique based on a common-path interferometer. 14 Acoustic waves are thermoelastically excited at a ϳ4 m Gaussian spot ͑full width at half maximum intensity͒ in the sample using optical pulses normally incident from the substrate side at wavelength 415 nm, repetition rate 80 MHz, du...

Scanning ultrafast Sagnac interferometry for imaging two-dimensional surface wave propagation

“…Moreover, by in addition taking the two-dimensional spatial Fourier transform, the dispersion relation of the surface wave propagation can be derived. 6 It is also possible to control the repetition rate of the optical pulses using a pulse picker to allow a variable recovery time for the sample to excitation. The frequency of operation of the interferometer is limited at high frequencies to the inverse of the optical pulse duration, and operation up to 50 THz should be relatively straightforward.…”

“…The detailed acoustic spectrum for such thermoelastic generation is described elsewhere. 5,6 As explained in Sec. II A, the SAWs are detected through the outward surface motion of the sample, which only contributes to the quantity ␦ .…”

“…Surface motion or strain-induced refractive index changes, in particular, provide suitable mechanisms for the optical sensing of surface acoustic waves ͑SAWs͒ on solids with visible optical wavelengths. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Developments in this field have been driven by the possibilities for nondestructively monitoring SAW propagation for the characterization of the elastic properties of isotropic and anisotropic materials, the mechanical properties of thin films, and SAW devices such as filters. [15][16][17][18][19][20] Moreover, the imaging of SAW propagation on crystals is of fundamental interest because of the complex focusing patterns that arise from the variation of sound velocity with propagation direction.…”

“…[15][16][17][18][19][20] Moreover, the imaging of SAW propagation on crystals is of fundamental interest because of the complex focusing patterns that arise from the variation of sound velocity with propagation direction. [1][2][3][4][5][6] Various optical detection techniques for SAW have been proposed: knife-edge techniques, [13][14][15] interferometric techniques, [4][5][6]17,18,21,22 holographic techniques, 7,8,[10][11][12]15 Schlieren techniques, 16 diffraction techniques, 19 and Brillouin scattering techniques. 15,23 Full information on the SAW field for a general broadband wave disturbance can be most simply obtained by real time detection, and the knife-edge and interferometric techniques have proved most successful for this.…”

Interferometric imaging of surface acoustic waves on a glass sphere

“…7,10 The acoustic field f͑r , t͒ ͑where r represents the position x = a x and y = a y on the curved surface of the sphere͒, corresponding to ⌬ in experiment, can be expressed for our small ͑Ϯ10°͒ rotation angles as a combination of Fourier transforms in the spatial and temporal domains…”