Watching Ripples on Crystals

Abstract

We present a new method for imaging surface phonon focusing and dispersion at frequencies up to 1 GHz that makes use of ultrafast optical excitation and detection. Animations of coherent surface phonon wave packets emanating from a point source on isotropic and anisotropic solids are obtained with micron lateral resolution. We resolve rounded-square shaped wave fronts on the (100) plane of LiF and discover isolated pockets of pseudosurface wave propagation with exceptionally high group velocity in the (001) plane of TeO 2 . Surface phonon refraction and concentration in a minute gold pyramid is also revealed. DOI: 10.1103/PhysRevLett.88.185504 PACS numbers: 63.20.Dj, 62.65. +k, 68.35.Iv, 77.65.Dq Sound waves in crystals, dependent on the fourth-order elastic constant tensor, display a rich array of anisotropic propagation phenomena. Despite a crystal being homogeneous, a point acoustic source in the bulk can lead to singularities in acoustic flux in certain directions owing to the angular dependence of the phase and group velocities of the three acoustic polarizations [1]. This phonon focusing effect was first discovered in the bulk [2], but surface phonons were predicted to produce equally intriguing focusing patterns [3]. In the 10 MHz -1 GHz range, where acoustic wavelengths are typically 3 300 mm, various methods have been suggested for two-dimensional surface phonon imaging, such as stroboscopic probing, the sprinkling of powder on the surface, or detection by immersed point-focus transducers [4][5][6]. However, despite the growing interest in the field of surface acoustic wave devices, no technique has been successful in imaging surface phonon focusing in real time. Such imaging allows direct access to the dispersion characteristics of the wave propagation and the possibility of following the temporal evolution of cuspidal structures. In this Letter we image the propagation of coherent surface phonons at frequencies up to 1 GHz in real time, allowing animations of pointexcited surface phonon wave packets to be made with picosecond temporal and micron spatial resolutions.We use an ultrafast optical pump and probe technique with a common-path interferometer [7]. Surface phonon wave packets are thermoelastically excited in thin metal films on transparent substrates with optical pulses of wavelength 415 nm, repetition rate 80 MHz (one pulse every 12.5 ns), duration ϳ1 ps, and pulse energy ϳ0.3 nJ, producing a maximum transient temperature rise ϳ100 K. This pump light is focused at normal incidence through the substrate to a circular spot of diameter D ഠ 2 mm (full width at half maximum intensity; see Fig. 1). Out-ofplane (z) surface motion is detected interferometrically with ϳ1 pm resolution by the use of two probe pulses at an interval of t 510 ps, focused at normal incidence to a single spot of diameter ϳD on the front surface of the film. These pulses, of wavelength 830 nm, are derived from the same laser as the pump. In a simple modification of the apparatus of Ref.[7], we divide the output beam from ...

Wave-front images of acoustic waves in the (100) and (001) surfaces ofTeO2

“…These theoretical images for the lattice displacement u 1 are consistent ͑both in shape and in brightness͒ with the experimental images for the particle velocity u 1 obtained by Sugawara et al 2 We see the dominant anisotropic signature of elliptical shape at the center together with faint signals outside. The latter disappears rather quickly as time elapses.…”

“…This is consistent with the experimental situation. 2,3 More explicitly the initial displacement profile is…”

“…2,3 They used the optical pump and probe technique 4 to periodically excite surface phonons, illuminating an opaque thin film on a transparent substrate. With this technique they have imaged the wave fronts of acoustic waves on surfaces at frequencies up to 1 GHz.…”

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

“…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.…”

“…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.…”