Diffraction-Free Propagation of Rayleigh Waves Observed along Solid Spherical Surfaces
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ing is that nanoscale indium particles seem to self-organize into specific sizes— magic number sizes,” Allen said. In the October 23 issue of Physical Review Letters, Efremov, Schiettekatte, and co-workers show, using nanocalorimetry, that the particles appear to self-assemble into special “magic” sizes, where each size differs incrementally by a single complete shell of atoms. STEFFEN K. KALDOR
Diffraction-Free Propagation of Rayleigh Waves Observed along Solid Spherical Surfaces Vibration and surface acoustic wave propagation in elastic spheres has been studied extensively, especially in seismology, where an elastic sphere is viewed as the simplest model of the Earth. Recent experiments have shown that the method by which surface waves propagate along a sphere depends on whether they arise from a point source or a line source. In seismology studies, where the source is orders of magnitude smaller than the Earth’s radius, a point source assumption
MRS BULLETIN/NOVEMBER 2000
is valid, and the wave behavior is well understood. However, researchers Yusuke Tsukahara and Noritaka Nakaso of Toppan Printing Company Ltd. and Hideo Cho and Kazushi Yamanaka of the Department of Materials Processing at Tohoku University observed earlier this year that as the radius of the sphere becomes comparable in size to the source, markedly different wave-propagation behavior occurs that cannot be explained by a point-source analysis, suggesting diffraction-free propagation [Appl. Phys. Lett., 76 (2000) p. 2797]. Now, in the October 30 issue of Applied Physics Letters, the researchers present a model, along with supporting experimental evidence, to explain this observed phenomenon. When a point force is applied to the surface of an elastic sphere at the south pole, Rayleigh waves, in addition to bulk waves, propagate along the surface in all directions. As the wave front crosses the equator, it converges toward the north pole and then diverges back toward the south pole; this process repeats indefinitely. Experiments carried out with a 20-mm-diameter
sphere heated by a laser beam focused to a small spot demonstrate this behavior. However, experiments employing an 8mm-diameter sphere heated by a line source consisting of a traveling optical inteference pattern show surface waves which travel within a narrow path over the spherical surface rather than spreading out, that is, diffraction-free propagation. To explain this phenomenon, Tsukahara and co-workers postulate that a line source of finite length, located along the equator, generates a beam of Rayleigh waves that undergo two effects that balance, if the line source length is appropriately chosen. The first effect, due to the curvature of the spherical surface, causes the Rayleigh waves to converge toward the poles, while the second effect, diffraction from a finite aperture, causes the Rayleigh waves to spread out over the surface of the sphere. When these two effects cancel, diffractionfree propagation of a finite beam width is realized. To verify their theory, the researchers f
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