Dependence of surface wave nonlinearity on propagation
direction in crystalline silicon
R. E. Kumon, M. F. Hamilton (Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX 78712-1063), Yu. A. Il'inskii, E. A. Zabolotskaya (MacroSonix Corporation, 1570 East Parham Road, Richmond, VA 23228).
The nonlinearity matrix elements Rlm (corresponding to generation of harmonic l+m) for a surface wave in a crystal depend on both the plane of propagation and the direction of propagation in that plane [Hamilton et al., Nonlinear Acoustics in Perspective, R. J. Wei, ed. (Nanjing University Press, Nanjing, 1996), pp. 64-69]. We considered propagation at angle q with respect to the á100ñ direction in the (001) plane of crystalline silicon. Because of symmetry it is sufficient to investigate Rlm(q) for 0° £ q £ 45°. Consider first R11, which corresponds to second-harmonic generation. The sign of R11 indicates whether finite-amplitude effects cause a waveform to steepen forward or backward. We obtain R11 < 0 for 0° £ q < 21° and 32° < q £ 45°, with R11 > 0 for 21° < q < 32°. Moreover, it appears that all elements Rlm(q) have the same sign dependence and zero crossings (q @ 21° and q @ 32°). Numerical simulations reveal that for 0° £ q < 21° and 32° < q £ 45° positive segments of the longitudinal particle velocity waveform steepen backward in space (i.e., opposite what a sound wave does in air), they propagate almost linearly at q @ 21° and q @ 32°, and between these angles they steepen forward. Nonlinearity thus varies far more strongly than small-signal sound speed as a function of propagation direction. [Work supported by ONR.]
Technical Area: Physical Acoustics (Nonlinear Acoustics)
(PACS) Subject Classification number(s): 43.25.Fe