##
**Conference Abstract:**

**136th Meeting of the Acoustical Society of America, **

Norfolk, Virginia, USA (12-16 Oct 1998)
**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 *R*_{lm} (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 *R*_{lm}(q) for 0^{°} £ q £ 45^{°}. Consider
first *R*_{11},
which corresponds to second-harmonic generation. The sign of
*R*_{11} indicates whether finite-amplitude effects cause a waveform to steepen
forward or backward. We obtain *R*_{11} < 0 for 0^{°} £ q < 21^{°} and
32^{°} < q £ 45^{°}, with *R*_{11} > 0 for 21^{°} < q < 32^{°}.
Moreover, it appears that all elements *R*_{lm}(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

File translated from T_{E}X by T_{T}H,
version 0.9.

Ronald Kumon / Acoustics
Group / UT Austin / Created 13
May 1998 / Updated 13 May 1998