Dependence of surface wave nonlinearity on propagation direction in crystalline silicon

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, edited by R. J. Wei (Nanjing U.P., Nanjing, 1996), pp. 64–69]. Propagation at angle θ with respect to the 〈100〉 direction in the (001) plane of crystalline silicon was considered. Because of symmetry it is sufficient to investigate Rlm(θ) for 0°≤θ≤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. R11