Distributive deflection of Rayleigh waves

Asymptotically exact coupled-mode equations which govern the characteristics of distributive deflection of Rayleigh waves caused by a weak periodic corrugation of the free surface of an elastically isotropic half-space are deduced for the general case in which the wave vectors are not aligned with the grating vector. The theory is applied to obtain the characteristics of the selective deflection of a Rayleigh wave incident obliquely on a moderately long periodic array of shallow grooves etched on the free surface. The Brewster phenomenon of total transmission exists, with the Brewster angle depending only on the Poisson ratio. For angles of incidence sufficiently greater than the Brewster angle, the reflection coefficient is considerably larger than for normal incidence. For the special case of a 90° deflection caused by a grating whose length is sufficiently small, the experimental observations available in the literature are in good agreement with the present theoretical predictions. The dephasing effects caused by the wave frequency being different from the Bragg frequency and by the angle of incidence being different from the Bragg angle have also been examined.