Abstract:
When a beam of sound is incident on an elastic half-space at the Rayleigh angle, the rapid variation of the phase of the reflection coefficient produces the classical effect known as beam displacement. Considered here is the corresponding effect on the second harmonic component generated nonlinearly in the fluid. Experiments were performed in water with a 1-MHz beam radiated from a circular source of radius 1.2 cm. The beam was incident on an aluminum block at several angles near and at the Rayleigh angle. A quasilinear theory was developed in which the primary beam is decomposed into its angular spectrum. Analytic solutions were derived for second harmonic generation by pairs of angular spectrum components in the incident and reflected fields. The analytic solutions are superposed, and the second harmonic field is constructed from the resulting angular spectrum. There are no restrictions on source geometry or angle of incidence. Theory is in excellent agreement with experiment. Calculations reveal that in the reflected field, second harmonic components generated separately in the incident and reflected beams combine constructively in regions associated with specular reflection, and destructively in regions associated with radiation by the Rayleigh wave. [Work supported by ONR and the Schlumberger Foundation.]