Reflected Beam Displacements of a Slightly Divergent Ultrasonic Gaussian Beam on a Water-Glass Interface Near Rayleigh Angle Incidence

Two reflected beams of a slightly divergent ultrasonic Gaussian beam on a water-glass interface are observed and recorded by a Schlieren system. The lateral displacements of the two reflected beams are measured for incident angle θ_i in a wide range of 10° around the Rayleigh angle θ_c. The displacements decrease as the incident angle increases, which is different from the previous predictions for bounded plane-wave beams, where the displacements have extremum at the Rayleigh angle θ_c.The explanation is based on the fact that the Gaussian beam generated by an ultrasonic transducer with a button (or strip) back electrode is actually slightly divergent. We extend Bertoni and Tamir's theory (Appl. Phys. 2 (1973) 157) to this case, and our calculated curves of the displacements against the incident angle are in agreement with the experimental results for |θ_i - θ_c| < 2°.