Back reflection of ultrasonic waves from a liquid-solid interrace

A new acoustic phenomenon has recently been observed in experiments where a bounded beam of ultrasound is incident upon a smooth liquid-solid interface. A significant amount of coherent radiation is found to be backscattered in the general direction of incidence. The angle of back reflection is observed to be equal to the Critical Rayleigh angle or leaky wave angle. Most of these observations were made during experiments on the Schoch displacement effect, and therefore it has been tacitly assumed that the back reflection is strongly dependent upon the angle of incidence, as is the case for the beam shifting in the Schoch effect. We present a theoretical basis for this new phenomenon. A two-dimensional incident beam of Gaussian profile is considered. By a careful analysis we isolate that part of the field on the interface which has Fourier components corresponding to backward propagating waves in the liquid. This subset of the total wave field is then considered separately and it is shown to display a maximum in a certain direction, close to the critical Rayleigh angle. This peak in the angular pattern of the scattered field corresponds to an evanescent reflection boundary. We discuss the dependence of the effect upon certain parameters. The amplitude is shown to decrease as the beam width is increased, and it increases with increasing Schoch displacement. This backscattering ispresent for all angles of incidence; there is nothing inherently special about the Rayleigh angle.