Theory of Nonspecular Reflection. Effects for an Ultrasonic Beam Incident on a Solid Plate in a Liquid

Poles and zeroes of the infinite plane wave amplitude reflection coefficient are used to derive a theoretical prediction of the nonspecular reflection effects which have been observed for an ultrasonic beam incident on an isotropic solid plate in a liquid. It is shown that there are two types of nonspecular reflections, and they can be characterized in terms of a single parameter which requires a knowledge of the imaginary part of a pole of the infinite plane wave reflection coefficient. Theoretical predictions of nonspecular reflection intensities are presented. Finally, it is shown that the reflection characteristics for high-frequency beams incident on thick plates are the same as those expected for the reflection from a single liquidisolid interface, i.e., two infinite half-spaces. T INTRODUCTION HEORETICAL and experimental aspects of beam displacement phenomena have been actively studied since 1947 when Coos and Hanchen [ l ] demonstrated that a beam of light is displaced from the expected geometrically reflected beam upon reflection from the interface between two transparent media. In 1950 Schoch predicted [2] and later experimentally verified [3 J the beam displacement effect for an acoustic beam incident on a liquid/solid (L/S) interface. Schoch’s theory predicted that an incident bounded acoustic beam would be nonspecularly reflected in that the reflected beam would be displaced laterally along the interface while the reflected beam profile retained the same general shape as the incident beam profile. analysis of nonspecular reflection phenomena has been used Although the basic framework of Schoch’s theoretical Manuscript received May 17, 1976. This work was supported by the L. E. Pitts was with the Department of Physics, Georgetown UniverOffice of Naval Research, U.S. Navy. sity, Washington, DC 20057. He is now with the Department of Physics, Mary Washington College, Fredericksburg, VA 22401. sity, Washington, DC 20057. He is now with the Schlumberger-Doll Research Center, Ridgefield, CT 06877. sity, Washington, DC 20057. T. J. Plona was with the Department of Physics, Georgetown UniverW. G. Mayer is with the Department of Physics, Georgetown Univerby later authors [4] , [ 5 ] , his theory did not account for two experimentally observed phenomena: 1) the reflected sound field for certain bounded acoustic beams has a point of null sound intensity which is not present in the incident sound beam and 2) the main portion of the reflected sound field is accompanied by a sound field which becomes weaker as it extends for a considerable distance along the interface, away from the incident beam. This field is called the “trailing sound field. ” Assuming an incident beam which is approximately Gaussian, a schematic example of these two phenomena is shown in Fig. 1. have since been reconciled by Bertoni and Tamir [5]. A principle difference between Schoch’s analysis and that of Bertoni and Tamir is that the latter has emphasized the use of complex poles of the plane wave amplitude reflection coeffiThese discrepancies between Schoch’s theory and experiment