Light Diffraction by Ultrasonic Waves as a Multiple-Scattering Process

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Abstract
Past theoretical studies of light diffraction by ultrasound have for the most part been severely limited in scope by the complexities of the analytical methods employed and by the consequent need to use simplifying restrictions in order to obtain useful results. Recently, however, a new analytical approach has been devised that yields valid quantitative results for arbitrarily specified conditions. This method, developed initially at the Physics Department of Michigan State University by Hargrove, has been extended at the Lockheed Research Laboratories. It treats the diffraction phenomenon as a multiple-scattering process, with the elementary scatterers considered as a series of layers formed by subdividing the ultrasonic beam along planes parallel to its direction of propagation. The layers are taken thin enough that the diffraction in any one is accurately described by the Raman-Nath theory; and the cumulative effect of all of the layers is obtained by an iterative process carried out on a digital computer. Hargrove's analysis yielded results in very good agreement with existing experimental data and covered the range of conditions appropriate for such a comparison. This paper presents the results of a study of the case of normal incidence but for a range of conditions extending far beyond those previously considered. In addition, the case of oblique incidence has been studied for incidence angles between zero and the Bragg angle for the second diffraction order and for a wide range of other pertinent parameters. Based on results of the theoretical phase of this study, a new physical interpretation is given of the diffraction process and of the widely used criteria for so-called “normal” or Raman-Nath diffraction and for strong Bragg diffraction. [Work supported by the Independent Research Program of Lockheed Missiles & Space Company.]

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