Backscattering due to ray reverberations between nonconcentric surfaces of a thick shell: Ray stability, transitions in wavefront shapes, and observed scattering enhancements due to focusing.

Abstract

The paraxial ray stability analysis previously developed for laser resonators is applied to high‐frequency elastic wave reverberations across the thickness of a shell having nonconcentric surfaces. A previous summation of backscattered amplitudes from rays reverberant within concentric surfaces [S. G. Kargl and P. L. Marston, J. Acoust. Soc. Am. 88, 1114–1122 (1990)] is found to lie on the boundary between stable and unstable resonators. Shifting the center of the inner surface of the shell away from the direction of the source produces a stable resonator. Rays reverberant between such nonconcentric surfaces produce a far‐field focusing that is periodic in the number of internal bounces. Exact ray tracing, used to identify scattered wavefront shapes near focal conditions, reveals the presence of glory rays (off‐axis rays which are exactly backscattered). Shifting the inner surface of the shell toward the source produces an unstable resonator and no focused rays. The existence of backscattering enhancement...