Backscattering enhancements for tilted solid plastic cylinders in water due to the caustic merging transition: observations and theory

Bulk shear and longitudinal waves give rise to important contributions to the scattering of ultrasound by tilted finite plastic and rubber cylinders in water. This occurs in situations where either the shear or longitudinal speed is less than the speed of sound in the surrounding water. At a certain critical tilt angle, large backscattering enhancements are observed for finite cylinders, where the wave vector can reverse direction upon reflection from the cylinder truncation. The scattering process is analogous to the enhancement produced by the merging of rainbow caustics of primary rainbow rays in the scattering of light by long dielectric cylinders, also known as the caustic merging transition C. M. Mount, D. B. Thiessen, and P. L. Marston, Appl. Opt. 37, 1534-1539 (1998)]. A ray theory was developed to model the backscattering mechanism at the critical tilt angle. It employs the idea of the Bravais effective refractive index, convenient for constructing ray diagrams for the projections of rays in the base plane of the cylinder. There is general agreement between the theory and the experiment down to relatively low ultrasonic frequencies (ka as small as 10). The enhancement is the most significant backscattering contribution for a wide range of tilt angles.