Bravais effective refractive index for tilted plastic cylinders and the caustic-merging transition in the meridional plane: Demonstration of an optical analogy

Abstract

Some solid scatterers in water such as plastic cylinders do not support leaky Rayleigh waves because the shear wave velocity of the solid is less than the speed of sound in water. The high-frequency scattering from such objects is generally weak. In that case the ray diagram for transmitted shear waves is analogous to the refraction of light by an object in air. For a tilted cylindrical object, the projection of rays on a base plane may be determined by ignoring the tilt by replacing the true refractive index n by the Bravais value (n2−sin2γ)1/2/cosγ where γ is the tilt. For a circular cylinder, when the Bravais value reaches 2, the rainbow caustics merge in the meridional plane defined by the incident wave vector and the cylinder’s axis [C. M. Mount and P. L. Marston, in Light and Color in the Open Air (OSA, Washington, DC, 1997), pp. 14–16]. The merged caustics greatly enhance the scattering because of the far-field focusing of a cusp point. The analysis is also relevant to light scattering by icicles and to the scattering of sound by certain liquid-filled cylinders. [Work supported by the Office of Naval Research.]