Analysis of scattering by spheres having a negative acoustical refractive index

Abstract

Electromagnetic waves having oppositely directed phase and group velocities propagate in metamaterials having a negative permeability and negative permittivity [J. B. Pendry and D. R. Smith, Phys. Today 57(6), 37–44 (2004)]. Such materials are predicted to have unusual electromagnetic scattering properties [R. Ruppin, Solid State Commun. 116, 411–415 (2000)]. If it is possible to fabricate acoustical materials having a simultaneously negative effective elastic modulus and density (in a dynamical sense), the mechanical energy flux will have the opposite direction as the wave-vector associated with phase evolution. Rays descriptive of the energy flux refracted by such hypothetical materials at interfaces with ordinary fluids would be characterized by a negative acoustical refractive index. Partial-wave-series calculations of high frequency scattering by fluid spheres having an acoustical refractive index at (or close to) 1 reveal backscattering enhancements associated with glory rays which, unlike ordinary spheres [P. L. Marston and D. S. Langley, J. Acoust. Soc. Am. 73, 1464–1475 (1983)], require only a single internal chord. Generalized Lamb waves on elastic shells having opposite phase and group velocities also cause enhanced backscattering associated with unusual rays [G. Kaduchak, D. H. Hughes, and P. L. Marston, J. Acoust. Soc. Am. 96, 3704–3714 (1994)].