Elastic wave transparency of a solid sphere coated with metamaterials

The elastic wave transparency phenomenon of a solid sphere coated with metamaterials is investigated in a solid host medium having nonzero shear modulus. The first three scattering coefficients of the coated sphere are derived in the Rayleigh limit and expressed in terms of the effective parameters of the coated sphere assemblage. It is found that the effective bulk modulus, mass density, and shear modulus of the coated sphere system dominate the zeroth, first, and second order scattering effects, respectively. Quasistatic transparency conditions are obtained by setting these scattering coefficients to be zero. It is also shown that the obtained transparency conditions are the same as those derived from the neutral inclusion concept. Obtained results from full-wave analyses show that the given conditions can well predict the transparency induced by metamaterials even in the regime far beyond the Rayleigh limit.