Axially incident plane-wave scattering from an impedance sphere with two constant isotropic impedance surfaces

The canonical problem of an axially symmetric, isotropic impedance sphere with two constant impedance surfaces is formulated and solved for the case of a normally incident plane wave. Although the solution involves the truncation of an infinite series and numerical inversion of a linear system, its properties of a rapidly converging truncation process, evaluation of matrix elements in terms of known special functions, and rapid generation of remaining modal coefficients allow for an accurate representation of the fields. This is especially important near the impedance junction where discontinuities in some field components are expected. These properties make this solution an ideal test case for more general scattering codes.