This article analyzes the response of a sphere with radially anisotropic permittivity dyadic (RA sphere), in both the electrostatic and full electrodynamic settings. Depending on the values and signs of the permittivity components, the quasistatic polarizability of the RA sphere exhibits several very different interesting properties, including invisibility, field concentration, resonant singularities, and emergent losses. Special attention is given to the anomalous losses that appear in the case of certain hyperbolic anisotropy values. We show that their validity can be justified in a limiting sense by puncturing the sphere at the origin and adding a small imaginary part into the permittivity components. A hyperbolic RA sphere with very small intrinsic losses can thus have significant effective losses making it an effective absorber. With different choices of permittivities, the RA sphere could also perform as a cloak or a sensor. The Mie scattering results by an RA sphere are used to justify the quasistatic calculations. It is shown that in the small parameter limit the absorption efficiency of an RA sphere is nonzero for certain lossless hyperbolic anisotropies. The absorption and scattering efficiencies agree with the quasistatic calculations fairly well for spheres with size parameters up to 1/3.
- radial anisotropy