Peculiarities in the dielectric response of negative-permittivity scatterers

This study analyzes polarizability properties of spherically layered small inclusions that possess negative permittivity. Conditions for invisibility to external electric fields are derived. The complementary principle for two-dimensional scatterers is used to derive special properties of self-complementary inclusions. A singular behavior between the limits of invisibility and infinite response is underlined for a hollow circular shell. A similar, although not as drastic, phenomenon is shown to take place for the three-dimensional hollow sphere.