A Study of Negative Permittivity and Permeability for Small Sphere

When analyzing a small dielectric sphere with Mie´s series or at low frequencies, we will have singularities if the permittivity or permeability is -2. This letter shows that for electrodynamic situation, this singularity is only a result of error in the asymptotic analysis and will not appear in actual cases. However, for the electrostatic case, if one can create a permittivity of -2, this singularity does result in an infinite field.