Mie Coefficients

We consider the scattering of electromagnetic radiation by a spherical particle, known as Mie scattering. The electric and magnetic fields are represented by multipole fields, and the amplitudes are the Mie scattering coefficients. Properties of the particle are mainly contained in these coefficients. We have studied the dependence of these coefficients on the various parameters, with an emphasis on the dependence on the particle radius. Central to this discussion is what is known as the ‘Mie circle’. Without absorption in the particle or the embedding medium, the Mie scattering coefficients lie on this universal circle in the complex plane. We have studied the location of the Mie scattering coefficients on this circle as a function of the particle radius. The Mie circle also serves as a reference for the case when there is absorption in the particle or the medium. In the limit of a small particle, a peculiar divergence appears in the expression for the Mie coefficients, known as the Fröhlich resonance. We show that this apparent singularity is a consequence of the fact that the limit of a small particle fails in the neighborhood of this resonance, and we derive an expression for the correct small-particle limit in the neighborhood of this resonance.