Recurrence relations for the Mie scattering coefficients

Abstract

The Mie scattering coefficients satisfy recurrence relations:an−1, bn−1, an, and bn determine an+1, and bn+1. It is therefore possible, in principle, to generate the entire set from the first four, which has a simple interpretation. Each term in a multipole expansion of an electrostatic field can be obtained by differentiating the preceding term. The Mie coefficients are terms in a multipole expansion of a particular electromagnetic field, namely, that scattered by an arbitrary sphere. By analogy, it is not surprising that all these coefficients can be generated from the electric and magnetic dipole and quadrupole terms. Moreover, the recurrence relations for the Mie coefficients contain finite differences, in analogy with the infinitesimal differences (derivatives) in the multipole expansion of an electrostatic field.