The Mie scattering coefficients satisfy recurrence relations: a_n-1, b_n-1, a_n, and b_n determine a_n+1, and b_n+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

© 1987 Optical Society of America

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