Systematic behavior of the Mie scattering coefficients of spheres as a function of order

The Mie scattering coefficients of large homogeneous dielectric spheres are shown to vary systematically with order. A general analysis of the coefficients gives formulas that depend only on two real electric and magnetic multipole phase angles. Such angles decrease in a quasimonotonic manner with order and explain the cutoff of Mie and Gegenbauer coefficients at order n approximate to alpha, the outer size parameter of the sphere, independently of the refractive index to first order. When the relative refractive index of the sphere m is moderately greater than unity, the multipole phase angles become integer values of pi at large orders and approach zero by a sequence of steps in the form of a descending staircase. It is also shown that Rayleigh-Debye scattering corresponds to the limiting case of m-1-->0.