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 $n\approx \alpha$, 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 $m-1\mathrm{}\to 0$.