Patterns in the ripple structure of Mie scattering

We study the ripple structure in the scattered intensity predicted by Mie scattering theory in the angular behavior of the scattered intensity for homogeneous, dielectric spheres. We find that for small values of the phase shift parameter rho = 2kR absolute value(m - 1), where k = 2 pi/lambda, R is the sphere radius, and m is the relative refractive index, the ripples are periodic with spacing equal to pi when plotted versus the dimensionless qR, where q = 2k sin(theta/2) and theta is the scattering angle. However, as rho increases, this outcome switches to nonuniform spacing of approximately pi cos(theta/2). The latter spacing is equivalent to a uniform spacing of pi/kR when plotted versus theta.