Patterns in Mie scattering: evolution when normalized by the Rayleigh cross section

An alternative to using the traditional scattering angle theta to describe light scattering from a uniform dielectric sphere is the dimensionless parameter qR, where R is the radius of the sphere, q = 2k sin(theta/2), and k is the wavenumber of the incident light. Simple patterns appear in the scattered intensity if qR is used in place of theta. These patterns are characterized by the envelopes approximating the scattered intensity distributions and are quantified by the phase-shift parameter rho = 2kR/m - 1/, where m is the real refractive index of the sphere. Here we find new patterns in these envelopes when the scattered intensity is normalized to the Rayleigh differential cross section. Mie scattering is found to be similar to Rayleigh scattering when p < 1 and follows simple patterns for p > 1, which evolve predictably as a function of p. These patterns allow us to present a unifying picture of the evolution of Mie scattering for changes in kR and m.