Patterns in Mie scattering

This work demonstrates that heretofore undisclosed patterns emerge when the Mie scattered intensity for an arbitrary sphere of radius R and refractive index In is plotted versus the dimensionless parameter qR, where q = 4 pi lambda(-1)sin(theta/2) is the scattering wavevector at scattering angle theta for wavelength lambda. When the interference ripple structure is ignored, three power law regimes can appear. These regimes are dependent on the phase shift parameter rho = 2kR\m - 1\, where k is the wave number, with the behavior having universal aspects for a given rho. To explain these patterns use is made of a general concept that the scattered intensity is the square of the Fourier transform, i.e., the structure factor, of the illuminated portion of the scattering object. If we make an approximation that the illuminate portion of the sphere is an annular shell at large rho, Fourier transformation of the shell, and scaling arguments can explain these power laws and the length scales associated with their crossovers. However, such an approximation is severe and an exact explanation of the new patterns is still lacking. (C) 2000 Elsevier Science B.V. All rights reserved.