Extrema in the light-scattering indicatrix of a homogeneous sphere

Abstract

Formation and migration of extrema in the angular dependency of the light-scattering intensity (an indicatrix), under variation of the size and the refractive index of a homogeneous sphere, have been studied analytically and numerically. Approximations of Wentzel-Kramers-Brillouin (WKB), Rayleigh-Gans-Debye (RGD), Fraunhofer diffraction, and anomalous diffraction (AD) have been considered for the relative refractive index ranging from 1.025 to 1.200. Utilization of these approximations has allowed us to reveal the generalized coordinates. The plot of extrema locations of the indicatrix calculated from the WKB approximation with these coordinates has shown a universal mechanism of formation of the indicatrix structure. We determined the upper boundary of the angular region of Fraunhofer diffraction (FD) applicability. An analysis of the extrema has shown that locations of the different minima migrate monotonically when the size of the sphere is varied. An empirical equation that relates the minimum location to the sphere size has been produced. It has been shown that the distance between minima is insensitive to variations of the relative refractive index. The disappearance of the minima with an increasing relative refractive index has been discussed.