Application of Riccati-Bessel functions in light scattering

Abstract

Riccati-Bessel functions, written as combinations of amplitude and phase functions, have been used to re-express Mie theory. This leads to a simple physical explanation of the scattered phase angle as the sum of a phase shift arising from the optical path difference across the particle radius and an interfacial phase difference at the surface of the particle. The mathematical properties of the different phase angles are examined in detail by treating the order as a continuous variable.