The discretized Mie formalism a novel algorithm to treat scattering on axisymmetric particles

Abstract

In this paper, a new algorithm is proposed for the analysis of scattering on nonspherical axisymmetric particles. The solution of the non - separable Helmholtz equation is performed by use of the Method of Lines - a powerful technique for solving partial differential equations if appropriate boundary conditions hold. As a result, a numerical generalization of the well known Mie theory for spheres is found. The simple concept and the improved convergence behavior, compared to existing methods, are the main advantages of this new algorithm. Besides a detailed theoretical description, first applications to spheres, shifted spheres, and ellipsoidal particles are discussed with special emphasis to the polarimetric differential scattering coefficients. The particular characteristics of shifted spheres for the investigation of the convergence behavior are demonstrated.