Improved-anomalous diffraction approximation for accurate extinction, scatter, and absorption efficiency calculations

Abstract

In the 1950s H.C. van de Hulst heuristically developed a simple formula, called anomalous diffraction approximation (ADA), which closely represents the extinction efficiency derived from Mie theory for spherical dielectric particles in certain limits. The method is computationally fast and can be applied to non-spherical particle shapes, thus it is very useful. The formula works best for large size parameters (proportional to radius over wavelength) and for the refractive index ratio of the particle to background close to one. Because of its usefulness, work has continued to develop this approach for a variety of particle shapes and a greater range of size parameter and refractive index. In this paper a more rigorous foundation is used that begins with the scalar Helmholtz equation and leads to the ADA formulas with appropriate approximations for both dielectric and conducting particles. By relaxing some of the approximations and accounting for the polarizability response of the particle to the applied field, an improved-ADA formula is derived. It more accurately predicts the extinction and absorption efficiencies over the full range of the particle size parameter and for real part of refractive index ratios from just less than one up to 2.5 and for the imaginary part much less than 1.