Rayleigh scattering and the internal coupling parameter for arbitrary particle shapes

A general method for calculating the Rayleigh scattering by a particle of arbitrary shape is introduced. Although analytical solutions for Rayleigh scattering exist for spheres and ellipsoids, analytical solutions for more complicated shapes don’t exist. We find that in general the Rayleigh differential cross section goes as k 4 V 2 | α ( m ) | 2 where k = 2 π / λ and λ is the wavelength, V is the volume of the particle and α ( m ) the average volume polarizability which is dependent on the shape and the complex index of refraction, m. We use existing computational techniques, the discrete dipole approximation (DDA) and the T-matrix method, to calculate the differential scattering cross section divided by k 4 and plot it vs V 2 to determine | α ( m ) | 2 . Furthermore, we show that this leads to a general description of the internal coupling parameter ρ arbitrary ′ = 2 π k V A | α ( m ) | where A is the average projected area of the particle in the direction of incident light. It is shown that this general method makes significant changes in the analysis of scattering by particles of any size and shape.