A new practical approach to light scattering by spheroids with the use of spheroidal and spherical function bases

Abstract

The approximation of real non-spherical scatterers by spheroids is used in various applications. It often requires fast massive calculations of the optical properties of spheroids. The most powerful approach to that is known to be a field expansion in terms of spheroidal wave functions, in particular, in the way suggested by Farafonov over 30 years ago. We improve the main shortcomings of such an approach. Our solution is formulated in terms of normalised spheroidal functions, and firstly for their definition given by Meixner & Schäfke, which is computationally favourable and is required by the unique subroutines recently created to compute these functions. By means of T-matrix transformations we solve a long-standing major problem of Farafonov’s version, namely the accuracy and time losses for one kind (TE mode) of the incident wave polarisation. Apart from this and other improvements of this solution, for the first time we relate its single particle spheroidal T-matrix to the standard spherical one which is widely employed for particle ensembles. The constructed algorithm has been extensively numerically tested. It is found to be very accurate for dielectric spheroids with the aspect ratio a/b reaching 100 and the diffraction (size) parameter xa=2πa/λ as large as 300, where a and b are the major and minor semi-axes, respectively, λ is the wavelength. The algorithm is supplied with a program interface to the free package CosTuuM to perform parallel computations of various optical properties for ensembles of spheroids with different distributions over orientation (alignment) and shape.