Separation of variables method for light scattering by two-layer spheroids with size parameters up to 1000

A spheroid has one more degree of freedom than a sphere, namely the aspect ratio defined as the ratio of the length of the rotational axis to that of the other axis perpendicular to the rotational symmetry axis. Previous studies demonstrated that the optical properties of natural nonspherical particles can be reasonably represented by those of spheroids. A two-layer spheroid has different refractive indices for the inner and outer layers, and accounts for both nonsphericity and inhomogeneity of a natural particle. However, there is no accurate method applicable to the computation of the optical properties of two-layer spheroids with small-to-large size parameters. This study develops what we believe to be a novel solution based on the separation of variables method in the spheroidal coordinate system to compute the optical properties of two-layer spheroids (SVM2L). Accurate and numerically stable techniques, including the Tikhonov regularization, are used to implement the SVM2L. The present SVM2L method can be robustly applied to two-layer spheroids with size parameters up to 1000, which are specified with respect to their semi-major axis lengths.