Comparison of the light scattering methods using the spherical basis

A comparative analysis of the widely known methods for solving the problem of light scattering by nonspherical particles—of the method of separation of variables (MSV), of the extended boundary condition method (EBCM), and the point-matching method (PMM), which use the spherical wave functions as a basis for the expansions of the fields—is carried out. In the scientific literature, these methods have been analyzed independently of one another in spite of their evident similarity: The same expansion coefficients are determined from similar set of equations and all optical characteristics are calculated with the same formulas. The ranges of applicability of the methods for dielectric spheroids and Chebyshev particles are studied in the same manner. It was found that, when considering the far-field zone, theoretical conditions of mathematical correctness of the EBCM and the MSV, apparently, differ fundamentally, although, as was shown, the methods themselves are extremely closely related. The performed numerical calculations suggest that the EBCM is preferable for spheroids, the MSV is preferable for Chebyshev particles, and the PMM, which is the most time-consuming method, gives satisfactory results in many cases when two other methods are inapplicable. Since the methods supplement one another well and their programs differ only in several tens of operators, we propose combining these methods within the framework of one universal program.