Applicability of the T-matrix method and its modifications

Abstract

The range of applicability of the T-matrix method and its modifications for solving the problem if the scattering of electromagnetic radiation by nonspherical, axially symmetric particles is investigated analytically and numerically. The use of this method for calculating the characteristics of scattered radiation in the farfield region (the extinction and scattering cross sections, the scattering indicatrix, etc.) is shown to be appropriate for “weak-Rayleigh-type” particles. This condition is met when the intersection of the analytic continuations of the scattered and internal fields contains a ring with the center at the origin of coordinates. For a reliable calculation of the scattered field in the near-field region, it is necessary that a particle be a “Rayleigh-type” one (i.e., the Rayleigh hypothesis be valid for it). In this case, the singularities of the scattered field must occur inside a sphere lying inside a scatterer. Spheroidal particles are weak-Rayleigh-type ones if their semiaxes ratio is $a/b < (\sqrt {2 + 1} )$, and they are Rayleigh-type ones if $a/b < \sqrt 2$. Numerical calculations for spheroids and Chebyshev particles corroborate these conclusions. However, the indicated boundaries are “ spread” (toward the expansion), because the expansion coefficients for the fields are determined with the use of the reduced (i.e., finite) systems. The limiting sizes of the particles for which the T-matrix method gives plausible results are primarily determined by their geometry (shape).