Properties of the T matrix in the Rayleigh approximation

Abstract

We have examined the properties of the T matrix in the Rayleigh approximation (i.e., in the electrostatic problem) for axisymmetric particles using an analog of the extended boundary condition method (EBCM). The T matrix can be constructed by two methods. In the first method, the field inside of the particle is initially determined and then the “scattered” field is found. In terms of the second approach, the problem is formulated straight for the scattered field. Theoretically, the two schemes are equivalent. Based on the refined analysis of a vast amount of numerical calculations for Chebyshev particles and pseudospheroids, it has been shown that, taking into account the influence of calculation errors, the second approach is much more efficient than the first one for determining the scattered field and the T matrix taking into account its symmetric character. Numerical investigations of the range of applicability of the EBCM have unambiguously confirmed theoretical inferences. Namely, the T matrix can be constructed by the EBCM only if there exists a nonempty intersection of analytical continuations of the expansions of the scattered and internal fields in terms of spherical functions. In other words, the radii of convergence of these expansions should satisfy the condition R1 < R2, which depends only on the particle shape.