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The relations between the T-matrices emerging when solving the problem of light scattering by a spheroid by applying the expansions of the electro-magnetic fields in the employing spheroidal and spherical bases are found. The behavior of the obtained relations is numerically studied, and it is noted that in a wide range of the task parameter values the calculation of the spheroidal T-matrix and its corresponding transformation is the only practical way to derive the spherical T-matrix often used in applications. [ABSTRACT FROM AUTHOR]

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 R < R, which depends only on the particle shape. [ABSTRACT FROM AUTHOR]

A procedure for analytical averaging of the attenuation and scattering cross sections for systems of chaotically oriented axially symmetric particles was developed for the first time within the framework of the modified T-matrix method and the method of separation of variables for spheroids. These approaches essentially complement each other: one is applicable to axially symmetric scatterers of different shape but is inefficient if the ratio of the maximum to the minimum size of the particles exceeds 3–5; the other is applicable only to spheroids, but the ratio of the major semiaxis to the minor one can be considerable, for example, 100 and larger. © 2004 MAIK “Nauka / Interperiodica”. [ABSTRACT FROM AUTHOR]

The range of applicability of the T-matrix method and its modifications for solving the problem of 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 < (√2 + 1), and they are Rayleigh-type ones if a/b < √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). [ABSTRACT FROM AUTHOR]