General Systropy in Spherical Scatterers

This paper discusses a spherical scatterer whose anisotropy axes are defined by the spherical coordinates. Such a scatterer is called systropic sphere. Electrostatic scattering from systropic spherical objects has been studied earlier but with some restrictions. This paper provides a generalized method for studying the systropic sphere. More specifically, the paper focuses on the electrostatic scattering of the systropic sphere described by two quantities: the axial and the transverse polarizabilities. The axial polarizability does not depend on the azimuthal permittivity component, which simplifies the problem sufficiently to make it a subject to an analytical approach. In contrast, the transverse polarizability depends on the azimuthal permittivity component, which makes the problem complex enough to require a semi-analytic approach. This paper describes a novel way to study the systropic sphere. An important parameter in the systropy research is the ratio between the two tangential permittivity components, called systropy ratio. The novel method drastically extends the scope of the systropy research, by allowing a wider range of systropy ratios, a range that covers the whole set of positive real numbers. While the range of systropy ratios has been formerly restricted to square numbers, the new method that uses Gegenbauer polynomials, can solve the more general case.