Polarizability of dielectricprolate half ellipse

This article presents a method for solving the polarizability of a dielectric prolate half ellipse as a function of its relative electric permittivity. The considered geometry consists of two conjoined half ellipses with different permittivities. The polarizability depends on the excitation field direction, therefore can be presented in the form of dyadic consisting of two components that are series and parallel polarizabilities. The method is based on analytical series expansions with coefficients obtained as a numerical solution of a matrix equation.