損失誘電体楕円筒と線波源による放射電磁界

抄録

The radiation patterns of a line current near the dielectric elliptic cylinder have been analyzed as a boundary-value problem for the two-dimensional electromagnetic wave equation using Mathieu functions and modified Mathieu functions. No reports based on exact calculation of Mathieu functions with consideration of their convergence have been published because the complex eigenvalues of Mathieu functions cannot be calculated easily. Recently, computational programs for calculating the complex eigenvalues have been derived. Developing these programs we can prepare the computational programs for calculating the analytic solutions of the boundary-value problem for the radiation and scattering of a lossy dielectric elliptic cylinder by a line current. We describe, in this paper, the method of calculating complex eigenvalues of Mathieu functions, the convergence of the series of Mathieu functions and the radiation-pattern characteristics of an infinitely long filament of an electric current source parallel to the elliptic cylinder which has the complex relative permittivity ε_r ∗.