Generalized Telegraphers' and Helmholtz Equations for Conformal Structures With Bi-Anisotropic Loading Materials

Abstract

This paper introduces a proper set of rotations and variable changing in order to write Maxwell's equations in the generalized orthogonal curvilinear reference system just as in the Cartesian case. These transformations are very useful to strongly minimize the analytical difficulties that arise when handling equations involved in the solution of electromagnetic fields for conformal structures. First, a new set of telegrapher-like equations, called the "Generalized Transmission Line (GTL) equations", is obtained, relating the transverse field components in general conformal structures loaded with bi-anisotropic materials. Then, new Helmholtz equations formally identical to the Cartesian ones, but effective in the generalized curvilinear reference system, are also derived.