Artificial Field Equations for a Region Where μ and ε Vary with Position

Abstract

I. Theory. The field equations developed admit of solutions in regions where μ and ε vary with position. For regions of zero conductivity, they are symmetrical with respect to electric and magnetic quantities, and the TM case can be derived from the TE. Fields derivable from a single component 4-potential are examined, and their propagation equations are found. A table relates the tensor and pseudo-tensor components to the usual vector components. II. Applications in cylindrical polar coordinates. For the TE case, three types of solution exist, called A, B, or C, where the E field is parallel to the elementary vectors dz, dr or rdθ, respectively (for the TM case, H replaces E). In each TM or TE case, two possible distributions of μ and ε occur, leading to separable propagation equations. TEM waves can be derived from both TM and TE cases, but the impedances are different. TE, TM and TEM waves for certain specific distributions of μ and ε, and their applications to curved guides, horns, and co-axial lines are considered. Some expressions are obtained for the fields, propagation constants, cut-off frequencies, and impedance. These solutions are not necessarily of the most general type, for to meet the conditions that restrict their choice, μ and ε are taken to be independent of the coordinate to which the transverse component of E (in TE) or H (in TM) is parallel.