Surface modes along two parallel circular ferrite rods magnetized longitudinally

Abstract

A method is presented for solving the problem of propagation along many parallel ferrite rods magnetized axially. The characteristic determinant is derived from the reciprocity theorem where auxiliary electric and magnetic current sources are suitably selected. Using this method, the dispersion relations and the mode configurations of surface modes along two rods are shown and discussed in detail for both the cases of parallel and antiparallel magnetizations. For each case there generally exists a pair of modes with the same mode number which are backward waves. For the parallel magnetization, the field patterns in the transverse plane are symmetric and antisymmetric, respectively, about the point bisecting the straight-line segment that connects the centers of two rods. For the antiparallel case, the respective modes have the symmetrical and antisymmetrical electric field patterns about the vertical bisector of the same segment; and the results are reversed for the magnetic field patterns. Therefore, the field patterns of the latter first (or second) mode in the half-space exactly coincide with those of the corresponding mode along a single rod over a plane magnetic (or electric) conductor. The latter first mode disappears as the spacing between two rods becomes narrower than a limit. The distributions of the time-averaged power density for all the above modes are found to be symmetric about the above-mentioned vertical bisector. For some modes, there exists a slight local forward power flow in rods, accompanied with a much larger backward flow in the other region. This region with forward flow is found to appear when the strong coupling between two rods occurs. The coupling effects between two rods are more remarkable for the antiparallel case than for the parallel case, and they tend to become weaker for higher modes and for the larger spacing.