Orthogonality Properties for Modes in Passive and Active Uniform Wave Guides

Abstract

Orthogonality relations are given for the ``four-vector'' guided modes of anisotropic uniform wave guides and for the ``six-vector'' guided modes of uniform wave guides containing unidirectional electron beams with axially independent dc velocities. In general, these orthogonality relations involve both the modes of the given wave guide and those of an appropriate ``adjoint'' wave guide. A description is given for the adjoint wave guides associated with wave guides which contain media whose characteristics are restricted only by the requirement that they be axially independent and which, if bounded, are subject to a variety of boundary conditions arising from idealizations of actual boundaries.

Transverse operator method for wakefields in a rectangular dielectric loaded accelerating structure

“…It should be noted that in contrast to the analysis of [28][29][30][31][32][33][34], we consider the Sturm-Liouville second order operator with an alternating sign weight function. It will be shown below that the integral relation derived in [28,29] is a consequence of the bi-orthogonality of the eigenfunctions as well as the similarity of the operator to a self-adjoint operator.…”

“…Theoretical analyses of dielectric accelerating structures with rectangular geometries have been reported in a number of publications [23,[25][26][27][28][29][30][31]. To determine the amplitudes of individual Cherenkov radiation modes excited in a rectangular waveguide with dielectric slabs, the impedance matching technique was used in the earlier papers [23,25,26].…”

“…In this paper, we applied a transverse operator method that was used previously as an analytical algorithm for wave propagation of modes in a waveguide with complex loading, where the rectangular waveguide is partially filled with dielectric, ferrite, ferroelectric, or any type of anisotropy is present (chiral loading, for example) [28][29][30][31][32][33][34]. Some specific version of transverse operator method called the mode basis method was developed and applied to the analysis of wave propagation in conical antennas with dielectric filling [35,36].…”

Determination of Propagation Constants and Material Data From Waveguide Measurements

“…A general formalism for anisotropic waveguides was presented in a series of papers in the late fifties [5][6][7][8], but they have had surprisingly few followers. The bianisotropic case is treated by [21] and [4].…”

“…In order to deduce the general properties of this formulation, the quasi-orthogonality results from [4,8,21] are used extensively, and they are repeated in Section 4.…”