Waveguides With Non-Parallel Planar Boundaries

[摘要] The major part of this work is concerned with spectrally synthesised fields, in two dimensional tapered waveguides with planar boundaries. The derivation of the spectral objects of interest are from work by Arnold and Felsen [1], in which the tracking of plane wave species throughout the wedge environment is manipulated into a modal form. The collective form of the ray species (mode) is facilitated by the application of the Euler-Maclaurin summation formula [2]. The application of this summation formula furnishes the concept of an Intrinsic Mode and a source induced field which is maintained to be a Green's function for the tapered geometry. Numerical calculation of Intrinsic Modes has been a feature of several authors' work [3,4,5,6], but in this exposition a highly efficient numerical algorithm is developed, by using Fast Fourier Transform routines [7], which exploit the oscillatory nature of the spectrum. This high efficiency enables confirmation of the power conserving property of the Intrinsic Mode on a transverse cross--section as it traverses the cut-off region of the Adiabatic Mode, provided that at least an asymptotic form of the Euler-Maclaurin remainder is included. The Intrinsic Mode and the source induced spectral field are shown to be exact solutions of the tapered geometry (excluding the apex) and the latter is demonstrated to possess all the properties of a Green's function. This work also examines derivations and properties of four different contemporary theories, and attaches plane wave significance to their approximations by consideration of their wave vector loci. The marching algorithm methods--- Beam Propagation Method [8] and the Parabolic Equation Method [9]--- are compared and assessed with the Intrinsic Mode and the Green's function for the wedge environment (calculated using Fast Fourier Transforms). The final section deals with applications of the Green's function using the Kirchhoff integral representation. Here propagation of fields represented on a boundary are investigated. A method of calculating reflection loss from simple connected structures is also examined.

[发布机构] University:University of Glasgow

[关键词] Electrical engineering