Full-wave analysis of dielectric waveguides using tangential vector finite elements

Abstract

In this paper, the biorthonormal-basis method has been used to model the complex wave-propagation constant and the transversefield pattern in inhomogeneously filled waveguides with lossless and lossy dielectrics. The differential operator governing the transverse fields is transformed into a linear-matrix eigenvalue problem, using the eigenvectors of an auxiliary problem to expand the modes of the original problem. This method has been applied to the calculation of the complex modes in dielectric-rod-loaded circular waveguides and dielectric-slab-loaded rectangular waveguides, which provides an example demonstrating the capability of the method to include the dielectric losses directly in its formulation. The method is free of spurious modes and, in most cases (as in the systems shown in this paper), the integrals involved in the matrix elements can be obtained analytically, and the only numerical approximation is the finite number of modes used for the expansion of the fields. The high accuracy necessary to obtain complex modes is fully achieved by our method. On the contrary, other methods involve serious difficulties. ACKNOWLEDGEMENTThis work was financially supported by the Ministerio de Ciencia y Tecnología (grant TIC2000-0591-C03-03), Spain. INTRODUCTIONInclined slots in the narrow wall of a rectangular waveguide, so-called edge slots, have been widely used in radars and satellite systems. These slots extend onto the broad walls of the waveguide to produce resonance, which complicates the analysis of narrow wall slots. Furthermore, fabrication of planar arrays become difficult, since metallic spacers should be placed in between the guides, which in turn increases the back radiation of the array. A number of investigations have been reported on these slots [1][2][3][4]. In all these works, the edge slot is tilted to excite and penetrate the broad walls of the waveguide. Hashemi-Yeganeh and Elliott [5] analyzed untilted edge slots excited by tilted wires in a rectangular waveguide. One of the most important results they obtained in their study was the discovery of the possibility of a resonant condition between the slot and tilted wires, which does not require the slot to be continued onto the broad walls. This permits embedding an array of these composite elements in a ground plane. In their analysis it was assumed that the slot is embedded in an infinite ground plane. Hirokawa et al. [6] analyzed this structure by including the actual structure, using a spectrum of the two-dimensional solutions (S2DS) method [7]. Their results show that the effect of modelling the actual outer cross section of the waveguide, instead of assuming an infinite ground plane, is small. Actually, the difference is smaller than the measurement error in the experimental setup. Hirokawa and Kildal another excitation technique by inserting a dielectric plate into the slot on which conducting strips are etched. Again, a resonance can occur which does not require the slot to be continued onto the broad walls. These two methods of exc...

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