Complex eigenfrequency spectra and regularities of waveguide structure scattering characteristics

Abstract

The undertaken investigation pursued two main goals. First, the product expansions of frequency dependences of S-matrix elements of waveguide systems in terms of their eigenfrequencies were obtained. Second, these expansions were used for the investigations of frequency response peculiarities, for a more reasonable interpretation of known regularities and for searching the new resonance phenomena in multimode band.

Principal idea of the reconstruction problem solution consists in the determination of the relationships between the zeros and the poles of S-matrix elements on the basis of analytical continuation of general relations of electromagnetics to the multisheet complex-frequency Riemann surface. In forming the canonical products by zero and pole sets, the problem of noncompactness of the multisheet surface has to be solved. Its partial solution consists in finding the explicit forms of local univalent mappings that would image some intervals of the real frequency axis into an univalent region. It permits to solve analytically the reconstruction problem for the wide frequency band but not in the vicinity of separate eigenfrequency as it took place in earlier works. By this way we can carry out the examination of the influence of not only the first "physical" sheet’s eigenfrequencies, but also higher sheet's ones on the scattering characteristics.

The following interesting physical results were obtained on this analytical basis and with the aid of numerical calculations of frequency spectra of several waveguide elements: the well- known total reflection effects due to locked modes can be correctly explained only by invoking the information about the nearby low quality eigenmode, the full transformation of one of the mode packet to other can be observed in multimode band, when the excitation frequency coincides with the eigenfrequency from the real axis of one of the Riemann surface higher sheets, the feature of "resonance-antiresonance" pair on the frequency responses depends on the kind of symmetry of operating high-quality eigenmode and background low-quality one; it is possible to find the eigenfrequency on the real axis of one of the Riemann surface higher sheets, that provides a resonant total absorption phenomenon of incident mode, and so on.

By the presented approach, one can work out new simulation and design procedures for various types of the frequency-selective systems, to create the spectral passports, and to use them for approximation of the frequency responses of the classic waveguide elements, and so on.