Oscillations in Slotted Resonators with Several Slots: Application of Approximate Semi-Inversion

Abstract

Abstract-We consider oscillations in cylindrical slotted resonators formed by combinations of rectangular domains with several slots cut in the walls using the methods of approximate semi-inversion of integral operator-valued functions with a logarithmic singularity of the kernel. The initial boundary value problems for the Helmholtz equation are reduced to Fredholm integral equations and systems of integral equations of the first kind with a logarithmic singularity. In the case of narrow slots, the dispersion equations are obtained and evaluated using perturbations and the small-parameter method. Eigenfrequencies and eigenfields are calculated explicitly. The values of geometrical and material parameters are determined that lead to the interaction of oscillations. The results obtained are used for improving the design of filters and switches on the basis of simple model prototype structures.

Resonance frequencies of arbitrarily shaped dielectric cylinders

“…In [4,5,11,14], and [15], the existence of RFs was demonstrated for certain families of shielded and open metal-dielectric scatterers formed in the cross section by (bounded) domains (particularly, in [11] for the union or rectangular domains with slots on the common part of the boundary) and 'slotted' open domains (a cavity-backed slotted screen in [5]). However, these results have never been extended to the case when the boundary curve of a cylindrical dielectric scatterer is a single arbitrary smooth (or piecewise smooth) simply-connected contour.…”

“…Comprehensive asymptotic analysis and explicit formulas for RFs of narrow-slot scatterers (as segments of small-parameter series) are presented in [4] and [14]. The study was extended in [5,11] where particularly multi-slot and multi-strip scatterers were considered, both shielded and open.…”

“…We note that, actually, our achievements and the techniques and results of H. Ammari and coworkers complement each other in many aspects. Particularly, we paid a considerable attention to the determination of CNs of logarithmic integral operators on one or several integration intervals (in planar [5,11,14,15] and circular [39] domains) using asymptotic semi-inversion and performing, in [5,14,20] and several other works, detailed studies of small-parameter series.…”