Publisher Correction: Geometrical Perturbation Techniques and Approximate Analysis for Eigenmode Splitting and Shifting in Electromagnetic Planar Dual-Mode Resonators.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Geometrical Perturbation Techniques and Approximate Analysis for Eigenmode Splitting and Shifting in Electromagnetic Planar Dual-Mode Resonators.

Dual-mode electromagnetic resonators are used in numerous systems and applications in physics and engineering. They rely on degenerate-mode splitting to control the spectral properties of the system that employs them. Controlling (splitting or shifting) these eigenvalues to fully tune the frequency response, however, is a nontrivial problem that involves the use of geometrical perturbation theory as well as lossy electronic elements that enable the tuning process. In this paper we present novel geometrical techniques to control the eigenmodes of dual-mode resonators, highlighting the strong connection between the chosen geometry and performance (measured by the unloaded quality factor, Q0). Key advantages of the presented structures include electronic geometric tunability for frequency splitting and shifting, as well as the use of buried feeds to improve insertion loss and return loss performance. Field analysis is used to show how the performance is degraded by geometry itself, rather than by the tuning elements. The discussion includes derivation of approximate analytical models that highlight the sources of performance degradation in the geometry even before any tuning elements are inserted. The presented concepts are verified by measurements on perturbed microwave resonators.

Center Frequency Stabilization in Planar Dual-Mode Resonators during Mode-Splitting Control.

Shape symmetry in dual-mode planar electromagnetic resonators results in their ability to host two degenerate resonant modes. As the designer enforces a controllable break in the symmetry, the degeneracy is removed and the two modes couple, exchanging energy and elevating the resonator into its desirable second-order resonance operation. The amount of coupling is controlled by the degree of asymmetry introduced. However, this mode coupling (or splitting) usually comes at a price. The centre frequency of the perturbed resonator is inadvertently drifted from its original value prior to coupling. Maintaining centre frequency stability during mode splitting is a nontrivial geometric design problem. In this paper, we analyse the problem and propose a novel method to compensate for this frequency drift, based on field analysis and perturbation theory, and we validate the solution through a practical design example and measurements. The analytical method used works accurately within the perturbational limit. It may also be used as a starting point for further numerical optimization algorithms, reducing the required computational time during design, when larger perturbations are made to the resonator. In addition to enabling the novel design example presented, it is hoped that the findings will inspire akin designs for other resonator shapes, in different disciplines and applications.