Electrodynamics of a ring-shaped spiral resonator

Abstract

We present analytical, numerical and experimental investigations of electromagnetic resonant modes of a compact monofilar Archimedean spiral resonator shaped in a ring, with no central part. Planar spiral resonators are interesting as components of metamaterials for their compact deep-subwavelength size. Such resonators couple primarily to the magnetic field component of the incident electromagnetic wave, offering properties suitable for magnetic meta-atoms. Surprisingly, the relative frequencies of the resonant modes follow the sequence of the odd numbers, despite the nearly identical boundary conditions for electromagnetic fields at the extremities of the resonator. In order to explain the observed spectrum of resonant modes, we show that the current distribution inside the spiral satisfies a particular Carleman type singular integral equation. By solving this equation, we obtain a set of resonant frequencies. The analytically calculated resonance frequencies and the current distributions are in good agreement with experimental data and the results of numerical simulations. By using low-temperature laser scanning microscopy of a superconducting spiral resonator, we compare the experimentally visualized ac current distributions over the spiral with the calculated ones. Theory and experiment agree well with each other. Our analytical model allows for calculation of a detailed three-dimensional magnetic field structure of the resonators.Comment: 25 pages, 8 figure

Meta-metallic coils and resonators: Methods for high Q-value resonant geometries

“…(7) or from Eq. (13), that the net current per unit y-length in the foil is exactly equal to the step (or difference) in magnetic field across the foil,…”

“…Filamentary analogs of the foil SRS are of current interest for meta-material meta-atoms. 13,14 These references calculate resonance frequency but not Q-value.…”

Tunable Negative Permeability in a Three-Dimensional Superconducting Metamaterial

“…constructive and destructive interferences between the direct coupling of the loops and magnetic coupling of the loops to the metamaterial, respectively [35]. We observe higher-order modes corresponding to shorter-wavelength rf-current standing waves in the spiral, which have been extensively studied elsewhere [8,[36][37][38][39]. Above the T c of Nb, superconductivity is lost and the resonance is wiped out at 9.25 K. This demonstrates that such a compact device is not functional if made with thin films of normal metals due to the large ohmic losses.…”

Effects of Dielectric Substrates and Ground Planes on Resonance Frequency of Archimedean Spirals

“…When used as HTS NMR probe coils specifically, and in some other applications, it is typical for the spiral to be mounted on a dielectric substrate [6]. In many of the cases the effect of the substrate is modeled through the use of an effective dielectric constant [7], [8]. This approach uses a substitute value to model the effect of a dielectric instead of the actual dielectric constant.…”

“…In order to be able to predict the mode frequencies of most actual devices, the effect of the substrate also needs to be taken into account. For spirals on thick substrates, an effective dielectric constant given by (1+ ε r )/2 has been found to produce accurate results [7, 8]. However, the resonances of spirals on thin substrates are not consistently predicted with accuracy this way since the modes are not uniformly affected by the substrate.…”