Superconducting self-resonant spiral structures are of current interest for applications both in metamaterials and as probe coils for nuclear magnetic resonance (NMR) spectroscopy for high-sensitivity chemical analysis. Accurate spiral models are available in the literature for behavior of a spiral below and up to self-resonance. However, knowledge of the higher modes is also important. We present the relationships between the spiral parameters and the multiple mode frequencies of single sided spirals on dielectric substrates as modeled by method of moments simulation. In the absence of a ground plane, we find that the mode frequency has a linear though not necessarily harmonic dependence on the mode number. The effect of a thick substrate can be approximated by an effective dielectric constant. But when the thickness is less than 20% of the spiral trace width (router - rinner) this approximation is no longer accurate. We have developed a simple empirical formula to predict the higher modes.
Keywords: High-temperature superconducting (HTS) spiral resonators; nuclear magnetic resonance (NMR).