Fast and slow waves in a chain of superconducting split-ring resonators with staggered coupling strengths

The transmission and reflection spectra of a linear chain comprising superconducting split-ring resonators operating at 6 GHz, with staggered coupling strength are investigated. The collective mode and the associated transmission and reflection on resonances can be fully analyzed by employing finite-element simulations focused on the unit cell structure and an effective hopping model. Robust coupling energies, equivalent to approximately 4% of the resonant frequency, enable significant transmission through the collective modes. Furthermore, the resonance modes exhibit substantial quality factors, leading to distinct superluminal and retarding propagation effects for reflected and transmitted microwaves, respectively. The chain configuration allows for 200 ns in either advance or delay for a 1 µs microwave pulse at the resonance frequency. These findings shed light on the unique behavior of superconducting split-ring resonator arrays and their potential applications in microwave signal manipulation.