Collective coherence in nearest neighbor coupled metamaterials: A metasurface ruler equation

Abstract

The collective coherent interactions in a meta-atom lattice are the key to myriad applications and functionalities offered by metasurfaces. We demonstrate a collective coherent response of the nearest neighbor coupled split-ring resonators whose resonance shift decays exponentially in the strong near-field coupled regime. This occurs due to the dominant magnetic coupling between the nearest neighbors which leads to the decay of the electromagnetic near fields. Based on the size scaling behavior of the different periodicity metasurfaces, we identified a collective coherent metasurface ruler equation. From the coherent behavior, we also show that the near-field coupling in a metasurface lattice exists even when the periodicity exceeds the resonator size. The identification of a universal coherence in metasurfaces and their scaling behavior would enable the design of novel metadevices whose spectral tuning response based on near-field effects could be calibrated across microwave, terahertz, infrared, and the optical parts of the electromagnetic spectrum.