We systematically investigate the optical extinction spectra of planar gold split-ring-resonator square arrays operating at $\sim$200-THz frequency versus the lattice constant and versus angle of incidence. We find a strong dependence of the resonance damping on the in-plane wave vector, namely, the resonance damping increases (decreases) versus the in-plane wave vector for small lattice constants (large lattice constants). By comparison with two simple one-dimensional models as well as with more complete numerical calculations, this behavior is interpreted in terms of a long-range retarded interaction among the split-ring resonators. In contrast, the assumptions of only nearest-neighbor interaction and/or of an instantaneous interaction lead to a striking disagreement with the overall experimental facts.

• Received 14 April 2011

DOI:https://doi.org/10.1103/PhysRevB.84.085416