Realization of Negative Permeability in Vertical Double Split-Ring Resonators with Normal Incidence

With the rapid development of optoelectronics, methods for manipulating light-matter interactions are urgently required. In this work, three-dimensional double split-ring resonators (3D-DSRRs) have been designed via a metal-stress-driven self-folding method. The 3D-DSRRs eliminate the electric response from the meta-atoms and exhibit a magnetic dipole moment radiation power that is 1244.6-fold greater than that of two-dimensional metamaterials. By tailoring of the 3D-DSRR periodicity, the permeability is shown to vary from positive to zero, even reaching negative values under normal incidence. This strain engineering strategy provides an efficient method for designing and fabricating three-dimensional metamaterials and for increasing the variety of light-matter interactions in the mid-infrared region.