Fig. 1. (a) Magnetic field amplitude intensity detected at the center of the resonators; the inset is a schematic illustration of the metallic spiral structure. (b) Current distribution at z=0, (c) magnetic field at x=0, (d) electric field at x=0.

Fig. 2. Simulation and measurement setups of the MSS dimers are shown in (a) and (b), respectively. The near-field response spectra for a single MSS (black line) and MSS dimer (red line) in (c) simulations and (d) measurements. The insets correspond to the electric field maps for the split higher and lower modes, respectively.

Fig. 3. Dispersion diagrams of infinite chains of metallic spiral structures based on Lagrangian analytical mode (black line), coupled mode theory (red symbols), and numerical simulation (square symbols). The blue dash line is the dispersion of the light in free space.

Fig. 4. (a) Geometry of MSS chain. The red dash line indicates the observed cross section. The blue line indicates the observation line. The magnetic fields in the z=1  mm plane and y=0 plane are presented in (b) and (c), respectively.

Fig. 5. (a) Magnetic field distributions along the z axis; (b) magnetic field distributions on the cross sections of the MSS chain at 1.84 and 1.88 GHz.

Fig. 6. Magnetic field distributions along the MSS chain at different frequencies.

Fig. 7. (a) Simulation and experimental setup, (b) simulated and measured transmission spectra for the metamaterial resonator waveguides that consist of 10 MSSs, (c) simulated and (d) experimental amplitude of electric field Ez above the waveguide.

Fig. 8. (a) Simulation of transmission spectra for adjacent MSSs with varying gap size from 10 to 0.5 mm. (b) Resonance frequency of two modes as a function of gap size. (c) Dispersion relation with different gap sizes. (d) Transmissions of MSS chains with different gap sizes.

Fig. 9. Simulated vertical magnetic-field distributions of the waves on the MSS chain.