Electric and Magnetic Dipole Coupling in Near-Infrared Split-Ring Metamaterial Arrays

We present experimental observations of strong electric and magnetic interactions between split ring resonators (SRRs) in metamaterials. We fabricated near-infrared planar metamaterials with different inter-SRR spacings along different directions. Our transmission measurements show blueshifts and redshifts of the magnetic resonance, depending on SRR orientation relative to the lattice. The shifts agree well with simultaneous magnetic and electric near-field dipole coupling. We also find large broadening of the resonance, accompanied by a decrease in effective cross section per SRR with increasing density due to superradiant scattering. Our data shed new light on Lorentz-Lorenz approaches to metamaterials.

Figure 1

(a) Scanning electron microscope image of Au SRRs on glass. We fabricated SRR arrays with periodicities $d_{x,y}=300\mathrm{nm}$ and larger (inset). Each SRR has $l=200\mathrm{nm}$, $w=80\mathrm{nm}$, and SRR height 30 nm ($\pm 5\mathrm{nm}$). (b) Transmission spectra for square SRR arrays with split width $d=80\mathrm{nm}$ (polarization along $x$). The magnetic resonance at $1.4\mu \mathrm{m}$ blueshifts and broadens with increasing density.

Figure 2

(a) Frequency of the magnetic resonance versus lattice spacing. The frequency blueshifts when decreasing $d_y$ whether $d_y=d_x$ (black squares) or not (blue circles, $d_x=500\mathrm{nm}$), while it redshifts when decreasing $d_x$ (red triangles, $d_y=500\mathrm{nm}$). The inset shows raw spectra for $d_x=d_y=300\mathrm{nm}$ (black curve), $d_x=500\mathrm{nm}$, $d_y=300\mathrm{nm}$ (blue curve), $d_x=300\mathrm{nm}$, $d_y=500\mathrm{nm}$ (red curve). (b) FWHM of the magnetic resonance versus lattice spacing [color coding as in (a)]. Curves are theory [electrostatic in (a), electrodynamic in (b)].

Figure 3

Electrostatic calculation of the magnetic resonance frequency versus lattice spacing. Black curves: $d_x=d_y$. Blue curves: $d_y$ varies at fixed $d_x=500\mathrm{nm}$. Red curves: $d_x$ varies at fixed $d_y=500\mathrm{nm}$. For magnetic coupling only (a), resonances always blueshift with decreasing lattice spacing, while for electric coupling only (b), the behavior of the resonances for $d_x=d_y$ changes sign with respect to (c) (all couplings). Curves in (c) are reproduced in Fig. 2.

Figure 4

Effective extinction cross section per SRR derived from on-resonance transmission. The black dashed line indicates the cross section of a single SRR (from [20]). Black and red lines show the area $d_x{d}_y$ of the unit cell.