Tunable Graphene Split-Ring Resonators

This paper is a contribution to the joint Physical Review Applied and Physical Review Materials collection titled “Two-Dimensional Materials and Devices.”

A split-ring resonator is a prototype of a meta-atom in metamaterials. Although noble metal-based split-ring resonators have been extensively studied, to date, there is no experimental demonstration of split-ring resonators made from graphene, an emerging intriguing plasmonic material. Here, we experimentally demonstrate graphene split-ring resonators with deep subwavelength (about one hundredth of the excitation wavelength) magnetic dipole response in the terahertz regime. Meanwhile, the quadrupole and electric dipole are observed, depending on the incident light polarization. All modes can be tuned via chemical doping or stacking multiple graphene layers. The strong interaction with surface polar phonons of the ${\mathrm{Si}\mathrm{O}}_2$ substrate also significantly modifies the response. Finite-element frequency-domain simulations nicely reproduce experimental results. Our study moves one stride forward toward the multifunctional graphene metamaterials, beyond simple graphene ribbon or disk arrays with electrical dipole resonances only.

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Figure 1

Characterization of graphene layers and SRRs. (a) Schematic of a typical SRR array with normal incident far-infrared radiation. The incident light is polarized either parallel (E_||) or perpendicular (E_⊥) to the symmetry axis of the split ring. A square lattice array of the SRRs made of CVD graphene is located in the x-y plane. Geometric parameters are indicated: the ring outer diameter d₂, inner diameter d₁, a gap g and the period of the lattice p. (b) SEM micrograph of a SRR array with parameters of d₁= 100 nm, d₂= 400 nm, g = 100 nm, and p = 500 nm. The scale bar is 500 nm. (c) Drude response of one- to three-layer graphene on $\mathrm{Si}/{\mathrm{Si}\mathrm{O}}_2$ substrate. Dashed lines are corresponding fitted curves using Drude model with fitting parameters of Drude weight D and scattering rate $\gamma$. Their values (D and $\gamma$) are $8.2\times {10}^{10}{\mathrm{\Omega }}^{-1}{\mathrm{s}}^{-1},112\mathrm{c}{\mathrm{m}}^{-1};1.6\times {10}^{11}{\mathrm{\Omega }}^{-1}{\mathrm{s}}^{-1},106\mathrm{c}{\mathrm{m}}^{-1};2.2\times {10}^{11}{\mathrm{\Omega }}^{-1}{\mathrm{s}}^{-1}$, $125\mathrm{c}{\mathrm{m}}^{-1}$ for one to three layers, respectively. (d) Typical extinction spectra of an SRR array on Si substrate with parameters the same as that in the SEM image in (b). Red and blue curves are for the parallel and the perpendicular polarizations, respectively.

Figure 2

SRRs on Si substrate with varied diameter and split gap. (a) Measured and simulated extinction spectra for the SRRs with varied outer diameter. Both parallel and perpendicular polarization spectra are shown. Spectra are vertically offset for clarity. (b) Measured and simulated extinction spectra for the SRRs with increasing split gap from 70 nm, 100 nm to 150 nm. Spectra are vertically offset for clarity. (c) Peak positions and intensities of peak P₂ and peak P₃ as a function of the split gap g.

Figure 3

Spectra and field simulations. (a) Simulated extinction spectra of a typical SRR array with two different incident polarization directions. The measured spectra are shown in Fig. 1. The resonance modes are denoted as P₁, P_2, and P₃. (b) Simulated surface electric field magnitude distribution on the upper panels, and z-direction magnetic field magnitude (H_z) distribution (pseudo-color map) as well as surface current density (arrows) on the lower panels. The values in the scale bars shown in the bottom of the pseudo-color map are calculated assuming an incident electric field of 1 V/m.

Figure 4

Tunability of graphene SRRs on silicon substrate. (a) Extinction spectra of the typical double-layer graphene SRR array with an increasing doping level. This is the same SRR array with d₂ of 400 nm in Fig. 2 on Si substrate. Spectra for different doping levels are shifted vertically for clarity. (b) Frequencies of peak P₂ and peak P₃ (perpendicular polarization) as functions of the frequency of peak P₁ (parallel polarization). Solid lines are linear fits.

Figure 5

SRRs on ${\mathrm{Si}\mathrm{O}}_2/\mathrm{Si}$ substrate with one to three graphene layers. (a) Measured and simulated spectra of one- to three-layered graphene SRR arrays with the same geometric parameters as that of the SEM image in Fig. 1. Spectra are vertically offset for clarity. (b) Frequencies of the peaks (labeled in the simulation spectra) as functions of the layer number of graphene. Note that due to the hybridization with a surface polar phonon mode on ${\mathrm{Si}\mathrm{O}}_2$, the original electric dipole P₁ and quadrupole P₃ split into two branches. Here we denote them as P_1a, P_1b and P_3a, P_3b (some of them beyond the scope of our measurement). Since P₂ has a relatively low frequency, it shows little hybridization effect with the surface phonon, hence we do not treat it as two branches here.