Coupling Controlled Dual‐Band Tunable Electromagnetic Extraordinary Transmission in Graphene Hybrid Metasurfaces

A metasurface is a kind of ultrathin artificial composite composed of subwavelength elements with unique abilities in manipulating electromagnetic waves. However, the static nature of its conventional metallic/dielectric constituent material has limited its fixed functionality in narrow frequency ranges. The two‐dimensional carbon sheet, i.e., graphene, is a promising platform for effectively tuning the functionality as well as operation frequency band of metasurface. Here, the authors propose and demonstrate a kind of graphene hybrid metasurface for dual‐band extraordinary electromagnetic transmission (EET). The metasurface is composed of two graphene/metal hybrid resonators with EET properties. It is shown that the EET of the graphene hybrid metasurfaces can be tuned by increasing the bias voltage on the graphene from 0 to 3 V. Furthermore, it is found that the transmission amplitude and operating frequency band of EET can be controlled by changing the relative position and thus the coupling of the two graphene hybrid resonators. The proposed design strategy of the hybrid metasurfaces is promising for many applications based on active EM or optical modulations.

with two discrete resonators positioned in holes for dual-band EET and a coated graphene-electrolyte-graphene sandwich layer for tunability. The sandwich graphene structure can be electrically biased for controlling the strength of the transmissive window. Furthermore, we found that the line-shape of the dual-band transmissive windows and the modulation depth of the transmission spectrum can be further improved by properly designing the coupling of the resonators. The tunability of EET based on electrically biased graphene and the coupling of the resonant modes provide useful methodologies for realized novel EM wave window or smart filtering devices for application in communications, sensing, etc. Figure 1 schematically shows the structure of the graphene hybrid metasurface, which is composed of perforated metallic structure and coated graphene sandwich layer. The metallicperforated structure is designed with electric and magnetic resonators placed in holes for dual-band EET response. It is patterned on the teflon substrate, and the thickness of the copper and the teflon substrate are 35 µm and 1 mm, respectively. The graphene sandwich layer is biased to electrically tuning the EM properties of the metasurfaces. In the sandwich layer, a monolayer graphene is attached to a polyethylene terephthalate (PET) substrate (125 µm thick), and it will serve as the electrode for biasing graphene. A diaphragm paper (50 µm thick) is entirely soaked in ionic liquid ([DEME]

Results and Discussion
[TFSI]). The anions and cations in the diaphragm paper can move to the upper and lower graphene electrodes and gradually approach the electrode surface, in that the graphene sandwich layer serves as a supercapacitor when the bias voltage applied to the graphene electrodes increases. The carrier concentration on the graphene can be modulated to control the electrical conductivity of the graphene by varying the bias voltage.
In the frequency band considered here, the wavelength of the EM wave is much greater than the thickness of the graphene. Therefore, graphene can be modeled as a twodimensional plane of zero thickness. The conductivity of the monolayer graphene can be obtained from the Kubo's formula, which includes two parts: intraband item and interband item. [68] Since the energy of EM wave in this band is not enough to excite the energy level transition of graphene, the interband item can be ignored, and the conductivity can be simplified as: [69,70] 2 2cosh 2 g i ntra where e is the electron charge, K B and ћ are the Boltzmann's constant and the reduced Plank's constant, respectively. T is the room temperature. τ is the scattering rate, and E F is the Fermi level. Furthermore, the microwave frequency range we studied is rather narrow, in that the surface conductivity or resistance can be modeled as a constant in comparison with experimental results.
We study the two individual structures on the metal layer for dual-band EET response. Two holes are perforated on the metal layer, which shows low transmission. Then, two resonant structures with different EM modes are coupled to the holes for enhanced transmission around the resonant frequency. As shown in Figure 2a, when the incident electric field is parallel to the gap-bearing sides of the split ring resonator (SRR), a narrower resonance is excited at 8.736 GHz with a transmittance of 78.1% due to the electric coupling of the incident wave to the magnetic resonance (high-Q) of the SRR (green metallic structure unit on the right in Figure 1. For the symmetric electric resonator (SER) (blue unit on the left in Figure 1), since the instantaneous surface currents of the symmetric SRR structures are in the same direction, oscillating along the direction of the electric field and forming an electric mode, with a wider resonance (or low-Q) at 10.536 GHz (transmission 98.4%). If we integrate the two model resonators together, there will be a higher transmittance at two resonant frequencies as discussed below.
We studied the tunability of the graphene sandwich layer first. As shown in Figure 2b, when the bias voltage is increased from 0 to 4 V, the sheet resistance of the graphene sandwich layer decreases from 1500 to 230 Ω sq −1 , demonstrating that the bias voltage can effectively modulate the sheet resistance of the graphene sandwich layer. The prepared graphene sandwich structure is shown in the red box in the upper right corner of Figure 2b, the teflon substrate and the metallic pattern were cut to dimensions of 22.86 × 10.16 mm 2 corresponding to the crosssection of a standard waveguide WR90 employed for measurement in the experiments.
For the dual-band EET response, two holes are simply perforated in the metallic layer and two different resonant structures are placed in each of the holes in the measured frequency range. The resonators in the two holes can couple with the incident wave to achieve the extraordinary transmission (as in Figure 2a). When both the resonators are excited, the results show that the EET due to the magnetic resonator shows a higher transmission, while the EET from the magnetic Figure 1. Schematic illustration of the graphene hybrid metasurface consisting of the patterned metallic layer and the electrically biased graphene sandwich structure. The green metallic structure on the right is a split ring resonator (SRR), and the blue metallic structure on the left is a symmetric electric resonator (SER).

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mode shows lower transmission. The low transmission from the SRR is due to the weak coupling strength with the incident wave or magnetic mode. Then, the designed perforated metallic layer structure was stacked with the prepared graphene sandwich layer (with biasing wires connected), the transmission coefficient of the graphene metasurface was measured under different biasing voltage. The transmission spectra of the graphene metasurface with metallic SRR and SER structures under different resistances and voltages are shown in Figure 3a,b, respectively.
We can see that the experimental results agree well with the simulated results. As the voltage increases, the transmission of the graphene metasurface decreases at the two resonant frequencies, and the transmission at the high frequency transmission peak is higher than the low frequency transmission peak. In the experiments, when the voltage increases from 1.0 to 1.5 V, the transmission decreases from 36.9% to 26.4% at the high frequency peak and the transmission at the low frequency peak decreases from 24.6% to 16.9%. Increasing the voltage further, the transmission spectrum changes slowly. As the voltage changes from 2.5 to 3.0 V, the transmission at the high frequency peak decreases from 16.3% to only 14.9%. It is obvious that the two EET peaks (Figure 3b) are located at the resonant frequencies of SRR and SER (Figure 2), a SER (structure in the left hole) is with a low-Q resonance mode, while the SRR (structure in the right hole) is with a high-Q resonance.
The destructive interference of the two modes induces a sharp drop on the transmission below 9.0 GHz, which is exactly the picture of the Fano resonance. The electric field intensity distributions at the two resonant peaks are shown in Figure S1 (Supporting Information). For the measured results showed in Figure 3a, there are two weak transmission peaks around 8.3 and 11.4 GHz. It is due to the sample inclination in the experimental operation. There is an air gap between the sample and the upper and lower metal inner wall of the waveguide, relevant simulation analysis on the air gap is presented in Figure S2 (Supporting Information).
It is a new freedom to control the coupling of resonant modes compared with change the geometries or dimensions for designing the optical properties of various metasurfaces. [71] It would be interesting to investigate the influence of the coupling of magnetic and electric resonators for control the EET spectrum and its tunabilities in hybrid metasurfaces. The two holes are first replaced with a large hole (showing in the insets of Figure 4), also electric resonator is changed to connect with the magnetic SRR structure.
Two kinds of structures are investigated (insets in Figure 4a,c) for considering the influence of the coupling on the dual-band EET. The couplings are considered for two cases: (i) the SRR placed back-to-back with the electric resonator; (ii) the SRR placed facing to the electric resonator. Figure 4a,b shows the calculated and measured transmission  www.advelectronicmat.de spectra of the first coupling case, the schematic diagram of the hybrid and the sample are shown as the insets. The simulated and measured results also have good agreement, with the coupling of the resonant modes, the two EET peaks show very close amplitude, and the transmissions of the graphene hybrid metasurface at the two different resonant frequencies are very close when the voltage/sheet resistance changes. The measured transmission decreases from 36.1% to 26.8% at the high frequency transmission peak and decreases from 40.1% to 31.1% at the low frequency with the bias voltage changing from 1.0 to 1.5 V, showing a larger drop off of 9.3% and 9%, respectively. As the voltage further increases, the transmittance also slowly decreases. The transmission drops only from 16.9% to 15.7% as the voltage increases from 2.5 to 3.0 V at the high frequency peak and drops from 20.1% to 19.3% at the low frequency peak.
Numerically calculated fields at the resonant frequencies are usually helpful in understanding the operation mechanisms of the metasurfaces. We show in Figure 5 the calculated surface current density on the graphene metasurface at the two transmission peaks. The surface current distributions at the resonant frequencies of 8.956 and 11.064 GHz of the back to back coupling case are shown in Figure 5a,b (no voltage is applied on the graphene sandwich layers). At the resonant frequency of 8.956 GHz, the instantaneous surface currents at the top and bottom of the left-hand pattern of the second graphene hybrid metasurface are in the same direction, oscillating along the electric field and forming a dipole resonance. The coupling is strong because the direction of oscillation is in the same direction as the external electric field. At the resonant frequency of 11.064 GHz, the incident wave is electrically coupled to the magnetic resonance of the SRR of the right-hand, causing a current ring. We also notice that the electric resonance oscillates in the same direction as the external electric field. It is more like a hybrid resonant mode at 11.064 GHz.
For the coupling case with SRR facing to the electric resonator, a schematic diagram of the hybrid metasurface is shown in the inset of Figure 4c and the fabricated sample is shown in the inset of Figure 4d. The calculated and measured transmission spectra of the metasurface are shown in Figure 4c,d. With the increasing voltages, the graphene metasurface has a wider transmission band and higher transmittance around the high frequency peak. The transmission is higher than 50% from 10.33 to 11.01 GHz (with a bandwidth of 0.68 GHz) when the graphene is not biased. Figure 5c,d shows the surface current density on the graphene metasurface at the resonant frequencies of 8.932 and 10.628 GHz. It is obvious that the resonance around 10.628 GHz is a kind excited hybrid mode due to the coupling of the two resonators. The surface currents on the electric resonator and the SRR structure are of comparative amplitude, the expanding of the transmission band and the increased transmission originate from the strong coupling of the EET resonators.
To intuitively compare the EET and its modulation in graphene hybrid metasurfaces with coupling and without coupling, the enhanced transmission under different biasing voltages are plotted in Figure 6 for the three metasurface samples. With the increasing of the biasing voltage from 0 to 3 V, the transmission changes from 45.3% to 14.9% for the uncoupled case while the transmission changes from 47.7% to 19.3% and from 53.7% to 21.8% for the back-to-back and facing coupling cases. Obviously, the coupling of the EET resonators in the graphene hybrid metasurfaces are helpful in enhancing the maximum transmission of the EET. And the EET peak bandwidth and the spectrum lineshape are significantly modulated or improved by introducing the EM coupling in the EET metasurfaces by comparing the results in Figures 3 and 4.

Conclusion
In summary, we have demonstrated graphene hybrid metasurfaces with electrically tunable dual-band EET. The electric and magnetic resonators are introduced in perforated holes for enhanced transmission in freely controlled frequency bands. Considering the biasing voltage on graphene layers, the dualband EET can be remarkably modulated by simply changing the voltage from 0 to 3 V. More importantly, we found that the couplings between the electric and magnetic resonators in EET hybrid metasurface contribute significantly on the modulation of the operation bandwidth, the transmission amplitude of the dual-band EET, and the modulation depth of the tunable graphene hybrid metasurfaces. The proposed design strategy to actively tuning EM properties considering the EM coupling in graphene hybrid metasurface is promising for application in communications, sensing, etc.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.