Broadband Terahertz Transmission Modulation Based on Hybrid Graphene-Metal Metamaterial

Lan-Ju Liang, Zhang Zhang, Xin Yan, Xin Ding, De-Quan Wei, Qi-Li Yang,Zhen-Hua Li, and Jian-Quan Yao

Abstract—A novel patterned metamaterial,composed of graphene layer and metal periodic array of split ring resonators (SRRs) and cross-shaped resonators (CSRs), with broadband terahertz (THz)wave modulation was proposed and theoretically studied. It demonstrated that a broad passband high transmission of over 96.1% in the frequency range from 1.02 THz to 1.66 THz and two narrow band resonance frequencies f1 and f2 could be generated. The modulation depth of transmission was 29.2% when the graphene layer was covered on the metal metamaterial surface,and the modulation depth could be further increased by increasing the Fermi energy of graphene layer and reached approximately 79.5% at 1.0 eV in a broadband THz frequency range. The resonance frequencies of f1 and f2 were blue-shifted, and their modulation depths reached about 63.2% and 18%, respectively. These results show that the ultrathin graphene-metal metamaterial exhibits potential to achieve highperformance active THz devices and may offer widespread applications.

1. Introduction

A metamaterial, consisting of a two-dimensional patterned metal structure, has been proposed and studied recently, whose electromagnetic properties are determined by subwavelength resonant elements[1]-[4]. It is a promising material for engineering novel devices, such as reflection devices, biosensors, tunable filters, and polarization modulators due to the unique optical physics and control of incident electromagnetic waves[5]-[9]. In recent years, terahertz (THz) waves have attracted increasing interests for its promising future in applications of communications, military radar, biology, and medical sciences[10]-[16]. Many kinds of THz devices have been proposed to exploit potential applications especially for active modulators[17]-[23]. However, the complicated manufacturing and lower modulation efficiency have been constraints on the developments of metamaterials to obtain tunable performance devices in practical applications operated at THz frequencies.

Graphene, a single-layer with hexagonally arranged carbon atoms, has attracted much attention due to its excellent properties such as high carrier mobility and charge carrier densities, which offers a superior solution to the modulation device[24]-[30]. On the basis of graphene structure, active THz modulators were proposed and characterized over the past several years. Liet al. proposed a graphene metamaterial hybrid structure and the modulation depth of transmission was 29.0% in the frequencies from 0.6 THz to 0.9 THz[31]. Liet al.proposed a graphene-silicon hybrid metamaterial and the modulation depth of transmission was 61% at the 0.67 THz[32].For current THz modulators, there are still many shortcomings,such as small modulation depth and narrowband width.Therefore, performance characteristics of tunable devices should be further improved for practical applications in THz technology.

In this paper, we numerically investigated on the transmission modulation devices in the THz range based on a hybrid graphene metamaterial deposed on the flexible substrate by using finite integration time domain (FITD). Although,some researches have studied the graphene-modulated split ring resonators (SRRs) devices[33], the active modulation characteristics of the hybrid structure of the graphene-metal metamaterial are still needed studying extensively. In our designed structure, the metal metamaterial is covered with graphene layer, leading to a flat band in transmission.Meanwhile, graphene allows the control on voltagemodulated surface plasmon at the interface, which can tune the transmission characteristics of incident waves at THz frequencies. By varying graphene’s Fermi energy (EF)levels, the flat-band transmission decreases from 68.0% to 19.7%, and the resonance frequencies are also changed. WhenEFis 1.0 eV, the transmission modulation depth reaches 79.5%in broadband THz frequencies, ranging from 1.05 THz to 1.65 THz. Moreover, the modulation depths are 63.2% and 18.0%for the resonance frequenciesf1andf2, respectively. This proposed hybrid graphene metamaterial presents better features compared with conventional THz modulation because of its flat-broadband range and large range modulation.

2. Computational Methods

The structure design of metamaterial and the full wave numerical simulations are performed by commercial finite element package computer simulation technology (CST)microwave studio. Fig. 1 (a) shows the schematic of the proposed hybrid graphene-metal metamaterial deposited on top of SiO2/Si. The thicknesses of SiO2and Si layers are 300 nm and 1 μm, respectively. In our simulation, SiO2is considered as a nondispersive dielectric with a relative permittivityThe bottom layer is polyimide film, and the thickness of polyimide is 30 μm, as shown in Fig. 1 (b). The dielectric constant and loss tangent of polyimide are 3.10 and 0.05, respectively. The designed metal structure is composed of SRRs and cross-shaped resonators (CSRs), the thickness of the metal structure is 200 nm. The geometrical parameters are as follows:P=120 μm,w1=5 μm,w2=6 μm,d=6 μm,L=90 μm,andL2=40 μm, as shown in Fig. 1 (c). All the simulation results are calculated by using the frequency domain solver, and the unit-cell boundary conditions in thex-yplane and floquet ports in thezdirection are adopted for the designed structure.

Fig. 1. Structure of hybrid graphene-metal metamaterial: (a) 3D view, (b) side view, and (c) the unit cell of the metal metamaterial with the geometrical parameters of P=120 μm, w1=5 μm, w2=6 μm,d=6 μm, L=90 μm, and L2=40 μm.

Graphene layer can be modeled as a two-dimensional material and can be described by surface conductivity. Its surface conductivity can be retrieved by the Drude model at the THz region, as follows[34]:

whereZ0=377 Ω andare the vacuum and substrate impedances, respectively, andis the complex impedance of the graphene-metamaterial layer.According to (1), graphene’s surface conductivity can be controlled by varying itsEF, thereby changing the impedance and transmission efficiency of the metamaterial.Thus, the transmission amplitude can be modulated through the hybrid graphene-metal metamaterial with differentEFlevels.

3. Results and Discussion

3.1 Broad Flat-Band Transmission of the Designed Metal Metamaterial

First, in order to clarify the modulation mechanism of the hybrid metamaterial structure, we investigated the transmissions of the designed metal metamaterial (sold line),SRRs (dash line), and CSRs (dot line) using CST Microwave Studio without graphene layer of three structures, as shown in Fig. 2 (a). When the polarization of the incident THz waves was perpendicular to the gap-bearing side of SRRs, a flat region emerged as a wide passband with a transmission efficiency over 96.1% from 1.02 THz to 1.66 THz, and two resonance frequencies were generated at 0.71 THz and 1.90 THz, respectively. From the transmission spectra of the SRRs(dash line) and CSRs (dot line) structure and the surface current distributions atf1andf2, it can be seen that the strong surface current distributions in two side lengths of SRRs atf1demonstrated an enhanced dipolar coupling, which is closely related to the polarization of the incident waves. To verify this polarization dependent effect, the according electric field distributions along different directions (ExandEy) are also presented in Figs. 2 (d) and (e). It is clearly seen that the electric field distributions change largely with the polarization of the incident waves transforming fromx- toy-direction. On the other hand, the electric field distributions atf2are similar with that atf1, indicating the same dipolar resonance due to the anisotropic electric field distribution (not shown here). It is worthy note that there is no evidenced inductance-capacitance(LC) resonance which will drive the circulating surface currents in the SRRs loop as reported in other research works[38],[39]. This may be interpreted by the SRRs-CSRs coupling effect. It can be seen from Figs. 2 (b) and (c) that the surface currents also appear in the CSRs structure, the interactions of higher mode resonances for SRRs and the dipolar resonance for CSRs produce a mixed-mode resonance, which would prevent the formation of circulating currents in the SRRs structure,resulting in the decrease, even elimination of LC resonance mode.

Fig. 2. Transmission, surface electric field, and charge density distribution of the designed metamaterial, SRRs, CSRs structure without graphene: (a) THz transmission spectra; simulated surface current distribution at (b) f1=0.71 THz and (c) f2=1.90 THz, and simulated electric field distributions at f1 along (d) x-direction and(e) y-direction.

3.2 Graphene-Metal Hybrid Metamaterial

We also characterized the THz transmission spectra of the designed hybrid metamaterial graphene, as shown in Fig. 3.The broadband transmission decreased from 96.1% to 68.0%,and the flat-transmission bandwidth decreased from 1.10 THz to 1.62 THz when the monolayer graphene was transferred on the metamaterial surface. The THz transmission atf1increased from 0 to 40% (ΔT=0) and showed a strong redshift in the resonant region from 0.71 THz to 0.59 THz (Δf=0.12 THz),while that atf2increased from 10% to 27% (ΔT=17%) and showed no obvious resonant frequency shifts.

Fig. 3. THz transmission spectra of the bare metal and hybrid graphene-metal metamaterial.

From the above analysis, we know thatf1is a dipole oscillator model for SRRs. This resonance frequencyf1can be determined byis the average permittivity of the surrounding medium anddis the length of the SRRs arm. When the graphene layer was deposited on the surface of metamaterial, thewas increased, which resulted in the redshift of the resonancef1. Furthermore, the change in transmission was determined onto (4). When graphene layer was deposited on the metamaterialwas increased, resulting in the transmission of graphene metamaterial changing. The simulation results showed that the proposed hybrid ultrathin graphene metamaterial device can modulate the resonance frequency and transmission in the THz frequencies.

3.3 Hybrid Graphene-Metal Metamaterial with Different Fermi Levels

In order to further study the characteristics of the hybrid graphene metamaterial, the THz transmission spectra under various Fermi levels of graphene were studied. The carrier concentrationncorresponds to the Fermi energy of graphene,thus we can obtain[40]:

whereε0andεrare the permittivities of vacuum and silicon dioxide, respectively,tsis the thickness of silicon dioxide,andeis electron charge. Then, based on (5) and (6), we obtain

Fig. 4 (a) shows the transmission spectra of the bare metamaterial and hybrid graphene metamaterial with variousEFlevels. The transmittance of the bare metamaterial approaches 96.1%. When the metamaterial was covered with graphene layer, the broadband average transmission decreased from 68.1% to 19.7% with the grapheneEFfrom 0.3 eV to 1.0 eV. In addition, the flat-band transmission exhibited little change in bandwidth but the flat band blue-shifted to higher frequencies in the band location. Table 1 shows a detailed description of the transmission performance for different graphene chemical potentials. To demonstrate the flat property of the passband, the transmission ripple was also calculated. In the flat-band region, the ratio of the difference between the maximum and minimum transmissions to the maximum transmission is referred as transmission ripple. It is found that the ripple decreased from 5% to 3% in a broadband THz frequency range, and the flat characteristic becomes much better with the increase of theEFlevel. When theEF=1.0 eV,the transmission is 19.7%. Therefore, the simulation results demonstrate that this hybrid graphene metamaterial can realize on-to-off switching responses of the THz waves.

Both the resonance frequenciesf1andf2blue-shifted with the increase ofEF. Fig. 4 (b) reveals the resonance frequency with differentEFlevels with simulated data.The straight lines show the exponential fits to the simulation data. The fitting functions forf1andf2are described byrespectively. The resonance frequenciesf1andf2are 1.58 THz and 2.33 THz at 1.0 eV, respectively.

Fig. 4. Modulated results of the metamaterial under different grapheme EF: (a) THz transmission spectra and (b) resonance frequencies f1 and f2.

The modulation depths of resonance frequency and transmission are defined asrespectively. Note that to define the modulation depth of transmission strictly, the transmission of the bare metamaterial and graphene-metamaterial at different Fermi energy,TmaxandTrespectively, are adopted as the average values in the range from 1.05 THz to 1.65 THz.Therefore, from Table 1, the transmission modulation depth(ΔT/Tmax) achieves 79.5%, and that of the resonance frequenciesf1andf2are 63.2% and 18.0%, respectively with an applied Fermi energy of 1.0 eV.

Table 1: Transmission properties with different EF levels

Fig. 5 shows the real and imaginary conductivitiesy change of graphene by continuously adjustingEF. It shows that the real and imaginary conductivitie of graphene was increased with increasingEFlevel.

Fig. 5. Graphene conductivity with different EF levels at THz frequencies: (a) real and (b) imaginary parts.

Additionally, the resonance frequency shift ofdetermined byfrom (3). Andis negative in the frequency range from 0.4 THz to 2.8 THz with different grapheneEF. Therefore, the resonance frequencies off1andf2were blue-shifted by increasingEF. The modulation depth of the resonance frequencyf1was larger than that off2because of the larger change infor the same change inEF.

The modulation depth of the resonance frequencyf1was larger than that off2because of the larger change infor the same change inEF. According to the resistor-inductance-capacitance (RLC)-series electrical circuit,the bare metamaterial impedance can be directly written asThe capacitance can be expressed aswhen the monolayer graphene was layered on top of the metamaterial, whereCis the capacitance of the bare metamaterial,σis the graphene layer conductivity, andW0/L0is the effective aspect ratio of the conducting graphene[37]. The conductivity of graphene layer was increased with increasingEF, thereby enhancing theCgand decreasing theZmeta(ω) of the hybrid graphene metamaterial.Simultaneously, the transmission amplitude of the proposed structure can be dynamically controlled according to (4). On the other hand, the graphene layer manifests ‘metallic’properties more obviously with increasingEF, and the transmission efficiency decreases in broad frequencies.

4. Conclusions

In conclusion, we have designed a novel ultrathin THz modulator based on hybrid graphene-metal metamaterial.The proposed metamaterial structure exhibited a flat broad passband transmission response in THz frequencies. The modulation depth of transmission was 29.2% when graphene was layered on the metamaterial, meanwhile that of 79.5% was achieved through adjusting the graphene’sEFto 1.0 eV in a broadband THz frequency range. The modulation depths of resonance frequenciesf1andf2were 63.2% and 18.0%, respectively. These results demonstrate that this kind of ultrathin hybrid graphene metamaterial enables effective manipulation of THz waves, and this new modulator may offer widespread applications in the wireless communications, imaging systems, biomedical sensing, and so on.