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Abstract
A novel graphene-based metamaterial absorber with actively tunable bandwidth, intensity and frequency, working at the terahertz (THz) spectral region, was designed and numerically investigated in this paper. The actively controlled absorption characteristics in the graphene absorber were achieved by integrating two identical-sized graphene disc elements to construct a supercell, in which two elements of all unit cells were connected respectively by the electrical isolation graphene wires to form selectively electrostatic doping. The surface current distributions and the circuit model analysis were conducted to reveal the absorption mechanism and predict the tuning mechanism. Moreover, by selectively tuning two gate voltages to change the Fermi energy reconfiguration state of two graphene elements, the absorption bandwidth, intensity and frequency of the metamaterial absorber could be actively controlled. In addition, a striking switching contrast was obtained by switching the reconfiguration state of the two discs. Therefore, this work paves a pathway for the realization of actively controlled terahertz waves based on electrically reconfigured graphene metamaterials.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The metamaterial absorber (MA) is another new type of electromagnetic wave absorber (EMA) first proposed by Landy in 2008, which is normally composed of the patterned metallic unit cell, metallic ground plane, and dielectric layer between them [1]. Compared with the traditional EMAs, the novel MAs exhibit many merits, including ultra-thin configuration, compact structure, light weight, perfect absorption and easily tunable resonances, etc [2-3]. In recent years, the MAs have attracted considerable attentions due to the potential applications in detecting, imaging, and sensing [4–6]. Currently, various metamaterial absorbers have been designed and fabricated over the wide range of electromagnetic spectrum from microwave [7-8] to terahertz [9-10], and even to optical frequency [11-12]. Unfortunately, most of the metamaterial absorbers reported so far can only operate at a certain frequency or in a narrow frequency range due to resonant nature in metamaterial structure, which greatly hampers their practical applications.
Generally, active control of the metamaterials is achieved by integrating active material into the resonator geometry or as a surrounding medium [13–15]. Based on similar mechanisms, recently, the MAs can also realized either absorption frequency tuning, or absorption intensity tuning, or absorption bandwidth tuning by combining the patterned metallic array with the ferrite [16-17], microfluidic [18-19], liquid-crystals [20-21], semiconductor [22-23], MEMS [24-25] or active lumped element [26–28]. However, the metamaterial absorber simultaneously achieving active control of frequency, intensity and bandwidth is yet to be reported so far because of their frequency dependent material properties, complexity in the fabrication process, and need for bulky systems to provide the external control. Moreover, such absorber will be a critical component in the communication, detection, sensing, spectrometry, and imaging applications [4, 6]. Therefore, it is urgently necessary to develop or design a novel type of metamaterial absorber with actively controlled absorption characteristics and simple structure.
Since discovered in 2004, graphene has arisen widely interests due to unique properties [29–31]. In contrast to the traditional noble metal, more importantly, the graphene conductivity can be flexibly tuned by electrostatic or chemical doping [32]. Currently, a great of tunable graphene metamaterials have been theoretically investigated and experimentally demonstrated by patterning, stacking or integrating graphene to explore novel tunable devices [33–37]. Therefore, these graphene-based metamaterials open up new approaches for actively controlling absorption characteristics of the metamaterial absorber. Motivated by the above fundamental studies, in this paper, we proposed an actively controlled graphene metamaterial absorber (GMA) operating in the THz spectral region, in which the unit cell structure is composed of two graphene discs with identical size. Moreover, two elements of all unit cells connect respectively with the corresponding metallic pads by the separated graphene wires to realize selectively electrostatic doping. By selectively tuning Fermi energy of two graphene discs, the absorption bandwidth, intensity and frequency can be actively controlled. Therefore, the proposed graphene metamaterial absorber with tunable absorption bandwidth, intensity and frequency would exhibit potential applications in the next generation THz wireless communication, THz imaging, materials detection, biological sensing, and frequency selective thermal emitters.
2. Design and simulations of the structure
As well known, the plasmon excitations in the traditional metal metamatarials are mainly determined by the width of basic structure [38]. Once structural parameters are fixed, however, such metamaterials work only at a narrow frequency range. For a given graphene micro-ribbon array, interestingly, plasmon resonance can be further tuned in situ using electrostatic doping, where the plasmon frequency varies with carrier concentration (n) as n1/4 [39]. In this paper, we designed a terahertz graphene metamaterial absorber (GMA) with actively controlled absorption frequency, intensity and bandwidth, as shown in Fig. 1. Figure 1(a) shows the schematic of the designed metamaterial absorber, which includes a patterned graphene top layer, a metallic ground plane bottom layer and a SiO2 spacer layer between them. The unit cell of the patterned top layer is composed of two graphene discs with identical size, termed as Disc_1 and Disc_2 respectively, as shown in Fig. 1(b). In this structure, by optimizing spacer thickness to cancel out the reflection, the destructive interference between THz waves reflected from the patterned graphene and ground plane gives rise to perfect absorption, which is different from the absorption by the confined intraband plasmons of graphene ribbons [40]. Moreover, two discs of all unit cells are electrically connected to the corresponding metallic pads (Pad 1 and Pad 2) respectively by the separated graphene wires, as shown in Fig. 1(a). Here, the introduction of the electrical isolation is crucial for the selective doping to enable advanced control of the absorption spectrum.
Fig. 1 Designed terahertz GMA with tunable absorption frequency, amplitude and bandwidth: (a) schematic of GMA, (b) close-up view of unit cell, and (c) cross-sectional view of GMA.
When a bias voltage is applied between the pad and the substrate, Fermi energy of the graphene disc can be tuned due to the electrostatic doping. Thus, Fermi energy of two graphene discs can be independently controlled by changing the corresponding bias voltage, obtaining multiple resonant modes closely positioned together in the absorption spectrum, as a result, realizing active control of the absorption characteristics. Here, the bias voltage applied to two graphene disc resonators is termed as Vg1 and Vg2 respectively, as shown in Fig. 1(c). Compared to the previously reported tunable MAs [20, 22–24, 28], more importantly, the GMA designed here not only has simple unit cell structure and fabrication processes, but also can actively control and reconfigure the absorption bandwidth, intensity and frequency.
In order to verify actively tunable absorption response of the designed GMA, numerical calculations are carried out using the commercial finite difference time domain (FDTD) softwave package (CST Microwave Studio), where periodic boundary conditions are used for a unit cell in x- and y-directions, and perfectly matched layer boundary condition is applied in z-plane. The plane wave polarizing along x-direction is normally incident to the structure surface along z-direction, as shown in Fig. 1(a). Since thickness of the ground plane is much larger than its skin depth, the GMA transmission is close to zero, and the absorption intensity A can be calculated by A = 1 – R, where the A may achieve 100% as the R (reflection) is close to zero. In our numerical calculations, the structural parameters are as following: r = 26μm, d = 120μm, w = 2μm, tm = 0.2μm, td = 0.3μm, Px = 240um, and Py = 120μm (as shown in Fig. 1(b)), while the relative permittivities of the SiO2 layer and the frequency independent conductivity of metal gold are taken as 3.9 and 4.09 × 107S/m, respectively. To simplify numerical calculations, we assume the graphene to be an effective medium with thickness of tg = 0.34nm and relative complex permittivity of εr(ω) = 1 + jσ(ω)/(ωε0tg), in which the conductivity σ(ω) can be described as [41]:
where ε0 is the permittivity of vacuum, ω is the frequency of the incident wave, EF is the Fermi energy, Г is the scattering rate (Г = 2.4 THz), T is the temperature of the environment (T = 300 K), e is the charge of an electron, kB is the Boltzmann’s constant, and ħ = h / 2π is the reduced Planck’s constant.3. Results and discussions
3.1 Principle of GMA
To understand actively tunable absorption characteristics, two different GMAs, composed of only a graphene disc array and two graphene discs array respectively, are studied under different applied voltages. The calculated absorption spectra of two GMAs with different Fermi energy are shown in Fig. 2. For the GMA consisting of only a graphene disc array with Fermi energy of 0.1eV, a narrow absorption peak of 99.5% is observed at 1.31THz due to impedance match between the absorber and free space, which is significantly higher than the absorption intensity of the previous grapheme absorbers [42-43]. Moreover, the absorption peak blueshifts gradually with Fermi energy of graphene disc, as shown in Fig. 2(a). This blue-shifting behavior can be attributed to change in the resonant frequency of the graphene disc, in which the resonant frequency can be written as f0 ∝ EF [44-45]. Therefore, this is a simple way to achieve agile tuning of the absorption frequency comparing with other tunable methods [23, 25, 28]. In addition, it is also noticed that the absorption intensity decreases slightly at higher frequencies due to the increased loss in graphene which degrades the impedance match between the absorber and free space, as observed in previous reports [35, 46].
Fig. 2 Calculated absorption spectra of the designed terahertz metamaterial absorber consisting of (a) only a graphene disc array with different Fermi energy and (b) two graphene discs array with different Fermi energy.
As integrating two graphene discs with identical size but different Fermi energy into a supercell, however, a broadband absorption can be obtained due to the superposition of tow absorption peaks, as shown in Fig. 2(b). It is noticed that the absorber appears two absorption peaks A1 = 99.9% and A2 = 99.5% at 1.512THz and 1.537THz respectively when Fermi energy of the Disc_1 and Disc_2 are EF_g1 = 0.4eV and EF_g2 = 0.7eV respectively. Moreover, the absorption bandwidth with the absorption intensity of more than 80% is about 60 GHz. To understand the widened mechanism of the absorption bandwidth, the absorption spectra of the absorbers composed of only a graphene disc array with Fermi energy of 0.4eV and 0.7eV respectively are also provided, as shown in Fig. 2(b). It is observed that two absorption peaks at 0.4eV and 0.7eV are located at 1.506THz and 1.540THz respectively, and their absorption bandwidths are all very narrow. In addition, it is also noticed that their maximum absorption intensity is only about 92.5% and lower than the counterpart of the supercell-based absorber. Therefore, these results demonstrate that the supercell-based absorber can achieve better impedance-matched to free space by the effective near field coupling between two graphene discs, as observed in previous results [38].
To further elucidate actively tunable mechanism, the controlled absorption characteristics of the designed GMA can be also evaluated by the equivalent circuit [46-47], as shown in Fig. 3. In the circuit model, Zin represents the input impedance of the active absorption structure, and Z0 is the characteristic impedance of free space. While, two graphene discs of the unit cell structure can be equivalent to two parallel RLC circuits respectively, where C1 and C2 stand for effective capacitances between two graphene disc and metallic ground plane, R1 and R2 represent Ohm loss of two graphene discs, and L1 and L2 are effective inductances respectively, as shown in Fig. 3(b). Moreover, these parameters can be rewritten as follows respectively:
where τ is the relaxation time, q11 is the first eigenvalue of the equation governing the current on the discs (values of q11 for different 2r/Py have been given in table 2 of [48]), S1 = 0.6087r, K1 = 1.2937, and εeff = ε0 (1 + ns2)/2 is the average permittivity of the mediums surrounding the discs, in which the ns is the refractive index of the SiO2 layer. From above equations, we can ascertain that the effective capacitance C depends only on the structural parameter, while the effective resistance R and the effective inductance L depend not only the structural parameter but also Fermi energy of graphene disc. According to the effective RLC circuit model [49-50], the graphene disc can be treated as a oscillator circuit with resonant frequency f0, which is strongly dependent on the effective capacitance C and inductance L, i.e., . As applying a bias voltage between the top gate and substrate, the R and L can be actively controlled due to change in Fermi energy, as a result, the absorption frequency exhibits blue-shifting and the absorption intensity decreases as increase in Fermi energy, as observed in Fig. 2(a). Thus, the R and L can act as tunable elements, as shown in Fig. 3(c). Even with two graphene disc resonators of fixed size, therefore, their resonances can be actively controlled by selectively tuning Fermi energy of graphene discs to achieve multiple resonant modes, and the absorption bandwidth can be actively tuned.Fig. 3 Equivalent circuit of the proposed active graphene metamaterial absorber: (a) Three-dimensional sketch of the active absorber, (b) RLC equivalent circuit, and (c) tunable elements of unit cell
3.2 Bandwidth modulation
The key feature of the designed GMA consists in its active control of absorption spectrum. To examine tunable characteristics of the absorption bandwidth, the absorption spectra of the designed GMA are studied for various reconfiguration states, as shown in Fig. 4. To keep the central frequency unchange of absorption band, here, Fermi energy of only a graphene disc in the unit cell is tuned, such as Disc_2. As shown in Fig. 4(a), it is observed that the absorption bandwidth widens gradually as the reconfiguration state of two graphene discs changes from (0.20 and 0.20) to (0.20eV and 0.30eV) (grey region). When EF_g1 = EF_g2 = 0.2eV, only a narrow absorption peak is observed due to identical parameters of two graphene discs, and the full-width half maximum (FWHM) bandwidth is 64GHz, as shown in Fig. 4(b). As increase in the Vg2, Fermi energy of the Disc_2 increases, blueshifting the corresponding resonant frequency, a widened absorption band is obtained due to the superposition of tow absorption peaks. When further changing the reconfiguration state of two graphene discs (bottom row shown in Fig. 4(a)), the absorption peak will begin to split, and here the bandwidth becomes the widest (FWHM bandwidth of 96.8GHz). Through changing reconfiguration state of two graphene discs, therefore, the FWHM bandwidth increases by 51% from 64GHz to 96.8GHz without frequency shifting, which is different from the previous results obtain by MEMS technology [51]. Moreover, the FWHM bandwidth can further increase by integrating more graphene discs into a supercell.
Fig. 4 Calculated (a) absorption spectra and (b) FWHM bandwidth of the graphene metamaterial absorber at various reconfiguration states
In addition, it is clear enough to observe two absorption peaks at 1.448THz and 1.498THz when the reconfiguration state of two graphene discs is EF_g1 = 0.2eV and EF_g2 = 0.3eV, as shown in Fig. 4(a). To explore the forming mechanism of two absorption peaks, the corresponding surface current distributions are shown in Fig. 5. At 1.448THz, most currents are concentrated on the top Disc_1 with Fermi energy of 0.2eV and the corresponding bottom metal layer, as shown in Fig. 5(a) and Fig. 5(b). At 1.498THz, the surface currents are mainly focused on the top Disc_2 with Fermi energy of 0.3eV and the corresponding bottom metal, as shown in Fig. 5(c) and Fig. 5(d). Moreover, the currents formed on the top and bottom layers are anti-parallel. Therefore, these current distributions further demonstrate that the wideband absorption results from the superposition of tow resonances by the near field coupling.
Fig. 5 Resonant current distributions in one cell at different absorption peaks: (a) top and (b) bottom layers at 1.448THz, and (a) top and (b) bottom layers at 1.498THz
3.3 Intensity modulation
To qualitatively understand the absorption intensity modulation, the absorption spectra of the designed GMA at various reconfiguration states are calculated, as shown in Fig. 6. As two graphene discs with same Fermi energy (i.e., EF_g1 = EF_g2 = 0.26eV), a normalized absorption intensity of 94.6% is achieved at the interested frequency 1.461THz. Moreover, tuning the reconfiguration state of two graphene discs through loading different voltages between two Pads and substrate, the absorption intensity of the designed GMA at 1.461THz decreases monotonically due to two absorption peak separating (from top row to bottom row), as shown in Fig. 6(a). As reconfiguration state of two discs is EF_g1 = 0.10eV and EF_g2 = 1.40eV, the absorption intensity at 1.461THz is decreased to 5.8%, as shown in Fig. 6(b). As a result, the absorption intensity of the designed GMA at 1.461THz decreases by 88.8% from 94.6% to 5.8% and the corresponding modulation depth (Amod, (Amod = ΔA/Amax) is 94%, which is larger than the previous results [22, 52]. Such a graphene metamaterial, therefore, allows to simply and fast switch high-absorption state and low-absorption state by tuning the reconfiguration state of two graphene discs.
Fig. 6 Calculated (a) absorption spectra and (b) change in absorption intensity at 1.1461THz of the graphene metamaterial absorber at various reconfiguration states
To reveal the physical mechanism of the absorption intensity modulation, the effective impedance zeff (ω) of the designed GMA is calculated according to the following equation [53-54]:
where S11 and S21 are the scattering parameter, the retrieved effective impedance is normalized relative to the impedance of free space. The real and imaginary parts of the impedances at various reconfiguration states are shown in Fig. 7. It can be observed that the imaginary parts of the impedances at different reconfiguration states are almost the same and nearly zero at the interested frequency 1.461THz. On the other hand, the real parts of the impedances decrease from 0.99 to 0.02 at 1.461THz as the reconfiguration sate changes from (0.26 and 0.26) to (0.10eV and 1.40eV). The effective impedances of the GMA match worse to the impedance of the free space, leading to lower absorption intensity, as a result, realizing the absorption intensity modulation, as observed in Fig. 6(a) (from top row to bottom row).Fig. 7 Real and imaginary parts of the retrieved relative effective impedances at various reconfiguration states (normalized to free space impedance).
3.4 Frequency modulation
As well know, the frequency tunable structure not only can provide a compact unit cell but also exhibit a wide working range, which is needed for the practical applications in detection, imaging and stealth technology. Next, the frequency tunable properties of the proposed GMA are further investigated by applying different voltages on two Pads, as shown in Fig. 8. When the reconfiguration state of two graphene discs changes from (0.09 and 0.12) to (1.00eV and 1.80eV), Fermi energy of two discs become larger, decreasing the effective inductance, as a result, the absorption frequency exhibits a clear blueshift (from top row to bottom row), as shown in Fig. 8(a). Simultaneously, it can be seen that the absorption bandwidth of more than 90% changes slightly during the blueshift. This can be attributed that we optimize unit cell for the best absorption only at one particular reconfiguration state.
Fig. 8 Calculated (a) absorption spectra and (b) change in center frequency and more 90% absorption bandwidth of the graphene metamaterial absorber at various reconfiguration states
In addition, the concrete analysis of the absorption blueshift is displayed in Fig. 8(b). For example, when the reconfiguration state of two discs is 0.09eV and 0.12eV, the calculated absorption is 93.4% at center frequency (1.313THz) with more 90% absorption bandwidth of 42.3GHz. As further increasing Fermi energy of two discs, changing the reconfiguration sate of two discs, as a result, the absorption shifts continuously to higher frequency as along with a widened absorption bandwidth. Finally, when the reconfiguration state is 1.00eV and 1.80eV, the center frequency of absorption bandwidth is shifted to 1.580THz with more than 90% absorption bandwidth of 51.2GHz. Consequently, the frequency tuning range of 267GHz can be obtained by changing reconfiguration state of two discs. Moreover, the tuning frequency range can be further enhanced by tuning reconfiguration state in a larger region, as shown in Fig. 2(a).
3.5 High electro-optic switching contrast
As demonstrated above, the amplitude and frequency of the absorption spectra in the proposed absorber can be actively tuned by changing reconfiguration state of two graphene discs. Thus, the absorber can act as the electro-optic switching devices, which are highly attractive for terahertz based next-generation high-speed communication and non-invasive medical devices [55]. For the traditional electro-optic switches, generally, the two key performance parameters are high switching contrast and low actuation voltage [56]. In order to feature the designed GMA as an electro-optic switch, the electro-optic switching property of the designed GMA device is investigated at two various reconfiguration states, as shown in Fig. 9. Figure 9(a) shows the obvious absorption peak change between two reconfiguration states. For example, as the reconfiguration state of two graphene discs changes from (0.26 and 0.26) to (0.10eV and 1.40eV), the absorption peak at 1.461THz is split into two absorption peaks, located at 1.315THz and 1.592THz respectively, due to the decrease in Fermi energy of Disc_1 and increase in Fermi energy of Disc_2. As a result, the switching intensity of 88.8% at 1.461THz is obtained in switching range of 0.131THz, and the corresponding switching contrast (SC), defined as SC = (Amax - Amin)/ Amin, is calculated to be 1531%, which is six times higher than the previously reported results [57]. Moreover, the switching range and switching contrast can be improved by further decreasing Fermi energy of Disc_1 and increasing Fermi energy of Disc_2.
Fig. 9 Electro-optic switching characteristics of the proposed graphene absorber between two reconfiguration states: (a) absorption peak and (b) absorption frequency
Figure 9(b) shows the clear absorption blueshift between two reconfiguration states. As the reconfiguration state switches from (0.09 and 0.12) to (1.00eV and 1.80eV), the switching range of 0.267THz is observed. As a result, the switching intensity of 91.1% is achieved at 1.313THz, and the corresponding switching contrast is 3961%, which is 2.6 times higher than the switching contrast of the absorption peak as shown in Fig. 9(a). This high electro-optic switching contrast can be attributed to the larger change in Fermi energy between two reconfiguration states.
Conclusions
In summary, a novel graphene metamaterial absorber with actively tunable absorption bandwidth, intensity and frequency as well as high electro-optic switching contrast has been numerically demonstrated by integrating two graphene discs into a supercell. The absorption and tunable mechanisms of the proposed absorber can been explained by the surface currents and the circuit model. By changing reconfiguration state of two discs, the FWHM bandwidth at 1.451THz increases by 51% from 64GHz to 96.8GHz without prominent resonance frequency shift, the absorption intensity at 1.461THz obtains the modulation depth of 94%, and the absorption frequency exhibits the blueshift of 267GHz. In addition, the switching intensity of 91.1% is observed at 1.313THz when the reconfiguration state switches between (0.09eV and 0.12eV) and (1.00eV and 1.80eV), and the corresponding switching contrast is 3961%. Therefore, the active tuning, high switching contrast, simple design, compact size, and potentially fast response time make the proposed graphene metamaterial absorber to highly attractive for terahertz based next-generation high-speed communication and non-invasive medical devices. Moreover, the graphene-based metamaterial approach provides the ideal platform for realizing numerous advanced THz functionalities by integrating multiple graphene elements in the desired way to form more complex metamaterial unit cell.
Funding
National Natural Science Foundation of China (51672062, 51575149, 61501275 and 51402075); Heilongjiang Province Natural Science Foundation of China (F201309 and QC2015073); the Postdoctoral Science-Research Developmental Foundation of Heilongjiang Province (LBH-Q11082); the Youth Academic Backbone Support Plan of Heilongjiang Province Ordinary College (1253G026); Special Funds of Harbin Innovation Talents in Science and Technology Research (2014RFQXJ031); Science Funds for the Young Innovative Talents of HUST (201104).
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