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Abstract
Dynamically and independently tunable absorbers based on multilayer metal-graphene metamaterials are proposed to achieve multi-band and ultra-wide-band absorbing properties at mid-infrared frequencies. Dual-band, triple-band and even more bands absorption can be arbitrarily customized by etching the appropriate number of tandem gold strips in each meta-molecule, as well as stacking multiple metal-graphene layers. Through tuning the Fermi energy level of the graphene in each metal-graphene layer separately, the multiple absorption resonances can be dynamically and independently adjusted. With side-by-side arrangement of the gold strips in each supercell, the proposed structure is rendered to be a promising candidate for ultra-wide-band absorber. The extreme bandwidth exceeding 80% absorption up to 7.5THz can be achieved with a dual-layered structure, and the average peak absorption is 88.5% in the wide-band range for lossless insulating interlayer. For a triple-layered structure, the average peak absorption is 84.7% from 27.5 THz to 38.4 THz with a minimum of 60%. The absorption windows can be even further broadened with more metal-graphene layers. All these results will benefit the integrated microstructure research with simple structure and flexible tunability, and the multilayer structure has potential applications in information processing fields such as filtering, sensing, cloaking objects and other multispectral devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metamaterials are artificially structured Electromagnetic (EM) materials composed of periodically arranged subwavelength microstructures such as the concentric rings [1,2], the metal cut wires [3,4] and the metal split ring resonators [5,6]. Metamaterial-based absorbers (MMA) have attracted great attention since the work by Landy et al. [7] for their scalable property and the promising applications in optical cloaking [8], plasmonic sensors [9], and spectroscopy [10]. The traditional MMA is usually composed of three layers: a layer of periodically-arranged metallic patterns, a dielectric interlayer and a metallic ground plane. The single-band absorbers are limited in practical applications. Therefore, the MMAs with multi- and broad band absorption are proposed by introducing multiple resonators with different geometrical dimensions [11–13]. However, the optical properties of metamaterials based on metallic structures cannot be changed anymore once the structure has been fabricated, and usually come with an unsatisfactory modulation depth.
To realize the dynamically tunable resonant properties, some actively controlled elements, such as semiconductors [14], liquid crystals [15], and liquid metals [16] are applied in these metamaterials devices. Graphene, a flat monolayer of carbon atoms packed into a dense 2D honeycomb crystal lattice, has become a very promising material for its unique electrical properties [16–19], such as high electron mobility, flexible tunability, relatively low loss and tight field confinement. The most attractive one among these properties is that the conductivity of graphene can be dynamically tuned by changing the Fermi energy through chemical doping [20,21] or electrostatic gating [22]. Therefore, graphene based metamaterials [23,24] can provide an effective approach to achieve the dynamically tunable multispectral devices, such as absorbers [13], filters [25] and polarization converters [26]. For strong absorption is desired in photon detection [27], graphene-based optical antennas [28] and solar cells [29], the researches of graphene-metamaterials based absorbers in mid-infrared region become significant. Despite the recent investigations in graphene-based MMA [30–35], most of these metasurface-based absorbers suffer from narrow bandwidth, and the multiple absorption bands can’t be tuned independently. How to achieve independently tunable graphene-based absorbers with excellent absorptivity and ultra-wide bandwidth still remains a challenge.
In this work, dynamically and independently tunable absorbers consisted of multiple metal-graphene layers are proposed to achieve multi-band and ultra-wide band absorbing properties at mid-infrared frequencies. The absorption properties with various parameters of the meta-molecules are investigated. Not only by etching the appropriate number of tandem gold strips in a unit cell but also by stacking more metal-graphene layers, the multi-band absorbers can be achieved with an average absorptivity about 90% for lossless insulating interlayer. The resonances can be dynamically and independently tuned by adjusting the applied voltage bias on each graphene layer. By combining the gold strips with side-by-side arrangement, the average peak absorption is 84.7% from 27.5 THz to 38.4 THz with a minimum of 60%. The absorption band can be even further expanded with more metal-graphene layers. All these results demonstrated that the proposed structure based on multiple metal-graphene layers provide promising applications in filtering, sensing and cloaking objects.
2. Model construction and simulation
The proposed absorber is composed of multiple metal-graphene layers separated by thin dielectric films (i.e. MgF2 and CaF2), which are used as the insulating spacer with the refractive index 1.4 [36], and a gold block at the bottom serving as the metallic ground plane as depicted in Fig. 1(a). The thickness of the insulating spacer h1 and h2 are equal to 300 nm. Each metal-graphene layer consists of periodically arranged gold strips and a monolayer of graphene. The top and side view of the unit cell is shown in Figs. 1(b) and 1(c), respectively. For each layer, two parallel gold strips with an identical width of w = 0.5 μm are symmetrically attached on the center of the unit cell and separated from each other by a small gap d. The lengths of the gold strips are set as l1, l2, l3 and l4, respectively. The periods of the unit cell are Px on x direction and Py on y direction. The metallic pads on each graphene layer serve as the electrodes along with the gold substrate to tune the Fermi energy level of the graphene by applying a gate voltage. A plane wave polarized parallel to the x-direction (p-polarized) is used as the normal incident light. The surrounding medium are assumed to be uniform with the refractive index nr = 1. The thickness of the gold strips and the metallic ground plane are 100 nm and 2 μm, respectively.
Fig. 1 (a) Schematic of the proposed absorber based on metal-graphene metamaterials and the incident light polarization configuration. (b) Top view of the unit cell. (c) Side view of the unit cell. The thickness of the insulating spacer is assumed to be h1 and h2.
The proposed absorbers are numerically calculated using the finite elements solver COMSOL Multiphysics. The monolayer graphene is modeled as a surface current in the boundary conditions, which is defined as the product of graphene conductivity and the tangential electric field on the graphene plane. The conductivity of the gold is described by the Drude model with the plasma frequency wp = 1.36 × 1016 rad/s and the scattering rate Γ = 3.33 × 1013 rad/s in this work [37]. The optical properties of the graphene can be characterized by the complex surface conductivity σg. It consists of interband part and intraband part, and can be given by Kubo formula [38,39]: σg(ω, τ, μc) = σintra(ω, τ, μc) + σinter(ω, τ, μc). The interband and intraband transition contributions are modeled as:
where w is the incident angular frequency, kB is the Boltzmann constant, is the reduced Planck constant, e is the electron charge, and T is the temperature in kelvin, which is fixed to 300 K in this study. When the condition of kB < μc is satisfied, the value of chemical potential μc is equal to that of the Fermi energy level Ef which can be defined as, where n is the carrier concentration which is proportional to the gate voltage Vg on the graphene layer. The carrier concentration is given as n = εdε0Vg/ehd, where εd and hd is the relative permittivity and thickness of the insulating interlayer, respectively. The relaxation time characterizes the plasmon decay on account of impurities, where the Fermi velocity is = 106 m/s. The carrier mobility μ, which could reach higher than 105 cm2V−1s−1 in the recent experiment, is set as a easily achievable value 1318 cm2V−1s−1 corresponding to the relaxation time for Ef = 0.15 eV in this paper.Comparing with the interband transitions, the intraband transitions contributes mainly to the graphene conductivity for the lower frequencies satisfying ω<2Ef /ℏ, as shown in Fig. 2(a). According to the Maxwell equations, the real part of the graphene permittivity is in direct proportion to the opposite of the imaginary part of the graphene conductivity Im(σg); the imaginary part of the graphene permittivity, which characterizes the losses, is proportional to the real part of the graphene conductivity Re(σg). Figure 2(b) shows that the curves of Re(σg) tend to be smooth and the value increases with the relaxation time decreases, which represents the losses are enhanced. Figure 2(c) shows the ratio of Im(σg) to Re(σg) with various Fermi energy level to evaluate the electromagnetic properties of graphene. When the frequency satisfies the condition of Im(σg)/Re(σg)>1, low-loss plasmonic response of graphene is resulted. The graphene behaves as a lossy metal when Im(σg)/Re(σg)<1, and the negative ratio means the graphene behaves as a dielectric. And on the base of the above, we designed the metal-graphene based absorber working in the frequency from 20 THz to 50 THz.
Fig. 2 (a) The conductivity of graphene changes with various Fermi energy level, and the relaxation time τ is fixed as 0.0198 ps. (b) The conductivity of graphene changes with various relaxation time, and the Fermi energy level Ef is fixed as 0.15 eV. (c) The ratio of the imaginary part to real of the graphene conductivity with different Fermi energy level and the relaxation time τ is fixed as 0.0198 ps.
3. Results and discussion
3.1 Absorption characteristics of the basic unit cell of metal-graphene metamaterials
Figure 3(a) shows the calculated absorption spectrum of the single-layer and single-arm absorber. The gold strip’s width w is 0.5 μm and length l is 2.4 μm. The period of the unit cell is 5.2 μm both on x and y directions. The absorption peak is observed at 40.4 THz with a absorptivity of 85% for Fermi energy Ef = 0.15 eV. The distributions of electric field amplitude |E| on the metasufrace and the metallic ground plane are shown in Fig. 3(b) at its resonance frequency. One can see that the gold strip is strongly excited and the electric fields concentrate mostly around its edges and ends, which is a typical electric dipolar mode distribution. To further reveal the absorbing mechanism, the distribution of the surface current is simulated. The direction of the surface currents on the metal strip parallels with the electric field of the incident light, which indicates strong electric resonance [40]. The surface currents on the metallic ground plane are antiparallel to those on the metasurface and mainly concentrate on the center right below the metal strip. A magnetic moment attributed to the circulating currents can strongly interact with the magnetic field of the incident light, which is usually called a magnetic resonance [9,40–42]. Both the strong electric resonance and magnetic resonance contribute to the energy attenuation of the incident light, and prefect absorption of the proposed structure is achieved.
Fig. 3 (a) The simulated absorption spectrum of the basic unit cell of the metal-graphene metamaterials. (b) The distributions of electric field amplitude |E|, and the surface current on the unit cell and the metallic ground plane at its absorption peak. The small red arrows represent the magnitude and the direction of the surface currents.
In order to comprehend the absorption characteristics of the proposed structure, we simulated the absorption spectra varying with different structure parameters. Figure 4(a) exhibits the absorption as a function of the thickness of the insulating layer h, which changes from 200 nm to 1000 nm. This increased thickness leads to a slight red-shift of the resonance, and the spectra intensities become weaker gradually. The structure shows excellent absorptivity of almost 100%, when the thickness satisfies h<310 nm. Thus, h is fixed as 300 nm in the following investigations. Figure 4(b) shows the absorption spectra as a function of period P varying from 4.2 μm to 6.2 μm. It is evident that the absorptivity increases with the period, and the resonances nearly keep as a constant. Considering the demand for the miniaturization and high absorptivity, we choose P = 5.2 μm as the fixed period. Figures 4(c) and 4(f) are the absorption spectra with various length of gold strips, when the metal-graphene layer is located in the interface and inside of the dielectric layer, respectively. The resonances are both red shifted as the gold strip’s length increases, and a relatively stable absorptivity around 90% can be obtained. However, it is noteworthy that the resonances in Fig. 4(f) move to lower frequencies than that in Fig. 4(c) with the same gold strips’ length due to that the increased effective permittivity of the surrounding background medium leads to the increment of the effective capacitance of the unit cell. Thus, the resonance is associated with the surrounding medium and can be adjusted by varying the length of gold strip.
Fig. 4 Absorption spectra as a function of (a) the thickness of the dielectric layer h, (b) the period P = Px = Py, and (c) the length of the gold strip l (the metal-graphene layer is located in the interface of air and the dielectric layer). (d) Absorption spectra as a function of the Fermi level Ef. The color bars represent the value of absorption. (e) Absorption spectra as a function of the incident angle with p-polarization. (f) Absorption spectra as a function of the length of the gold strip l’ (the metal-graphene layer is located inside the dielectric layer). Unless otherwise specified, the Fermi energy level and carrier mobility is fixed as 0.15 eV and 1318 cm2V−1s−1, respectively.
Figure 4(d) illustrates the simulated absorption spectra when the Fermi energy changes from 0.15 eV to 0.6 eV. It is clearly that the two absorption peaks show a clearly blue shift with the Fermi energy level increases. The blue shift is caused by the inductive coupling between metasurface and graphene layer, and the change of the resonances can be evaluated by the rigorous perturbation theory proposed by S. H. Mousavi et al. [43]. Figure 4(e) shows the absorption spectra as a function of the angle of incidence for p-polarization in the range from 0° to 80° with Ef = 0.15 eV. It is obvious that the positions of the absorption peaks remain almost constant and the values exceed 85%, which means the resonance is insensitive to the incident angle. Thus, the proposed structure keeps a perfect absorption over a wide range of incident angle. The splitting of the absorption spectra, which is similar to Rabi splitting for the case of many atoms in an optical cavity [44,45], shows a clearly red shift with the incident angle increasing.
3.2 Dynamically and independently tunable multi-band absorbers
Figure 5(a) shows the schematic and the absorption spectrum of the absorber with single-layer and two tandem gold strips, by which two absorption peaks are realized. As depicted by the curves, the absorption peaks exhibit a clear blue shift as a whole with the Fermi energy increases. When Ef = 0.15 eV, the proposed structure with l1 = 2.4 μm and l2 = 3.2 μm shows strong absorption peaks at 40.4 THz and 31.4 THz, respectively. The absorption spectra of the proposed absorber changes with the angle of incidence for p-polarization in the range from 0° to 80° with Ef = 0.15 eV is shown in Fig. 5(b). Both the low- and high-order resonances are independent on the angle of incidence. The proposed absorber keeps an absorptivity exceeding 80%, and the spectra is disturbed from the Rabi splitting analogues. The two absorption bands of the proposed absorber are mainly determined by the length of the two gold strips which both act as the bright elements. In addition, the number of the absorption peaks can be further improved by etching more gold strips as shown in Fig. 5(c). When Ef = 0.15 eV, the absorber with three gold strips l1 = 2.0 μm, l2 = 2.6 μm and l3 = 3.4 μm shows strong absorption peaks at 47.4 THz, 38.0 THz and 29.6 THz, respectively. The absorber with three gold strips in each unit cell exhibits analogous responds to the incident angle, as shown in Fig. 5(d).
Fig. 5 The schematic and the simulated absorption spectrum of the absorber with: (a) single-layer and two tandem gold strips and (c) single-layers and three tandem gold strips. Absorption spectra as a function of the incident angle with p-polarization for the absorber with: (b) single-layer and two tandem gold strips and (d) single-layer and three tandem gold strips. The Fermi energy of graphene is fixed as 0.15 eV.
Though the absorption peaks of single-layer absorber show a clearly blue shift as a whole with the Fermi energy increases, they can’t be adjusted separately for that the gold strips on the same graphene layer are affected by the same Fermi energy. We investigated the independently tunable properties by stacking multiple metal-graphene layers with different applied gate voltage.
The schematic of the double-layers absorber is illustrated in Fig. 6(a), and the geometric parameters are consistent with those in Fig. 3(a) except l1 = 2.4 μm and l2 = 3.2 μm. The absorption with various Fermi energy level of the bottom graphene layer is simulated, and that of the top graphene layer is fixed as 0.15 eV. The graphene surface plasmons can be tightly concentrated at the graphene-dielectric interface attributed to the strong confinement factor, and the multi-layer graphene coupling affects the absorption spectra only when the thickness of insulating interlayer is below 200 nm [36]. The thickness is assumed to be 300 nm, so the coupling between the graphene layers can be neglected. As expected, the lower-order resonance moves towards higher frequencies while the higher-order resonance keeps unchanged. Thus the proposed absorber exhibits independently tunable properties. To better understand the resonance mechanism of the multilayer structure, the inset pictures depict the electric field distributions |E| with Ef1 = Ef2 = 0.15 eV at the corresponding resonance frequencies of the double layer structure. At the low-order resonance f1 (28.7 THz), the electric field concentrates almost entirely around the edges and ends of the longer gold strip. The proposed absorber shows the resonance characteristics in accordance with the longer gold strip. The shorter gold strip is strongly excited at the high-order resonance f2 (39.7 THz), while the excitation of the longer gold strip is relatively weak. Hence the absorber mainly exhibits the resonance characteristics of the shorter gold strip. The resonance mechanism of this double-layer structure is similar to the single-layer structure with two gold strips.
Fig. 6 Schematic (upper panel) and the simulated absorption spectra (lower panel) with various Fermi energy level of the proposed absorber with (a1) double layers structure, (a2) three layers structure, and (a3) double layers structure with multiple strips. The amplitude of electric field |E| at the absorption peaks for (b1) double layers structure, (b2) three layers structure, and (b3) the double layers structure with multiple strips. The Fermi energy of graphene is fixed as 0.15 eV.
The absorption peaks of the independently tunable absorber can be further improved by stacking more metal-graphene layers. The absorption properties of the three layers structure in Fig. 6(b) are analogous to the double layers structure. The width and center coordinates of each strips keeps unchanged, and lengths of the gold strips are 2.4 μm, 2.8 μm and 3.2 μm, respectively. The absorption peak at f1 (28.6 THz) changes towards the higher frequency attributed to the increasing Fermi energy level of the bottom layer graphene, while the resonances at f2 (31.8 THz) and f3 (39.4 THz) keep unchanged for the stable Fermi energy level. The electric field distributions at the corresponding resonances are shown by the inset pictures.
More absorption peaks can be realized by stacking multilayer metasurfaces and adding gold strips at the same time. Figure 6(c) shows the absorption spectrum of the double-layer structure with two gold strips in each supercell. The metal strips on the top layer are shorter compared with the other two on the bottom layer, which are 2.2 μm, 2.4 μm, 3.2 μm and 3.6 μm, respectively. As this, four absorption peaks can be obtained. Both the two lower resonances show clearly blue-shift, when the Fermi energy level of the top graphene layer is fixed and that of the bottom layer increases from 0.15 eV to 0.6 eV. The inset pictures exhibit the electric field distributions of the absorption peaks at 25.7 THz, 28.8 THz, 39.6 THz and 45.8 THz, respectively.
3.3 Dynamically tunable ultra-wide band and dual wideband absorbers
Ultra-wide band absorber is designed by introducing different geometrical dimensions of gold strips with side-by-side arrangement in the supercell, as shown in Fig. 7(a). The broadband absorption can be achieved, when the resonances induced by the metal strips are close enough. The dimensions are as follows: w = 0.5 μm, d = 2.0 μm, h = 300 nm, Px = l1 + l2 + 2d and Py = 3.5 μm. The black solid curve shows the absorption spectrum of the proposed absorber which is composed of two metal-strip resonators with length l2 = 2.9 μm and l1 = 2.7 μm, and the corresponding first- and second-order resonances occur at 33.7 THz and 35.8 THz. Therefore, the bandwidth of the ultra-wide band absorbers is expanded. The absorption magnitude decreases slightly with the gold strip l2 varying from 2.9 μm to 2.95 μm, and the bandwidth exceeding 80% absorption is broadened to 3.1 THz, as shown by the blue balls. The wideband shows a clearly blue shift with the increasing of Fermi energy level from 0.15 eV to 0.6 eV. For the gold strips l2 = 3.0 μm, the bandwidth defined by the spectra value above the 70.8% minimum is 4.0THz (from 32.6 THz to 36.6 THz), and the calculated average absorption [34] is 80.4%. However, the average absorptivity becomes lower than 80% when the gold strip length l2 continues increasing (purple curve).
Fig. 7 The absorption spectrum as a function of frequency for (a) single metal-graphene layer and (b) double metal-graphene layers ultra-wide band absorbers with various Fermi energy levels or different gold strips’ length.
The bandwidth can be broadened even further by stacking one more metal-graphene layer which indicates introducing more resonators, as shown in Fig. 7(b). The red dashed curve depicts the absorption spectrum of the proposed absorber which is composed of four metal-strip resonators with gold strips length l4 = 3.20 μm, l3 = 3.05 μm, l2 = 3.05 μm and l1 = 2.70 μm, respectively. By designing the first- or fourth-order resonances, the wideband can be adjusted as shown by the series solid curves with various strip length l4 from 3.15 μm to 3.25 μm. The bandwidth exceeding 80% absorption is about 7.5 THz for l4 = 3.20 μm, and the average peak absorption is 88.5%. By modifying the second- or third-order resonances, the flatness of the absorption wideband can be optimized with fixed bandwidth, as shown by the green dashed and blue ball curves. For a triple-layered structure, the average peak absorption is 84.7% from 27.5 THz to 38.4 THz with a minimum of 60%, as shown by the purple dashed curve.
Finally, dual wideband absorbers can be realized by designing two quite different sets of gold strips length in top and bottom layer. The absorption spectrum is shown in Fig. 8 with various Fermi energy levels of the bottom graphene layer from 0.15 eV to 0.6 eV, and the length of the gold strips are set as l1 = 2.25 μm, l2 = 2.50 μm, l3 = 3.15 μm and l4 = 3.40 μm. The bandwidth exceeding 80% absorption of the low- and high-order absorption wideband is about 2.2 THz and 3.4 THz, respectively. It is significantly that the low-order absorption wideband shows a blue shift with the increase of the Fermi energy level. Analogously, the high-order absorption wideband can be tuned independently by adjusting the Fermi energy level of the top graphene layer.
Fig. 8 The absorption spectrum for dual wideband absorbers as a function of frequency with various Fermi energy levels of bottom graphene layer from 0.15 eV to 0.6 eV, and the length of the gold strips are l1 = 2.25 μm, l2 = 2.50 μm, l3 = 3.15 μm and l4 = 3.40 μm.
4. Conclusions
In conclusion, dynamically and independently tunable absorbers based multilayer metal-graphene metamaterials are numerically investigated at mid-infrared frequencies. The proposed absorber is designed by the combination of different orders of resonances. Apart from adding the gold strips in each unit cell, the number of the absorption peaks can also be increased by stacking multiple metal-graphene layers. Further investigations demonstrate that the resonances of the single-layer absorber are insensitive to the incident angle. For the multiple metal-graphene layer structure, the location of the absorption bands can be tuned independently by adjusting the Fermi energy level of the graphene in each layer. The bandwidth of the broadband absorbers exceeding 80% absorption is up to 7.5 THz with the average peak absorption of 88.5%. For a triple-layered structure, the average peak absorption is 84.7% from 27.5 THz to 38.4 THz with a minimum of 60%, and the absorber with dual wideband is achieved by designing two quite different sets of gold strips length in top and bottom layer. Benefitting from these attractive properties, the proposed absorber may have potential applications in tunable filtering, sensing, cloaking objects and other multispectral devices.
Funding
National Key Research and Development Program of China (2018YFF01013001, 2017YFA0701000), and the National Natural Science Foundation of China (61701084, 61505022).
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