Investigation of graphene assisted tunable terahertz metamaterials absorber

Xiaoyong He; Xu Zhong; Fangting Lin; Wangzhou Shi

doi:10.1364/OME.6.000331

1. Introduction

With the rapid development of sources [1,2] and waveguides devices, terahertz (THz) technology has made great progress in recent years [3–6], showing potential prospects in many scientific research and practical application aspects [7, 8]. To the further development of THz waves, there is a high demand for the investigation of THz detectors and absorbers [9], especially in the application fields of compact THz image system, thermal sensors, and short-range wireless communication [10, 11]. Lack of naturally occurring materials with strong THz frequency selective absorption coefficients and difficult to fabricate device compatible with standard micro-fabrication, the detection and manipulation of THz waves is still a challenging work [12]. Presently, THz detection devices include bolometers, quantum-well infrared photo- detectors [13] and meta-materials (MMs) absorbers. Since firstly proposed by Landy et al. in 2008, the perfect MMs absorbers have attracted a great deal of interest and extensive attentions [14–17]. Integrated with suitable sources and bolometric sensors [18], the MMs absorbers (MMA) significantly facilitate the development of THz detectors and imaging systems operating at room temperature [19, 20]. Consisted of a tri-layer system with a top subwavelength structure patterns layer and a bottom metal layer separated by a continuous dielectric layer, the ideal MMA is characterized by the complete suppression of the transmission and reflection, i.e. complete dissipation [21].

As a two-dimensional (2D) material with the honeycomb lattice structure [22–24], graphene, has attracted considerable attention from both fundamental physics and enormous applications [25–28]. Besides the conventional plasmonic materials (metal or doped semiconductors), graphene is also a good candidate to explore the surface plasmons (SPs) devices [29–32]. The semiconducting graphene has also been experimentally achieved with a large band gap of more than 0.5 eV, which will boost the development of tunable graphene electronic devices [33]. Furthermore, because of the low carrier density of states near the Dirac point, the Fermi level of graphene layer can be tuned with small bias gate voltage. With the merits of broad spectral bandwidth and ultrafast response time, the graphene structure absorbers have received considerable attention. For example, the graphene Salisbury screen absorber was suggested, which consisted of the monolayer graphene and a metallic ground plane separated by a dielectric spacer layer with the thickness of quarter-wavelength [34]. With the graphene micro-ribbons patterns on the thick dielectric layers situated on the top of reflecting metal substrate, Alaee et al. theoretically studied the perfect MMs absorption phenomenon on the grounded of the Fabry-Perot model [35]. By replacing the metallic substrate with the semiconductor films, the tunable THz MMA has been investigated, which manifest that the absorption of the electric resonance decreases 23% and the dipole resonance increases more than 60% when the substrate conductivity changes in the range of 3.0 × 10⁵ S/m to 1.0 × 10⁷ S/m [36].

Absorbers, is urgently requirement to satisfy the development of THz noninvasive medical imaging, detectors, spectroscopic identification of hazardous materials and so on [37]. But for current THz detectors, there still exist many problems, such as narrow-band [38], low sensitivity, and the requirement of cryogenic temperature, which restricts its potential practical applications. It is also difficult to modulate the resonant peak with the fixed structure parameters. Though some multiband or broadband MMs structures have been proposed (e.g. anisotropic MMs structure [39]), but it depends on the multilayer structures and difficult to align in the fabrication. High efficient, tunable, multi-frequency or broadband agile MMA with simple structure and strong absorption are critically required to the development of the THz detection [11], especially in the design of hyper-spectral focal plane array imager. By using the graphene-SiO₂-Si-dielectrics-metal (GSiO₂SiDM) structures, we realize the tunable control of the absorption and reflection of the incident THz waves. Compared with presented MMA, the GSiO₂SiDM structure also manifests much better biocompatible properties, especially in the fields of label-free detection and good performance of biosensors. Therefore, the tunable absorption property of GSiO₂SiDM structure has been explored in the THz regime. The results manifest that the suggested graphene MMs absorber structure are compact, broadband, and flexible.

2. Theoretic model and research method

Figure 1(a) shows the sketch of side view of tunable GSiO₂SiDM structure. The thickness of the SiO₂ layer is 30 nm. The dielectric material is made from the polyimide layer with the thickness of 7.5 μm. The ground plane is Cu layer with the thickness of 0.2 μm. Figures 1(b)-1(d) show the top views of MMs unit cell structures, the circular (Fig. 1(b)), the rectangular (Fig. 1(c)), and the cross-shaped unit cell structure (Fig. 1(d)). The period lengths along x and y directions are d_x and d_y, respectively. The MMs structures are made of monolayer graphene with the thickness of 0.34 nm. The incident waves are normally transmitted through the GSiO₂SiDM structure along z direction.

Fig. 1 (a) The side view of the graphene MMs structure, the graphene patterns is deposited on the SiO₂/Si layers. 1(b)-1(d) The top views of geometry and dimensions of the several kinds of metamaterials unit cell structures. 1(b) the circular structure, D = 24 μm; 1(c) the rectangular structure, w = h = 24 μm; 1(d) the cross-shaped structure, w = 12 μm, h = 24 μm. The periodic length along x and y directions are both 32 μm.

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Graphene can be considered as a 2D material and described by a surface conductivity σ_g, which is related to the radiation frequency ω, chemical potential (μ_c, Fermi level E_f), the environmental temperature T, and the relaxation time τ. The conductivity of the monolayer graphene can be calculated by using the Kubo formula [40]:

\begin{array}{l} σ (ω, μ_{c}, τ, T) = σ_{inter} + σ_{intra} = \frac{j e^{2} (ω - j τ^{- 1})}{π ℏ^{2}} \times \\ \begin{matrix}  \end{matrix} [\frac{1}{{(ω - j τ^{- 1})}^{2}} \int_{0}^{\infty} \frac{\partial f_{d} (ε)}{\partial ε} - \frac{\partial f_{d} (- ε)}{\partial ε} d ε - \int_{0}^{\infty} \frac{f_{d} (- ε) - f_{d} (ε)}{{(ω - j τ^{- 1})}^{2} - 4 {(ε / ℏ)}^{2}} d ε] \end{array}

where f_d(ε) is the Fermi-Dirac distribution, j is the imaginary unit, ε is the energy of the incident wave, k_B is the Boltzmann’s constant, and ℏ is the reduced Planck’s constant. The first part of the above equation is the intra-band contribution, and the second part is for the inter-band contribution.

Rigorously, the dielectric constants of graphene are anisotropic, including the out-of-plane and in-plane parts. The out-of-plane dielectric constant is about 2.5 [41], and the in-plane dielectric constant can be written as:

ε_{g} = 1 + j \frac{σ_{g}}{ω ε_{0} Δ}

in which Δ is the graphene layer thickness, ɛ₀ is the permittivity of free space. The in-plane dielectric constant of graphene is much larger than of out-of-plane parts, which means that for the graphene dielectric constant the in-plane contribution dominates. Furthermore, since the wide graphene ribbon is adopted, the effects of spatial dispersion at low frequency can be omitted [42]. Therefore, the graphene can be assumed to be isotropic on condition that without magnetic fields. The Fermi level can be determined by the carrier concentration:

n_{d} = \frac{1}{π ℏ^{2} v_{F}^{2}} \int f_{d} (ε) - f_{d} (ε + 2 E_{f}) ε d ε

where v_F≈1 × 10⁶ m/s is the Fermi velocity.

3. Results and discussion

Figure 2 shows the absorptive and reflective spectral curves of the incident THz waves passing the GSiO₂SiDM structure. The circular unit cell structure is adopted. Periodic graphene patterns can help increase the coupling of incident field to the sub-wavelength MMs absorbers structures, enhancing the overall absorption. The radius of circular structure is 24 μm. The sketch of the graphene rectangular unit cell is shown in Fig. 2(b). The polarization of incident light is along y direction. Each piece of the MMs arranges in a square lattice, its periodic lengths along x and y direction (p_x and p_y) are both 32 μm. The simulation results have been obtained from the well-established CST Microwave Studio. The frequency domain solver is adopted with the unit-cell boundary conditions in the x-y plane and Floquet ports in the z direction to be terminated. By using the S-parameters from the simulation, the transmission (T(ω)) and reflection (R(ω)) of the GSiO₂SiDM structure can be calculated by the formula, i.e. T(ω) = |S₂₁|², R(ω) = |S₁₁|². Because the metallic ground plane, 0.2 μm, is much larger than the skin depth of the metal, the transmission is zero. Therefore, the absorption of GSiO₂SiDM structure is calculated as A(ω) = 1.0-R(ω). The simulation data has been acquired by using a workstation with 10 64-bit processors and 64 GB of RAM (Dell Precision T7910 5U).

Fig. 2 2(a)-2(c) show the absorption, reflection, ε and μ of the MMs structure based on the circular shaped unit cell. The Fermi levels of the graphene layer are 0.1 eV, 0.2 eV, 0.3 eV, 0.5 eV, 0.8 eV and 1.0 eV, respectively.

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Similar to the metallic patterns of MMA, the absorption (reflection) spectral curves of GSiO₂SiDM structure show obvious peaks (dips) versus frequency. The influence of Fermi level of graphene layer on the absorption spectrum can be found from Fig. 2(a). As the Fermi level increases, the absorption resonant peak shifts to higher frequency, i.e. blue shift. The reasons are shown in the following. The resonant frequency of MMA structure can be roughly described as ω = 1.0/(LC)^1/2. The total inductance includes the usual inductance to support current L_g and the kinetic inductance L_k. The kinetic inductance can be estimated as: L_k = α(m_e/(N_de²)), in which α depends on the structure parameters of unit cell, m_e is the electron mass, e is the electron charge, N_d is the carrier concentration [19]. Because the carrier density in graphene layer increases with its Fermi level, the value of kinetic inductance decreases, leading to the total inductance decreasing and resonant frequency increasing. Next, we discuss the influence of chemical potential on the absorption amplitude. As the increase of Fermi level, the MMA impedance approaches the value of free space wave, resulting into the absorption peak increasing. If the Fermi level is about 0.5 eV, the impedance of MMs absorbers structure matches well the value of the free space, the net absorption is achieved, and the bandwidth also become sharper. If E_f increases further, the value of graphene conductivity increases further and departs from the optimum sheet impedance, the value of absorption peak decreases. The reflection response curve vs. frequency of the GSiO₂SiDM structure can be found in Fig. 2(b). If the Fermi level of the graphene layer is low, e.g. 0.1 eV, the reflection is high. As the Fermi level increases, the value of reflection decreases, leading to the absorption increasing. Compared with the metallic MMA, the absorption and reflection spectral curves of the GSiO₂SiDM structure can be modulated in a broad range. For instance, if the Fermi level changes in the scope of 0.1-1.0 eV, the peak value of the absorbance can be modulated in the scope of 0.34-0.99, the modulation depth of A_mod is 60.6% (A_mod = (A_max-A_min)/A_max); the peak position can be modulated in the range of 1.20-1.84 THz, and the modulation depth of frequency f_mod (f_mod = (f_max-f_min)/f_max) is 34.8%. This is very important to the applications of THz absorbers. For instance, by changing the bias of applied gate voltage, the GSiO₂SiDM structure may permit “multi-color” imaging (in the range of 1.20-1.84 THz for our case) in a much more conveniently means, which is different from the metallic MMA depended on the various unit cells with distinct resonance frequencies [15]. The absorption bandwidth (which can be estimated by using the full width at half maximum, FWHM) is 0.64 THz (1.46-2.10 THz) near the resonant frequency of 1.70 THz, i.e. 37.65% of the center frequency. This is much larger than that of the metallic MMA structures, usually is no more than 20%. The resonant transmission spectrum of the GSiO₂SiDM structure is broad, which means that the suggested graphene MMA structure are very suitable for fabricating broadband absorber and would be good for applications to military radar devices.

In addition, Fig. 2(c) shows the value of ɛ and μ versus frequency at different Fermi levels. As the operation frequency increases, the value of ε shows a peak and μ displays a dip. By adjusting the structure parameters and Fermi level, the impedance of the suggested MMA approximately match with that of free space (Z = Z₀), so the reflection reaches the minimum value at specific frequency. As shown in Fig. 2(c), the difference between ɛ and μ decreases with the increase of Fermi level, leading to the value of impedance Z (μ/ε) decreasing. If the Fermi level is 0.5 eV, the difference between ε and μ is smallest, i.e. the real part of electric permittivity is roughly equal to the real part of the magnetic permeability. Thus, the impedance of MMA is close to the vacuum value, which means that the perfect impedance matching condition can be realized with the evident resonance coupling, the incident electromagnetic wave energy is not reflected. Consequently, the GSiO₂SiDM structure absorption reaches the net absorption, which can be found in Fig. 2(a) and 2(b). But If the Fermi level increases further, the difference between ɛ and μ increases, the impedance of the MM absorber is mismatched, resulting in the increasing R(ω) and decreasing T(ω), as shown in Fig. 2(b) and Fig. 2(c).

The surface current can be used to display the resonant characteristics of MMAs. The properties of current density and electric fields of the GSiO₂SiDM structures are well illustrated in Fig. 3. The surface current density, the x (E_x) and y (E_y) components of the electric fields can be found in Figs. 3(a)-3(c), respectively. The polarized direction is along y-direction. The 2D images (x-y plane) of the simulated spatial field distribution have symmetrical patterns. Red indicates high intensity and blue indicates low intensity. The simulation result is plotted at the resonant frequency of 1.70 THz, in according with the resonant peaks shown in Fig. 2(b). The surface current density can be used to display the resonating behavior of MMs absorbers. Figure 3(a) shows the direction and relative value of the surface current density, the surface current mainly concentrated in the unit cell region of graphene MMs structure, which means that the strong resonant coupling caused by graphene patterns. In addition, the local electric field amplitude of E_x and E_y can also be found in the color map in Fig. 3(b) and 3(c), respectively.

Fig. 3 3(a)-3(c) show the surface current density, E_x and E_y of the graphene MMs structures based on the circular-shaped unit cell. The polarization direction of the incident light is along y direction. The resonant frequency is 1.70 THz. The Fermi level of the graphene layer is 0.5 eV.

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Figure 4 shows the propagation properties of incident light through the GSiO₂SiDM structure based on the rectangular unit cell. The length and width of the rectangular structure are both 24 μm. The influence of Fermi level of the graphene layer on the absorbance can be found from Fig. 4(a). As the Fermi level of the graphene layer increases, the absorption peak shifts to higher frequency. If the Fermi level changes in the range of 0.1-1.0 eV, the peak value can be changed in the range of 0.32-0.99, the modulation depth of A_mod is 67.6%, the peak position can be tuned in the range of 1.05-1.58, the modulation depth of frequency f_mod is 33.5%. In addition, the influence of unit cell geometrical structure on the resonant properties is also obvious. For example, when the Fermi level of the graphene layer is 0.5 eV, the resonant frequency of the GSiO₂SiDM structure based on the rectangular unit cell (1.47 THz) is smaller than that of the circular unit cell structure (1.70 THz). The possible reasons are given as follows. The resonant frequency of the MMs structure can be written as: f = 1/(2π(LC)^1/2), in which L and C are the inductance and capacitance of the MMs resonators. For the results shown in Fig. 2 and Fig. 4, the area of the unit cell structure based on the rectangular A_R is 24 × 24 μm², while the area of the unit cell structure based on the circular A_C is π × 12 × 12 μm². The equivalent inductances of the unit cell are proportional to the area of the unit cell. Thus, the equivalent inductance of the rectangular unit cell is larger than that of the circular, resulting into the fact that the resonant frequencies of the MMs based on the rectangular unit cell structure shift to low frequency.

Fig. 4 4(a) and 4(b) show the absorption and reflection of the MMs structures based on the rectangular unit cell, the polarization of the incident wave is along y direction. The Fermi levels of the graphene layer are 0.1 eV, 0.2 eV, 0.3 eV, 0.5 eV, 0.8 eV, and 1.0 eV, respectively.

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For the rectangular unit cell MMA structure, the surface current density and electric field along x and y direction (E_x and E_y) can be found in Fig. 5. The according resonant frequency is 1.47 THz, i.e. the resonant peak shown in Fig. 4(a). The direction and size of the arrows in Fig. 5(a) indicate the direction and relative value of the surface current density, and the color map in Figs. 5(b) and 5(c) indicate the relative local electric field amplitude. Compared with the results in Fig. 3, the surface current density, the values of E_x and E_y of rectangular-shaped unit cell structure are smaller than those of the circular structure. The reasons are given in the follows. The active region area of a rectangular unit cell is larger than that of the circular one. Furthermore, for the circle unit cell structure, the length along y direction decreases from the circle center to the edge. This means that if the polarization along y direction is taken into account, the effective area of circle unit cell structure along y direction is still smaller than that of the rectangular structure even if the geometrical areas of them are the same. As the decrease of the active unit cell area, the surface modes can be better confined near the graphene pattern surface. As a result, the values of electric fields for the circular MMs are larger than that of the rectangular structure.

Fig. 5 (a)-5(c) show the surface current density, E_x and E_y of the graphene MMs structures based on the rectangular-shaped unit cell. The polarization direction of the incident light is along y direction. The resonant frequency is 1.47 THz. The Fermi level of the graphene layer is 0.5 eV.

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Figure 6 shows the propagation properties of incident THz light through the cross-shaped GSiO₂SiDM structure. The length and width of the rectangular structure are 24 μm and 12 μm, respectively. It can be found from Fig. 6 that the value of resonant peak for the absorption spectral curves increases and the peak position moves to the larger frequency with the increase of E_f. If the Fermi level of graphene layer is low, the reflection is high. But with the increase of the Fermi level, the reflection decreases and the absorption increases. If the Fermi level changes in the range of 0.1-1.0 eV, the peak value can be changed in the range of 0.25-0.99, the modulation depth of A_mod is 74.8%, the peak position can be tuned in the range of 1.12-1.77, the value of f_mod is 36.7%. It should also be noted that the influence of Fermi level of the graphene layer on the resonant frequency amplitude is larger.

Fig. 6 6(a) and 6(b) show the absorption and reflection curves of the MMs structures based on the cross-shaped unit cell, the polarization of the incident wave is along y direction. The Fermi levels of graphene layer are 0.1 eV, 0.2 eV, 0.3 eV, 0.5 eV, 0.8 eV, and 1.0 eV, respectively.

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For the cross unit cell MMA, the 2D simulation results have been shown in Figs. 7(a)-7(c). The simulation result is plotted at the resonant frequency of 1.62 THz, which corresponds with the resonant peak shown in Fig. 6(a). It should be noted that because the circular unit cell is a much more symmetric structure, the difference between the values of E_x and E_y are smaller than those of the cross-shaped structure. This means that the cross-shaped patterns should be taken when we fabricate the polarization sensitive absorbers in the future.

Fig. 7 7(a)-7(c) show the surface current density, E_x and E_y of the graphene MMs structures based on the cross-shaped unit cell. The polarization direction of the incident light is along y direction. The resonant frequency is 1.62 THz. The Fermi level of the graphene layer is 0.5 eV.

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Table 1 shows the absorption properties of graphene MMA structures, which manifest that the graphene MMs absorber shows well tunable frequency properties, f_mod is more than 30%. The reasons are shown in the following. As the Fermi level increases, its carrier concentration increases, the value of kinetic inductance L_k decreases, causing the total inductance decreases and the resonance frequency moves to larger frequency. For the case of the absorption modulation depth, because in the THz regime the intra-band contribution dominates, the carrier concentration of graphene layer increases significantly with the increase of Fermi level. Consequently, the resonance frequency shifts to high frequency obviously and can be modulated in a wide range with the increase of Fermi level. The value of absorption modulation depth can reach more than 60%, as shown in Tab. 1. For the several kinds of unit cell structure, their frequency modulation depth is almost same, while the absorption modulation depth of cross-shaped unit cell is largest. The reasons are shown in the following. For the incident THz waves, at the resonant frequency it is absorbed by the graphene patterns. The absorption is closely related to the unit cell area. The smaller area of the cross-shaped structure results into the weaker absorption (0.25). Thus, because of the same maximum values of absorption, amplitude modulation depth of the cross-shaped unit cell is largest, as shown in Tab. 1. In addition, the influences of the graphene pattern structure on the frequency and amplitude modulation is not very obvious. Thus, from the fabrication viewpoint, we can choose simple unit cell structure.

Table 1. The comparison of absorptive properties of several kinds of different unit cell structure

View Table

4. Conclusions

Based on the graphene/SiO₂/Si/dielectrics/metallic structure layers, the absorption and reflection properties have been investigated in the THz region, taking into account the effects of the Fermi level of graphene layer, different kinds of unit cell patterns and operation frequencies. The results indicate that the GSiO₂SiDM structure absorber is an excellent electromagnetic wave collector. Similar to the metallic cousin, the graphene MMA structure can also realize net absorption by choosing suitable Fermi level of the graphene layer and structure parameters. By varying the Fermi level of graphene layer, the absorption and reflection can be modulated in a wide range, the modulation depth of absorption amplitude can reach more than 60%. As the Fermi level increases, the resonant peak (dip) of the absorption (reflection) curve manifest evident blue shift phenomenon. The absorption curve of the GSiO₂SiDM structure is broad, which can be used to fabricate wideband absorber. The results are very useful to design novel waveguides devices, such as tunable bolometers, hyper-spectral focal plane array imager, thermal detectors, and understand the mechanisms of the graphene plasmonic structures.

Acknowledgments

This work is supported by the Funding of Shanghai Pujiang program under the Grant no.15PJ1406500, the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China, the Research Funding of Shanghai Normal University under the Grant no. SK201529, the Initial Funding of Scientific Rsearch for the Introduction of Talents of Shanghai Normal University, the Innovation Program of Shanghai Municipal Education Commission under the Grant no. 13YZ064, and the National Natural Science Foundation of China under the Grant no. 11004134.

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Investigation of graphene assisted tunable terahertz metamaterials absorber

Abstract

1. Introduction

2. Theoretic model and research method

3. Results and discussion

4. Conclusions

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (3)

Optical Materials Express

Unit cell structure	f_min-f_max (THz)	Δf /f_max (%)	A_min-A_max	ΔA/A_max (%)
Circular	1.20-1.84	34.8	0.34-0.99	60.6
Rectangular	1.05-1.58	33.5	0.32-0.99	67.6
Cross	1.12-1.77	36.7	0.25-0.99	74.8