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A tunable ultra-broadband terahertz absorber based on two layers of graphene ribbons
Optics and Laser Technology 122 (2020) 105853
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A tunable ultra-broadband terahertz absorber based on two layers of graphene ribbons Omid Mohsen Daraeia, Kiyanoush Goudarzib, Mohammad Bemania, a b
T
⁎
Department of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran Quantum Photonics Research Lab (QPRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
H I GH L IG H T S
of the ultra-broadband Terahertz absorber is based on Circuit Model. • Design absorber is based on Periodic Arrays of Graphene Ribbons. • This bandwidth of the absorber can be adjusted by the chemical potential. • The • Two various dielectrics have been used in the configuration of the device.
A R T I C LE I N FO
A B S T R A C T
Keywords: Graphene ribbons Terahertz Ultra-broadband absorption Absorber Transmission line model
In this paper, a novel configuration of a tunable ultra-broadband terahertz (THz) absorber based on two layers of graphene ribbons and two different kinds of substrate materials has been proposed. The recently suggested equivalent circuit theory of Periodic Arrays of Graphene Ribbons (PAGRs) with a developed transmission line model is utilized to design the structure of the THz absorber. Also, an equivalent series RLC branch is considered for each layer of PAGRs. By adopting the impedance matching approach, the real part of the input impedance of the proposed structure is tuned to be approximately matched to the free-space impedance in a wideband THz region. Then, the imaginary part of the input impedance is adjusted to near zero around the central frequency for increasing the proposed absorber's bandwidth. As a result, the normalized bandwidth of 70% absorption has reached up to 118% with only just two layers of graphene ribbons. Based on the purpose of this paper, the bandwidth of the proposed absorber has been controlled by the chemical potentials of the graphene ribbons.
1. Introduction Graphene is thin and two-dimensional (2D) layer of carbon atoms in a hexagonal lattice configuration. This material has attracted most of the researchers’ attention due to its capability and features in optical and electrical fields, such as high and tunable conductivity by the chemical potential [1–4], manageable plasmonic features [5], small thicknesses [6], the high-speed operation [7] and low losses [8], are some of the incomparable optical and electrical features of graphene. Due to the supporting of Surface Plasmon Polaritons (SPPs) in the THz regime, graphene is the most suitable material for designing THz absorbers [9,10]. In last decades, different structures of THz absorbers with various geometries of graphene have been designed, such as square patch [11], disks and ribbons [9], stacks [12], cross-shaped arrays [13] configurations. The THz absorber based on PAGRs with the normalized bandwidth of 114% to the central frequency has been ⁎
achieved in [14]. Its bandwidth of 70% absorption has not been indicated with different chemical potentials, the height of that proposed absorber has increased, and using three layers of graphene ribbons in that THz absorber has caused its fabrication more sophisticated. The normalized bandwidth of 70% absorption in the other studies has reached to less than 102%, while their central frequencies have been lower than 2.8 THz [15–17]. In this work, we have designed a novel tunable ultra-broadband THz absorber by two-layered PAGRs, which 5.8 THz is achieved for the bandwidth of 70% absorption, and the normalized bandwidth reaches up to 118%. The absorption coefficient for the proposed device can be tuned over a wide range by the chemical potential (applying electrical potential). For reducing the reflection coefficient of the device, the quarter wavelength transformer is utilized for the first layer of the PAGRs, which is placed a quarter of the wavelength of the incident THz wave. Also, for eliminating the reflection coefficient, the impedance of
Corresponding author. E-mail address: [email protected] (M. Bemani).
https://doi.org/10.1016/j.optlastec.2019.105853 Received 22 January 2019; Received in revised form 6 August 2019; Accepted 15 September 2019 Available online 26 September 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 122 (2020) 105853
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Fig. 1. (a) The side view of the proposed THz absorber based on two different substrates and two layers of graphene ribbons, also the unit cell shown in the center of the absorber, and (b) the overall view of the device with unit cell boundary conditions.
(L≫W). This device is made of two layers of PAGRs and two substrates with various materials. The first layer of the graphene ribbons and the gold sheet are separated by polyimide which has the refractive index (ns1 = 1.87). The second substrate is composed of a dielectric material with refractive index (ns2 = 1. 51) and it is located between two PAGRs. The second substrate can be chosen by a glassy material. The structure of this device can operate like as an unsymmetrical Fabry-Perot resonator, in which the gold sheet acts as a short circuit that can reflect the incident THz wave completely, on the other side, the graphene layers can partially reflect the THz wave. Moreover, the periods of the first and second layers of the graphene ribbons are illustrated by P1 and P2 respectively, and the widths of ribbons in the first and second layer are indicated by W1 and W2 respectively. Furthermore, Fig. 2(a) and (b) demonstrate the first and second layer of the graphene ribbons which their electrical conductivities and chemical potentials have been adjusted by external voltages. The graphene bridge is used for applying the external voltage to each graphene ribbon. The Chemical Vapor Deposition (CVD) method is one of the beneficial methods for fabricating this multi-layer structure [18]. For having maximum absorption and minimum reflection around
the designed device is adjusted to be approximately matched to the free-space impedance. In this paper, the circuit theory is used for designing the PAGRs to compare simulation results with the Circuit Model (CM) [1,19]. The device operates like as an unsymmetrical Fabry-Perot resonator, in which the incident THz wave can be trapped between two layers of the PAGRs and a reflecting surface [9]. The device has been simulated by the microwave CST studio, and the CM has also been simulated by MATLAB codes. The paper has been written in four sections. The second section describes the theoretical methods, then the third section is about simulation results and discussions, and the final section concludes the paper. 2. Theoretical methods The side view of the proposed unit cell structure is demonstrated in Fig. 1. The boundary conditions of the unit cell structure in x,y, and z directions are unit cell, unit cell, and open boundaries. So according to Fig. 1(b), with considering the unit cell’s boundary conditions, which the unit cell repeats along the x and y directions, thus, it is obvious that the length of the ribbons has been longer than the wide of the ribbons 2
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Fig. 2. The top view of (a) the second layer of PAGRs and (b) the first layer of PAGRs.
Electronic band structure of PAGRs can be calculated from the Schrodinger equation as follow [22,23]:
the central frequency, the impedance matching theory based on the quarter wavelength transformer has been used for the first substrate, so the first PAGRs is positioned upon a gold sheet by a λ/4 distance (λ is the wavelength of the incident electromagnetic wave) that has been considered from the circuit theory. The thickness of the first substrate is calculated by H1 = c/4ns1f0 [1,19], where c is the speed of light in the vacuum (or in the free space), ns1 is the refractive index of the first substrate, and f0 is the central THz frequency of the absorber. On the other hand, by the half-wavelength transformer (λ/2), the absorption of the device around the central frequency will diminish, according to Eq. (4). These expressions (λ/4 and λ/2 transformers) can be proofed by this equation. As shown in Fig. 1, the incident THz wave has Transverse Magnetic (TM) polarization with ϴ = 0° degree. CST utilizes the Finite Element Method (FEM) for the numerical simulation. The thickness of the graphene ribbons is considered to tg = 1 nm, which is equivalent to the thickness of ten layers of graphene, and the permittivity of graphene layers are written as follow:
εg = ε 0 +
E±, n, px = ±
(1)
Where ε0 and σg denote permittivity of the free space and the surface electrical conductivity of graphene. The surface electrical conductivity of graphene is presented by the Kubo formula that can be defined by the intraband and interband portions (σg = σintraband + σinterband) [9,20]. Although the conductivity of graphene is defined by these two portions, the interband portion can be underestimated because ħω ≪ 2μc for the THz regime, and the intraband portion can be defined as a dominant portion [21]. It should be noticed here, which μc , ω , and ħ are, correspondingly, the chemical potential (or Fermi Energy level), the angular frequency (its frequency is in the THz regime), and the reduced Planck constant that is defined by ħ = h/2π where h is the Planck constant. So the Kubo formula can be written without the interband portion as follow [1]:
σg =
e 2KT 2Ln [2 cosh(μc /2KT )] + jω)
πħ2 (τ −1
4
+ vF2 py2 , Eg =
h vF W
(3)
Where Eg = 2Δ0, vF, py, h, and W are the electronic bandgap, the Fermi velocity, the momentum of an electron in the y-direction, the Planck constant, and the width of the graphene ribbons. Grating in graphene ribbons makes graphene ribbons behave like a semiconductor, which its electronic bandgap can be tuned by the width of graphene ribbons as depicted in Fig. 3. Because, in the paper, the chemical potential in graphene ribbons has higher values than the electronic bandgap (2Δ0) of it, so the electrical conductivity of graphene is originated from the intraband portion of the surface electrical conductivity of graphene. If we do not apply any chemical potential to the graphene, so the interband conductivity will be more dominant than the intraband conductivity. In the recent works, the impedance of PAGRs has been modeled by a series RLC branch in the circuit theory [1,19,24]. In Fig. 4, the equivalent series RLC branches of PAGRs and the impedance of PAGRs are illustrated. Furthermore, the CM can describe the operation of the THz absorber, and how the incident wave is trapped between the graphene
σg jωtg
Eg2 n2
(2)
Where K, e, T, and τ indicate the Boltzmann constant, the electron charge, the surrounding temperature, and the relaxation time of the graphene’s electron respectively. In this paper, T is considered 300 K that is according to the room temperature, and τ is considered as 0.05 ps.
Fig. 3. The band gap structure of graphene ribbons. 3
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Fig. 4. The modeled RLC branches of PAGRs [1].
Fig. 5. The CM of the THz absorber consisting the impedances of two PAGRs, two substrates, and the gold sheet at the bottom of the proposed absorber considered as a short circuit. Table 1 The calculated eigenvalues for the first mode of the surface current density [1]. W/P
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Q1
0.725
0.710
0.689
0.658
0.620
0.571
0.507
0.420
Table 2 The calculated parameters for the unit cell structure of the proposed ultrabroadband THz absorber.
Proposed THz Absorber
The 1st Layer of the PAGRs
The 2nd Layer of the PAGRs
μc1 = 0.97 eV P1 = 4.39 μm W1 = 3.95 μm H1 = 9.15 μm
μc2 = 0.75 eV P2 = 6.58 μm W2 = 2.36 μm H2 = 9.96 μm
ribbons and the gold sheet. The free space impedance is indicated by Z0, thus, in Fig. 5, the impedances of substrates are indicated by Zs1 and Zs2, and these are calculated by Zs1 = Z0/ns1 and Zs2 = Z0/ns2 respectively, and the impedances of the PAGRs for the first and second layer are illustrated by ZG1 and ZG2 correspondingly. The equations of each equivalent impedance for the CM of this designed absorber are calculated for TM polarization as follow [19]:
Fig. 6. The surface electrical conductivity of graphene with different chemical potentials varying between 0.1 eV and 0.9 eV.
Za = Zs1
4
ZAu + jZs1 . tan(βs1 H1) ZAu ≅ 0 → Za = jZs1 tan(βs1 H1) Zs1 + jZAu . tan(βs1 H1)
(4)
Optics and Laser Technology 122 (2020) 105853
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Fig. 7. (a) The absorption and (b) return loss coefficient spectra with various chemical potentials for the first layer of the PAGRs and μc2 = 0.22 eV.
Z .Z ZL1 = ZG1 ‖Za = G1 a ZG1 + Za
Fig. 8. (a) The absorption and (b) return loss coefficient spectra with various chemical potentials for the second layer of PAGRs and μc1 = 0.97 eV.
(5)
Sn ≅
ZL1 + jZS 2. tan(βs2 H2) Zb = Zs2 ZS 2 + jZL1. tan(βs2 H2)
(6)
Z .Z ZL2 = ZG2 ‖Zb = G2 b ZG2 + Zb
(7)
Zinput = ZL2
(8)
L gn =
C gn =
P π ħ2 e 2 μc τ
Sn2
P π ħ2 = τ R gn Sn2 e 2 μc
(9)
(10)
Sn2 2 εeff
εeff = ε0
P qn (nm2 1 + nm2 2) 2
(13)
Where nm1 and nm2 are the refractive indexes of materials which are located on both sides of graphene ribbons, εeff is defined as the average permittivity of materials, and Sn can be calculated by the integral of eigenfunctions. Moreover, eigenfunctions have been defined by the manipulation current density on graphene ribbons, likewise, qn is the eigenvalue for the nth mode of the surface current density, and the eigenvalue for the first mode can be considered from Table 1 of [1]. In this paper, we have used the first mode of the surface current density on the PAGRs for calculating the eigenvalue. In Table 1, Q1 is a function of q1, which is considered by Q1 = q1W/π. The circuit model of the absorber has been considered to design and simulation of the proposed Ultra-broadband absorber with 4.51 THz as a central frequency, and μc1 = 0.97 eV and μc2 = 0.22 eV respectively for the chemical potentials of the first and second layer of the PAGRs. In the circuit model, the impedances of the graphene ribbons have been indicated by ZG1 and ZG2, which have been defined by resistances, capacitances, and inductances. But it should be noticed that the resonance can happen when Im(Zin) = 0. Therefore, the resonant angular frequencies have been considered by ωr1 and ωr2, and they can be written as follow [1,19]:
Where H1, H2, βs1 = (2πfns1)/c, and βs2 = (2πfns2)/c have represented the thickness of the first and second substrate and the propagation constants of the incident THz wave in the first and second substrate respectively. Also, the circuit theory can calculate the resistance, capacitance, and inductance of the graphene ribbons when they are used in the nth mode as follows [19]:
R gn =
8 W 9
(11)
ωr1 =
(12) 5
1 Lg1 Cg1
(14)
Optics and Laser Technology 122 (2020) 105853
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Fig. 9. (a) The absorption and (b) return loss coefficient spectrums with μc1 = 0.97 eV and μc2 = 0.22 eV by the FEM simulation and the CM. (c) The absorption and (d) return loss coefficient spectrums with μc1 = 0.97 eV and μc2 = 0.75 eV by the FEM simulation and the CM.
ωr 2 =
1 Lg 2 Cg 2
Table 2. The gold sheet is assumed as a short circuit in the circuit theory, and it can be assumed as a completely reflecting mirror in an unsymmetrical Fabry-Perot resonator. Therefore, the transmission coefficient of the absorber is about T(ωr) ≈ 0, and the absorption coefficient can be written only just by R(ωr) or the reflection coefficient:
(15)
The input impedance of the proposed absorber can be controlled by the thickness of the substrates, and it is perfectly tuned to be closely matched to the free-space impedance [9]. According to the procedure of the design of the THz absorber based on the CM, the quantities of the CM have been calculated according to these quantities: R1 = 220 Ω, L1 = 1.1 × 10−11 H, C1 = 1.22 × 10−16 F, R2 = 2.43 × 10+3 Ω, L2 = 1.21 × 10−10 H, and C2 = 1 × 10−17 F, so according to these quantities, the wides of the graphene ribbons (W) and the ratios between wides of the graphene ribbons and periods of the graphene ribbons (W/P) can be obtained from the following equations [1]:
W 9 π ħ2 = 2 P 8 e μc τ R gn
W=
A = 1 − |R (ωr )|2
As we know, the reflection coefficient (or the return loss coefficient) is calculated as a function of Z0 and Zin, and it is given by [14]:
R (z in , z o) =
z in − z o z in + z o
(19)
Furthermore, we have designed an ultra-broadband THz absorber which its absorption can be adjusted by chemical potential (μc). This operation can realize the tunable ultra-broadband THz absorber with various bandwidths in the THz regime. In Fig. 6, the surface electrical conductivity of graphene in the THz regime with various chemical potentials is illustrated. Since the graphene can support Surface Plasmon Polaritons (SPPs), which its surface electrical conductivity can be controlled by the chemical potential. According to Fig. 6, the electrical conductivity of graphene, which is including Imaginary and Real Parts, can be altered by various chemical potentials from 0.1 eV until 0.9 eV. The electrical conductivity of graphene increases by tuning the chemical potential in this range, also the unit of the electrical conductivity of graphene is considered by Siemens (S). In Fig. 7, the absorption and the return loss coefficient spectrums are plotted with different chemical potentials for the first PAGRs, and
(16)
Q1 e 2 μc 2 ħ2 εeff ωr2
(18)
(17)
3. Simulation results and discussions In this part, the operation of the ultra-broadband THz absorber is demonstrated by designing the CM. In this model, the input impedance of the unit cell structure has been tuned closely to Z0 (the free space impedance) that is equal to 376.8 Ω. The calculated parameters for designing the device have been achieved, and they are demonstrated in 6
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calculated quantities can be obtained, respectively as follow: τV 2
μC1 = μF [19], if we set µ = 0.154 m2/(V.s) [26], τ = 0.05 (ps ) and VF = 1.73 (m/s) [27] thus, the chemical potential can be adjusted on 0.97 eV. For the next step, the chemical potential for the first layer of the graphene ribbons is adjusted on μc1 = 0.97 eV, then the chemical potential for the second layer of the graphene ribbons is manipulated by μc2 that is changeable from 0.22 eV until 0.97 eV, so the absorption and the return loss coefficient spectrums are plotted in Fig. 8. As a result, the bandwidth of the ultra-broadband THz absorber is adjusted by the chemical potentials correspondingly. The best bandwidth of the proposed absorber has been achieved when the quantities of μc1 and μc2 have been adjusted on 0.97 eV and 0.75 eV respectively, which the result with bandwidth (BW) about 5.8 THz has depicted in Fig. 8(a) via blue color. In Fig. 9, the bandwidth of more than 70% absorption are achieved by the Finite Element Method (FEM), which are equal to BW = 5.046 THz and 5.8 THz. Fig. 9 also compares simulation results and the CM for the proposed absorber with μc1 = 0.97 eV, μc2 = 0.22 eV, and μc2 = 0.75 eV. The spectra in Fig. 9 show the good approximation between the theoretical and the simulation method. For achieving the absorption coefficient over 0.7, we should adjust the quantity of the return loss coefficient as follow: |R(ωr )| < 0.54 . In Fig. 9(c), we achieved 5.8 THz for the bandwidth of 70% absorption, and it is 118% of the central frequency in the THz regime, so it can be achieved by the FEM simulation with μc1 = 0.97 eV and μc2 = 0.75 eV. According to Fig. 1, the THz absorber has been designed based on two layers of PAGRs, so it has two resonance frequencies in different ranges of the THz region, and it has ultra-broadband absorption according to Fig. 9. Because of the designing device just in two different resonant frequencies for reaching the ultra-broadband absorption, the absorptions’ spectra in Fig. 9 have a decreasing ripple in approximately 6 THz. For solving this decreasing ripple, the THz absorber can be designed based on more than two layers of PAGRs, and it might have absorption spectra over 70%. On the other hand, with increasing the layers of PAGRs, the structure of the device will become more complicated, and the financial fee for fabricating this device will increase. As a result, the purpose of this paper has been the design of the ultra-broadband THz absorber based on just two layers of PAGRs and with simple structure. According to Fig. 9, by increasing the accuracy of simulation such as increasing mesh cells, the deviation between the FEM and the CM will decrease. Although we have decreased deviation between the FEM and the CM, little deviation has remained between the FEM and the CM,
Fig. 10. The calculated real and imaginary parts of the normalized input impedance by the CM with various chemical potentials (a) μc1 = 0.97 eV and μc2 = 0.22 eV and (b) with μc1 = 0.97 eV and μc2 = 0.75 eV.
the chemical potential for the second PAGRs is μc2 = 0.22 eV. Based on the calculated quantities for the chemical potential of the first layer of PAGRs, the electron mobility of graphene on a substrate, the relaxation time, and the graphene’s Fermi velocity, so these
Fig. 11. The comparative spectra of TM and TE polarizations for (a) absorption and (b) return loss coefficient spectra. 7
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Table 3 The comparison of the proposed THz absorber based on PAGRs with some recent reported THz absorbers based on PAGRs. Ref
Number of Graphene Layers
Central frequency (THz)
Height of the proposed THz absorber (μm)
Bandwidth (THz)
Normalized Bandwidth of 70% absorption (%)
[14] [19] Proposed structure
3 1 2
2.8 2.15 4.94
26.67 25 19.11
3.2 2.1 5.8
114% 102% 118%
Fig. 12. (a) The absorption and (b) return loss coefficient spectrums based on different incident angles.
4. Conclusion
which is due to the difference between the FEM and the CM. The CM is the theoretical method, but 3D-FEM simulation is a numerical method, which considers many parameters, and it is very close to the experimental method. The input impedance of the designed THz absorber is normalized to the free-space impedance (Z0 = 120 π), which is indicated by the real and the imaginary parts in Fig. 10. As depicted in Fig. 9(a) and (c), there is a drop in absorption, which indicated with the red circle around 6 THz. Because maximum absorption can occur based on the impedance matching conditions, which are Im (Zin) = 0 and Re(Zin) = Z0. The origin of the drop in Fig. 9(a) and (c) around 6 THz depends on the impedance mismatching conditions, which is shown in Fig. 10(a) and (b) via the red circle. For the impedance matching conditions, Im (Zin) = 0 and Re(Zin) = Z0, also in Fig. 10(a) and (b) as shown via the red circle around 6 THz, we have a little impedance mismatching, which is the origin of the absorption drop. For achieving the broadband absorption, the imaginary part of the input impedance should be adjusted near zero. Therefore, in Fig. 10, the imaginary part of the normalized input impedance of the proposed THz absorber is near zero around the central frequency. This novel THz absorber can be used in imaging and biosensors [25]. The absorption and return loss coefficient spectra based on TE and TM polarizations have depicted in Fig. 11. According to Fig. 11, the proposed device can absorb TM waves better than TE waves, because the incident wave of the absorber has the magnetic field along the y-direction that has been indicated in Fig. 1. In Table 3, the proposed THz absorber has been compared with the recent designed THz absorbers based on PAGRs. For realizing the absorption of the THz wave in different angles, the absorption and return loss coefficient spectra have been shown by Fig. 12, in which the incident angle has been varied from 0 until 40 degrees.
In this paper, we have presented a novel tunable ultra-broadband THz absorber with two layers of PAGRs and two various substrate materials, in which the bandwidth of the absorption could be tuned by the chemical potentials correspondingly. In the CM, we have assumed the series RLC branch for each layer of PAGRs; furthermore, the thickness of the graphene ribbons has been assumed 1 nm, which is equivalent about the thickness of ten graphene layers. Furthermore, we have proposed the transmission line model for analyzing the structure of the THz absorber. As a result, the normalized bandwidth of 70% absorption of the designed THz absorber has reached up to 118% in the THz regime. The return loss coefficient remained less than 30% in this regime. Therefore, the height of the proposed absorber has decreased, and the normalized bandwidth of 70% absorption has increased. References [1] A. Khavasi, B. Rejaei, Analytical modeling of graphene ribbons as optical circuit elements, IEEE J. Quant. Electron. 50 (6) (2014) 397–403. [2] F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, Y.R. Shen, Gate-variable optical transitions in graphene, Science 320 (5873) (2008) 206–209. [3] A. Andryieuski, A.V. Lavrinenko, Graphene metamaterials based tunable terahertz absorber: effective surface conductivity approach, Opt. Exp. 21 (7) (2013) 9144–9155. [4] S.B. Parizi, B. Rejaei, A. Khavasi, Analytical circuit model for periodic arrays of graphene disks, IEEE J. Quant. Electron. 51 (9) (2015) 1–7. [5] F.H.L. Koppens, D.E. Chang, F.J.G.D. Abajo, Graphene plasmonics: a platform for strong light–matter interactions, Nano Lett. 11 (8) (2011) 3370–3377. [6] F. Bonaccorso, Z. Sun, T. Hasan, A.C. Ferrari, Graphene photonics and optoelectronics, Nat. Photonics 4 (9) (2010) 611. [7] F. Xia, T. Mueller, Y.M. Lin, A.V. Garcia, P. Avouris, Ultrafast graphene photodetector, Nat. Nanotechnol. 4 (12) (2009) 839. [8] J. Guo, L. Wu, X. Dai, Y. Xiang, D. Fan, Absorption enhancement and total absorption in a graphene-waveguide hybrid structure, AIP Adv. 7 (2) (2017) 025101. [9] S. Biabanifard, M. Biabanifard, S. Asgari, S. Asadi, M.C.E. Yagoub, Tunable ultrawideband terahertz absorber based on graphene disks and ribbons, Opt. Commun. 427 (2018) 418–425. [10] A. Tredicucci, M.S. Vitiello, Device concepts for graphene-based terahertz photonics, IEEE J. Sel. Top. Quant. Electron. 20 (1) (2013) 130–138. [11] M. Huang, Y. Cheng, Z. Cheng, H. Chen, X. Mao, R. Gong, Based on graphene
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A tunable ultra-broadband terahertz absorber based on two layers of graphene ribbons Omid Mohsen Daraeia, Kiyanoush Goudarzib, Mohammad Bemania, a b
T
⁎
Department of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran Quantum Photonics Research Lab (QPRL), Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
H I GH L IG H T S
of the ultra-broadband Terahertz absorber is based on Circuit Model. • Design absorber is based on Periodic Arrays of Graphene Ribbons. • This bandwidth of the absorber can be adjusted by the chemical potential. • The • Two various dielectrics have been used in the configuration of the device.
A R T I C LE I N FO
A B S T R A C T
Keywords: Graphene ribbons Terahertz Ultra-broadband absorption Absorber Transmission line model
In this paper, a novel configuration of a tunable ultra-broadband terahertz (THz) absorber based on two layers of graphene ribbons and two different kinds of substrate materials has been proposed. The recently suggested equivalent circuit theory of Periodic Arrays of Graphene Ribbons (PAGRs) with a developed transmission line model is utilized to design the structure of the THz absorber. Also, an equivalent series RLC branch is considered for each layer of PAGRs. By adopting the impedance matching approach, the real part of the input impedance of the proposed structure is tuned to be approximately matched to the free-space impedance in a wideband THz region. Then, the imaginary part of the input impedance is adjusted to near zero around the central frequency for increasing the proposed absorber's bandwidth. As a result, the normalized bandwidth of 70% absorption has reached up to 118% with only just two layers of graphene ribbons. Based on the purpose of this paper, the bandwidth of the proposed absorber has been controlled by the chemical potentials of the graphene ribbons.
1. Introduction Graphene is thin and two-dimensional (2D) layer of carbon atoms in a hexagonal lattice configuration. This material has attracted most of the researchers’ attention due to its capability and features in optical and electrical fields, such as high and tunable conductivity by the chemical potential [1–4], manageable plasmonic features [5], small thicknesses [6], the high-speed operation [7] and low losses [8], are some of the incomparable optical and electrical features of graphene. Due to the supporting of Surface Plasmon Polaritons (SPPs) in the THz regime, graphene is the most suitable material for designing THz absorbers [9,10]. In last decades, different structures of THz absorbers with various geometries of graphene have been designed, such as square patch [11], disks and ribbons [9], stacks [12], cross-shaped arrays [13] configurations. The THz absorber based on PAGRs with the normalized bandwidth of 114% to the central frequency has been ⁎
achieved in [14]. Its bandwidth of 70% absorption has not been indicated with different chemical potentials, the height of that proposed absorber has increased, and using three layers of graphene ribbons in that THz absorber has caused its fabrication more sophisticated. The normalized bandwidth of 70% absorption in the other studies has reached to less than 102%, while their central frequencies have been lower than 2.8 THz [15–17]. In this work, we have designed a novel tunable ultra-broadband THz absorber by two-layered PAGRs, which 5.8 THz is achieved for the bandwidth of 70% absorption, and the normalized bandwidth reaches up to 118%. The absorption coefficient for the proposed device can be tuned over a wide range by the chemical potential (applying electrical potential). For reducing the reflection coefficient of the device, the quarter wavelength transformer is utilized for the first layer of the PAGRs, which is placed a quarter of the wavelength of the incident THz wave. Also, for eliminating the reflection coefficient, the impedance of
Corresponding author. E-mail address: [email protected] (M. Bemani).
https://doi.org/10.1016/j.optlastec.2019.105853 Received 22 January 2019; Received in revised form 6 August 2019; Accepted 15 September 2019 Available online 26 September 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. (a) The side view of the proposed THz absorber based on two different substrates and two layers of graphene ribbons, also the unit cell shown in the center of the absorber, and (b) the overall view of the device with unit cell boundary conditions.
(L≫W). This device is made of two layers of PAGRs and two substrates with various materials. The first layer of the graphene ribbons and the gold sheet are separated by polyimide which has the refractive index (ns1 = 1.87). The second substrate is composed of a dielectric material with refractive index (ns2 = 1. 51) and it is located between two PAGRs. The second substrate can be chosen by a glassy material. The structure of this device can operate like as an unsymmetrical Fabry-Perot resonator, in which the gold sheet acts as a short circuit that can reflect the incident THz wave completely, on the other side, the graphene layers can partially reflect the THz wave. Moreover, the periods of the first and second layers of the graphene ribbons are illustrated by P1 and P2 respectively, and the widths of ribbons in the first and second layer are indicated by W1 and W2 respectively. Furthermore, Fig. 2(a) and (b) demonstrate the first and second layer of the graphene ribbons which their electrical conductivities and chemical potentials have been adjusted by external voltages. The graphene bridge is used for applying the external voltage to each graphene ribbon. The Chemical Vapor Deposition (CVD) method is one of the beneficial methods for fabricating this multi-layer structure [18]. For having maximum absorption and minimum reflection around
the designed device is adjusted to be approximately matched to the free-space impedance. In this paper, the circuit theory is used for designing the PAGRs to compare simulation results with the Circuit Model (CM) [1,19]. The device operates like as an unsymmetrical Fabry-Perot resonator, in which the incident THz wave can be trapped between two layers of the PAGRs and a reflecting surface [9]. The device has been simulated by the microwave CST studio, and the CM has also been simulated by MATLAB codes. The paper has been written in four sections. The second section describes the theoretical methods, then the third section is about simulation results and discussions, and the final section concludes the paper. 2. Theoretical methods The side view of the proposed unit cell structure is demonstrated in Fig. 1. The boundary conditions of the unit cell structure in x,y, and z directions are unit cell, unit cell, and open boundaries. So according to Fig. 1(b), with considering the unit cell’s boundary conditions, which the unit cell repeats along the x and y directions, thus, it is obvious that the length of the ribbons has been longer than the wide of the ribbons 2
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Fig. 2. The top view of (a) the second layer of PAGRs and (b) the first layer of PAGRs.
Electronic band structure of PAGRs can be calculated from the Schrodinger equation as follow [22,23]:
the central frequency, the impedance matching theory based on the quarter wavelength transformer has been used for the first substrate, so the first PAGRs is positioned upon a gold sheet by a λ/4 distance (λ is the wavelength of the incident electromagnetic wave) that has been considered from the circuit theory. The thickness of the first substrate is calculated by H1 = c/4ns1f0 [1,19], where c is the speed of light in the vacuum (or in the free space), ns1 is the refractive index of the first substrate, and f0 is the central THz frequency of the absorber. On the other hand, by the half-wavelength transformer (λ/2), the absorption of the device around the central frequency will diminish, according to Eq. (4). These expressions (λ/4 and λ/2 transformers) can be proofed by this equation. As shown in Fig. 1, the incident THz wave has Transverse Magnetic (TM) polarization with ϴ = 0° degree. CST utilizes the Finite Element Method (FEM) for the numerical simulation. The thickness of the graphene ribbons is considered to tg = 1 nm, which is equivalent to the thickness of ten layers of graphene, and the permittivity of graphene layers are written as follow:
εg = ε 0 +
E±, n, px = ±
(1)
Where ε0 and σg denote permittivity of the free space and the surface electrical conductivity of graphene. The surface electrical conductivity of graphene is presented by the Kubo formula that can be defined by the intraband and interband portions (σg = σintraband + σinterband) [9,20]. Although the conductivity of graphene is defined by these two portions, the interband portion can be underestimated because ħω ≪ 2μc for the THz regime, and the intraband portion can be defined as a dominant portion [21]. It should be noticed here, which μc , ω , and ħ are, correspondingly, the chemical potential (or Fermi Energy level), the angular frequency (its frequency is in the THz regime), and the reduced Planck constant that is defined by ħ = h/2π where h is the Planck constant. So the Kubo formula can be written without the interband portion as follow [1]:
σg =
e 2KT 2Ln [2 cosh(μc /2KT )] + jω)
πħ2 (τ −1
4
+ vF2 py2 , Eg =
h vF W
(3)
Where Eg = 2Δ0, vF, py, h, and W are the electronic bandgap, the Fermi velocity, the momentum of an electron in the y-direction, the Planck constant, and the width of the graphene ribbons. Grating in graphene ribbons makes graphene ribbons behave like a semiconductor, which its electronic bandgap can be tuned by the width of graphene ribbons as depicted in Fig. 3. Because, in the paper, the chemical potential in graphene ribbons has higher values than the electronic bandgap (2Δ0) of it, so the electrical conductivity of graphene is originated from the intraband portion of the surface electrical conductivity of graphene. If we do not apply any chemical potential to the graphene, so the interband conductivity will be more dominant than the intraband conductivity. In the recent works, the impedance of PAGRs has been modeled by a series RLC branch in the circuit theory [1,19,24]. In Fig. 4, the equivalent series RLC branches of PAGRs and the impedance of PAGRs are illustrated. Furthermore, the CM can describe the operation of the THz absorber, and how the incident wave is trapped between the graphene
σg jωtg
Eg2 n2
(2)
Where K, e, T, and τ indicate the Boltzmann constant, the electron charge, the surrounding temperature, and the relaxation time of the graphene’s electron respectively. In this paper, T is considered 300 K that is according to the room temperature, and τ is considered as 0.05 ps.
Fig. 3. The band gap structure of graphene ribbons. 3
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Fig. 4. The modeled RLC branches of PAGRs [1].
Fig. 5. The CM of the THz absorber consisting the impedances of two PAGRs, two substrates, and the gold sheet at the bottom of the proposed absorber considered as a short circuit. Table 1 The calculated eigenvalues for the first mode of the surface current density [1]. W/P
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Q1
0.725
0.710
0.689
0.658
0.620
0.571
0.507
0.420
Table 2 The calculated parameters for the unit cell structure of the proposed ultrabroadband THz absorber.
Proposed THz Absorber
The 1st Layer of the PAGRs
The 2nd Layer of the PAGRs
μc1 = 0.97 eV P1 = 4.39 μm W1 = 3.95 μm H1 = 9.15 μm
μc2 = 0.75 eV P2 = 6.58 μm W2 = 2.36 μm H2 = 9.96 μm
ribbons and the gold sheet. The free space impedance is indicated by Z0, thus, in Fig. 5, the impedances of substrates are indicated by Zs1 and Zs2, and these are calculated by Zs1 = Z0/ns1 and Zs2 = Z0/ns2 respectively, and the impedances of the PAGRs for the first and second layer are illustrated by ZG1 and ZG2 correspondingly. The equations of each equivalent impedance for the CM of this designed absorber are calculated for TM polarization as follow [19]:
Fig. 6. The surface electrical conductivity of graphene with different chemical potentials varying between 0.1 eV and 0.9 eV.
Za = Zs1
4
ZAu + jZs1 . tan(βs1 H1) ZAu ≅ 0 → Za = jZs1 tan(βs1 H1) Zs1 + jZAu . tan(βs1 H1)
(4)
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Fig. 7. (a) The absorption and (b) return loss coefficient spectra with various chemical potentials for the first layer of the PAGRs and μc2 = 0.22 eV.
Z .Z ZL1 = ZG1 ‖Za = G1 a ZG1 + Za
Fig. 8. (a) The absorption and (b) return loss coefficient spectra with various chemical potentials for the second layer of PAGRs and μc1 = 0.97 eV.
(5)
Sn ≅
ZL1 + jZS 2. tan(βs2 H2) Zb = Zs2 ZS 2 + jZL1. tan(βs2 H2)
(6)
Z .Z ZL2 = ZG2 ‖Zb = G2 b ZG2 + Zb
(7)
Zinput = ZL2
(8)
L gn =
C gn =
P π ħ2 e 2 μc τ
Sn2
P π ħ2 = τ R gn Sn2 e 2 μc
(9)
(10)
Sn2 2 εeff
εeff = ε0
P qn (nm2 1 + nm2 2) 2
(13)
Where nm1 and nm2 are the refractive indexes of materials which are located on both sides of graphene ribbons, εeff is defined as the average permittivity of materials, and Sn can be calculated by the integral of eigenfunctions. Moreover, eigenfunctions have been defined by the manipulation current density on graphene ribbons, likewise, qn is the eigenvalue for the nth mode of the surface current density, and the eigenvalue for the first mode can be considered from Table 1 of [1]. In this paper, we have used the first mode of the surface current density on the PAGRs for calculating the eigenvalue. In Table 1, Q1 is a function of q1, which is considered by Q1 = q1W/π. The circuit model of the absorber has been considered to design and simulation of the proposed Ultra-broadband absorber with 4.51 THz as a central frequency, and μc1 = 0.97 eV and μc2 = 0.22 eV respectively for the chemical potentials of the first and second layer of the PAGRs. In the circuit model, the impedances of the graphene ribbons have been indicated by ZG1 and ZG2, which have been defined by resistances, capacitances, and inductances. But it should be noticed that the resonance can happen when Im(Zin) = 0. Therefore, the resonant angular frequencies have been considered by ωr1 and ωr2, and they can be written as follow [1,19]:
Where H1, H2, βs1 = (2πfns1)/c, and βs2 = (2πfns2)/c have represented the thickness of the first and second substrate and the propagation constants of the incident THz wave in the first and second substrate respectively. Also, the circuit theory can calculate the resistance, capacitance, and inductance of the graphene ribbons when they are used in the nth mode as follows [19]:
R gn =
8 W 9
(11)
ωr1 =
(12) 5
1 Lg1 Cg1
(14)
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Fig. 9. (a) The absorption and (b) return loss coefficient spectrums with μc1 = 0.97 eV and μc2 = 0.22 eV by the FEM simulation and the CM. (c) The absorption and (d) return loss coefficient spectrums with μc1 = 0.97 eV and μc2 = 0.75 eV by the FEM simulation and the CM.
ωr 2 =
1 Lg 2 Cg 2
Table 2. The gold sheet is assumed as a short circuit in the circuit theory, and it can be assumed as a completely reflecting mirror in an unsymmetrical Fabry-Perot resonator. Therefore, the transmission coefficient of the absorber is about T(ωr) ≈ 0, and the absorption coefficient can be written only just by R(ωr) or the reflection coefficient:
(15)
The input impedance of the proposed absorber can be controlled by the thickness of the substrates, and it is perfectly tuned to be closely matched to the free-space impedance [9]. According to the procedure of the design of the THz absorber based on the CM, the quantities of the CM have been calculated according to these quantities: R1 = 220 Ω, L1 = 1.1 × 10−11 H, C1 = 1.22 × 10−16 F, R2 = 2.43 × 10+3 Ω, L2 = 1.21 × 10−10 H, and C2 = 1 × 10−17 F, so according to these quantities, the wides of the graphene ribbons (W) and the ratios between wides of the graphene ribbons and periods of the graphene ribbons (W/P) can be obtained from the following equations [1]:
W 9 π ħ2 = 2 P 8 e μc τ R gn
W=
A = 1 − |R (ωr )|2
As we know, the reflection coefficient (or the return loss coefficient) is calculated as a function of Z0 and Zin, and it is given by [14]:
R (z in , z o) =
z in − z o z in + z o
(19)
Furthermore, we have designed an ultra-broadband THz absorber which its absorption can be adjusted by chemical potential (μc). This operation can realize the tunable ultra-broadband THz absorber with various bandwidths in the THz regime. In Fig. 6, the surface electrical conductivity of graphene in the THz regime with various chemical potentials is illustrated. Since the graphene can support Surface Plasmon Polaritons (SPPs), which its surface electrical conductivity can be controlled by the chemical potential. According to Fig. 6, the electrical conductivity of graphene, which is including Imaginary and Real Parts, can be altered by various chemical potentials from 0.1 eV until 0.9 eV. The electrical conductivity of graphene increases by tuning the chemical potential in this range, also the unit of the electrical conductivity of graphene is considered by Siemens (S). In Fig. 7, the absorption and the return loss coefficient spectrums are plotted with different chemical potentials for the first PAGRs, and
(16)
Q1 e 2 μc 2 ħ2 εeff ωr2
(18)
(17)
3. Simulation results and discussions In this part, the operation of the ultra-broadband THz absorber is demonstrated by designing the CM. In this model, the input impedance of the unit cell structure has been tuned closely to Z0 (the free space impedance) that is equal to 376.8 Ω. The calculated parameters for designing the device have been achieved, and they are demonstrated in 6
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calculated quantities can be obtained, respectively as follow: τV 2
μC1 = μF [19], if we set µ = 0.154 m2/(V.s) [26], τ = 0.05 (ps ) and VF = 1.73 (m/s) [27] thus, the chemical potential can be adjusted on 0.97 eV. For the next step, the chemical potential for the first layer of the graphene ribbons is adjusted on μc1 = 0.97 eV, then the chemical potential for the second layer of the graphene ribbons is manipulated by μc2 that is changeable from 0.22 eV until 0.97 eV, so the absorption and the return loss coefficient spectrums are plotted in Fig. 8. As a result, the bandwidth of the ultra-broadband THz absorber is adjusted by the chemical potentials correspondingly. The best bandwidth of the proposed absorber has been achieved when the quantities of μc1 and μc2 have been adjusted on 0.97 eV and 0.75 eV respectively, which the result with bandwidth (BW) about 5.8 THz has depicted in Fig. 8(a) via blue color. In Fig. 9, the bandwidth of more than 70% absorption are achieved by the Finite Element Method (FEM), which are equal to BW = 5.046 THz and 5.8 THz. Fig. 9 also compares simulation results and the CM for the proposed absorber with μc1 = 0.97 eV, μc2 = 0.22 eV, and μc2 = 0.75 eV. The spectra in Fig. 9 show the good approximation between the theoretical and the simulation method. For achieving the absorption coefficient over 0.7, we should adjust the quantity of the return loss coefficient as follow: |R(ωr )| < 0.54 . In Fig. 9(c), we achieved 5.8 THz for the bandwidth of 70% absorption, and it is 118% of the central frequency in the THz regime, so it can be achieved by the FEM simulation with μc1 = 0.97 eV and μc2 = 0.75 eV. According to Fig. 1, the THz absorber has been designed based on two layers of PAGRs, so it has two resonance frequencies in different ranges of the THz region, and it has ultra-broadband absorption according to Fig. 9. Because of the designing device just in two different resonant frequencies for reaching the ultra-broadband absorption, the absorptions’ spectra in Fig. 9 have a decreasing ripple in approximately 6 THz. For solving this decreasing ripple, the THz absorber can be designed based on more than two layers of PAGRs, and it might have absorption spectra over 70%. On the other hand, with increasing the layers of PAGRs, the structure of the device will become more complicated, and the financial fee for fabricating this device will increase. As a result, the purpose of this paper has been the design of the ultra-broadband THz absorber based on just two layers of PAGRs and with simple structure. According to Fig. 9, by increasing the accuracy of simulation such as increasing mesh cells, the deviation between the FEM and the CM will decrease. Although we have decreased deviation between the FEM and the CM, little deviation has remained between the FEM and the CM,
Fig. 10. The calculated real and imaginary parts of the normalized input impedance by the CM with various chemical potentials (a) μc1 = 0.97 eV and μc2 = 0.22 eV and (b) with μc1 = 0.97 eV and μc2 = 0.75 eV.
the chemical potential for the second PAGRs is μc2 = 0.22 eV. Based on the calculated quantities for the chemical potential of the first layer of PAGRs, the electron mobility of graphene on a substrate, the relaxation time, and the graphene’s Fermi velocity, so these
Fig. 11. The comparative spectra of TM and TE polarizations for (a) absorption and (b) return loss coefficient spectra. 7
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Table 3 The comparison of the proposed THz absorber based on PAGRs with some recent reported THz absorbers based on PAGRs. Ref
Number of Graphene Layers
Central frequency (THz)
Height of the proposed THz absorber (μm)
Bandwidth (THz)
Normalized Bandwidth of 70% absorption (%)
[14] [19] Proposed structure
3 1 2
2.8 2.15 4.94
26.67 25 19.11
3.2 2.1 5.8
114% 102% 118%
Fig. 12. (a) The absorption and (b) return loss coefficient spectrums based on different incident angles.
4. Conclusion
which is due to the difference between the FEM and the CM. The CM is the theoretical method, but 3D-FEM simulation is a numerical method, which considers many parameters, and it is very close to the experimental method. The input impedance of the designed THz absorber is normalized to the free-space impedance (Z0 = 120 π), which is indicated by the real and the imaginary parts in Fig. 10. As depicted in Fig. 9(a) and (c), there is a drop in absorption, which indicated with the red circle around 6 THz. Because maximum absorption can occur based on the impedance matching conditions, which are Im (Zin) = 0 and Re(Zin) = Z0. The origin of the drop in Fig. 9(a) and (c) around 6 THz depends on the impedance mismatching conditions, which is shown in Fig. 10(a) and (b) via the red circle. For the impedance matching conditions, Im (Zin) = 0 and Re(Zin) = Z0, also in Fig. 10(a) and (b) as shown via the red circle around 6 THz, we have a little impedance mismatching, which is the origin of the absorption drop. For achieving the broadband absorption, the imaginary part of the input impedance should be adjusted near zero. Therefore, in Fig. 10, the imaginary part of the normalized input impedance of the proposed THz absorber is near zero around the central frequency. This novel THz absorber can be used in imaging and biosensors [25]. The absorption and return loss coefficient spectra based on TE and TM polarizations have depicted in Fig. 11. According to Fig. 11, the proposed device can absorb TM waves better than TE waves, because the incident wave of the absorber has the magnetic field along the y-direction that has been indicated in Fig. 1. In Table 3, the proposed THz absorber has been compared with the recent designed THz absorbers based on PAGRs. For realizing the absorption of the THz wave in different angles, the absorption and return loss coefficient spectra have been shown by Fig. 12, in which the incident angle has been varied from 0 until 40 degrees.
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