Broadband absorber with periodically sinusoidally-patterned graphene layer in terahertz range

We demonstrate that a broadband terahertz absorber with near-unity absorption can be realized using a net-shaped periodically sinusoidally-patterned graphene sheet, placed on a dielectric spacer supported on a metallic reflecting plate. Because of the gradient width modulation of the unit graphene sheet, continuous plasmon resonances can be excited, and therefore broadband terahertz absorption can be achieved. The results show that the absorber’s normalized bandwidth of 90% terahertz absorbance is over 65% under normal incidence for both TE and TM polarizations when the graphene chemical potential is set as 0.7 eV. And the broadband absorption is insensitive to the incident angles and the polarizations. The peak absorbance remains more than 70% over a wide range of the incident angles up to 60° for both polarizations. Furthermore, this absorber also has the advantage of flexible tunability via electrostatic doping of graphene sheet, which peak absorbance can be continuously tuned from 14% to 100% by controlling the chemical potential from 0 eV to 0.8 eV. The design scheme is scalable to develop various graphene-based tunable broadband absorbers at other terahertz, infrared, and visible frequencies, which may have promising applications in sensing, detecting, and optoelectronic devices. © 2017 Optical Society of America OCIS codes: (040.2235) Far infrared or terahertz; (240.6680) Surface plasmons; (310.3915) Metallic, opaque, and absorbing coatings; (130.3120) Integrated optics devices. References and links 1. W. Withayachumnankul and C. Fumeaux, “Terahertz absorption: Photonic crystal traps THz waves,” Nat. Photonics 8(8), 586–587 (2014). 2. C. F. Guo, T. Sun, F. Cao, Q. Liu, and Z. Ren, “Metallic nanostructures for light trapping in energy-harvesting devices,” Light Sci. Appl. 3(4), e161 (2014). 3. F. Alves, D. Grbovic, B. Kearney, N. V. Lavrik, and G. Karunasiri, “Bi-material terahertz sensors using metamaterial structures,” Opt. Express 21(11), 13256–13271 (2013). 4. J. Liu, L. Fan, J. Ku, and L. Mao, “Absorber: a novel terahertz sensor in the application of substance identification,” Opt. Quantum Electron. 48(2), 80 (2016). 5. D. S. Wilbert, M. P. Hokmabadi, J. Martinez, P. Kung, and S. M. Kim, “Terahertz metamaterials perfect absorbers for sensing and imaging,” Proc. SPIE 8585, 85850Y (2013). 6. J. Grant, J. Gough, and D. Cumming, “Terahertz metamaterial absorbers implemented in CMOS technology for imaging applications: scaling to large format focal plane arrays,” IEEE J. Sel. Top. Quantum Electron. 23(4), 4700508 (2017). 7. M. Mittendorff, S. Winnerl, J. Kamann, J. Eroms, D. Weiss, H. Schneider, and M. Helm, “Ultrafast graphenebased broadband THz detector,” Appl. Phys. Lett. 103(2), 021113 (2013). 8. S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012). 9. Z. H. Zhu, C. C. Guo, K. Liu, J. F. Zhang, W. M. Ye, X. D. Yuan, and S. Q. Qin, “Electrically controlling the polarizing direction of a graphene polarizer,” J. Appl. Phys. 116(10), 104304 (2014). 10. Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012). Vol. 25, No. 10 | 15 May 2017 | OPTICS EXPRESS 11223 #290843 https://doi.org/10.1364/OE.25.011223 Journal © 2017 Received 16 Mar 2017; revised 28 Apr 2017; accepted 28 Apr 2017; published 4 May 2017 11. J. Zhang, Z. Zhu, W. Liu, X. Yuan, and S. Qin, “Towards photodetection with high efficiency and tunable spectral selectivity: graphene plasmonics for light trapping and absorption engineering,” Nanoscale 7(32), 13530–13536 (2015). 12. T. Zhang, L. Chen, and X. Li, “Graphene-based tunable broadband hyperlens for far-field subdiffraction imaging at mid-infrared frequencies,” Opt. Express 21(18), 20888–20899 (2013). 13. C. T. Phare, Y. H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015). 14. W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014). 15. X. M. Liu, H. R. Yang, Y. D. Cui, G. W. Chen, Y. Yang, X. Q. Wu, X. K. Yao, D. D. Han, X. X. Han, C. Zeng, J. Guo, W. L. Li, G. Cheng, and L. M. Tong, “Graphene-clad microfibre saturable absorber for ultrafast fibre lasers,” Sci. Rep. 6(1), 26024 (2016). 16. G. Yao, F. Ling, J. Yue, C. Luo, J. Ji, and J. Yao, “Dual-band tunable perfect metamaterial absorber in the THz range,” Opt. Express 24(2), 1518–1527 (2016). 17. Q. Zhang, Q. Ma, S. Yan, F. Wu, X. He, and J. Jiang, “Tunable terahertz absorption in graphene-based metamaterial,” Opt. Commun. 353, 70–75 (2015). 18. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008). 19. R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012). 20. C. Pai-Yen and A. Alu, “Terahertz metamaterial devices based on graphene nanostructures,” IEEE Trans. THz Sci. Technol. 3(6), 748–756 (2013). 21. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012). 22. S. Ke, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Plasmonic absorption enhancement in periodic crossshaped graphene arrays,” Opt. Express 23(7), 8888–8900 (2015). 23. Y. Zhang, Y. Feng, B. Zhu, J. Zhao, and T. Jiang, “Graphene based tunable metamaterial absorber and polarization modulation in terahertz frequency,” Opt. Express 22(19), 22743–22752 (2014). 24. S. Yi, M. Zhou, X. Shi, Q. Gan, J. Zi, and Z. Yu, “A multiple-resonator approach for broadband light absorption in a single layer of nanostructured graphene,” Opt. Express 23(8), 10081–10090 (2015). 25. X. Shi, L. Ge, X. Wen, D. Han, and Y. Yang, “Broadband light absorption in graphene ribbons by canceling strong coupling at subwavelength scale,” Opt. Express 24(23), 26357–26362 (2016). 26. M. Amin, M. Farhat, and H. Bağcı, “An ultra-broadband multilayered graphene absorber,” Opt. Express 21(24), 29938–29948 (2013). 27. S. He and T. Chen, “Broadband THz absorbers with graphene-based anisotropic metamaterial films,” IEEE Trans. THz Sci. Technol. 3(6), 757–763 (2013). 28. Z. H. Zhu, C. C. Guo, J. F. Zhang, K. Liu, X. D. Yuan, and S. Q. Qin, “Broadband single-layered graphene absorber using periodic arrays of graphene ribbons with gradient width,” Appl. Phys. Express 8(1), 015102 (2014). 29. R. Ning, S. Liu, H. Zhang, B. Bian, and X. Kong, “A wide-angle broadband absorber in graphene-based hyperbolic metamaterials,” Eur. Phys. J. Appl. Phys. 68(2), 20401 (2014). 30. K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, and B. H. Hong, “Large-scale pattern growth of graphene films for stretchable transparent electrodes,” Nature 457(7230), 706– 710 (2009). 31. S. Lee, G. Jo, S. J. Kang, G. Wang, M. Choe, W. Park, D. Y. Kim, Y. H. Kahng, and T. Lee, “Enhanced charge injection in pentacene field-effect transistors with graphene electrodes,” Adv. Mater. 23(1), 100–105 (2011). 32. G. Jo, M. Choe, C. Y. Cho, J. H. Kim, W. Park, S. Lee, W. K. Hong, T. W. Kim, S. J. Park, B. H. Hong, Y. H. Kahng, and T. Lee, “Large-scale patterned multi-layer graphene films as transparent conducting electrodes for GaN light-emitting diodes,” Nanotechnology 21(17), 175201 (2010). 33. L. Wang, J. Zhang, N. Liu, Y. Wang, P. A. Hu, and Z. Wang, “Fast patterned graphene ribbons via soft– lithography,” Procedia CIRP 42, 428–432 (2016). 34. X. Wang and Y. Shi, “CHAPTER 1: Fabrication Techniques of Graphene Nanostructures,” in Nanofabrication and its Application in Renewable Energy, G. Zhang, N. Manjooran (Royal Society of Chemistry, Cambridge, 2014), pp. 1–30. 35. P. D. Cunningham, N. N. Valdes, F. A. Vallejo, L. M. Hayden, B. Polishak, X. H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” J. Appl. Phys. 109(4), 043505 (2011). 36. M. Faraji, M. K. Moravvej-Farshi, and L. Yousefi, “Tunable THz perfect absorber using graphene-based metamaterials,” Opt. Commun. 355, 352–355 (2015). 37. J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Graphene-based plasmonic switches at near infrared frequencies,” Opt. Express 21(13), 15490–15504 (2013). 38. J. S. Gómez-Díaz, M. Esquius-Morote, and J. Perruisseau-Carrier, “Plane wave excitation-detection of nonresonant plasmons along finite-width graphene strips,” Opt. Express 21(21), 24856–24872 (2013). Vol. 25, No. 10 | 15 May 2017 | OPTICS EXPRESS 11224


Introduction
Broadband terahertz absorbers have recently attracted increasing interests for their promising applications in terahertz trapping [1,2], sensing [3,4], imaging [5,6], and detecting [7].The absorbers can be realized by using various structures like layered Salisbury screen and periodic structures [8].The physical mechanism for achieving high absorption is that the electromagnetic fields need to be strongly confined inside the lossy materials.Graphene, as a material of single-layered carbon atoms arranged in a plane with honeycomb lattice, has excellent mechanical, chemical, and electrically tunable properties, which offer many interesting possibilities for terahertz and optical technologies.Especially, with the ability to support surface plasmons in the terahertz and infrared ranges, graphene has been applied in a wide range of terahertz and optical devices, such as polarizers [9], photodetectors [10,11], hyperlenses [12], modulators [13,14] and absorbers [15][16][17].It is found that a single sheet of undoped graphene is highly transparent with the light absorbance of 2.3% [8,18].To enhance the light confinement and transform this poorly absorbing graphene into a perfect absorber, various graphene absorbers with periodic structures including arrays of disks [8,11], ribbons [19][20][21], cross-shaped structures [22], as well as graphene and metal combined structures [23] have been proposed.However, these absorbers relying on the resonant structures of unit cells are usually very narrowband, which greatly limits their further applications in optoelectronic devices.
To achieve broadband absorption, various structures have been investigated.As one class of the typical structures, multi-resonator graphene structures [24,25] have been proposed to realize broadband absorbers.With small size different multiple resonators within the unit cell, the small frequency different resonances of the absorbers will be merged to form broadband absorption.As another kind of the effective structures, multi-layered graphene absorber structures have been proposed to develop some ultra-broadband graphene absorbers at terahertz frequencies [26,27].Recently, Zhu et al. have demonstrated a broadband terahertz absorber based on single-layered elliptical graphene ribbons with 43.3% normalized bandwidth of 90% absorbance [28].By using the isolated ribbon structure with gradient width, it has obviously broader absorption bandwidth compared with the conventional absorbers with fixed ribbon width.Besides, broadband terahertz absorbers based on the periodic structures with graphene-based hyperbolic metamaterials have also been studied [29].However, most of the above mentioned graphene-based broadband absorbers with multi-resonator, multi-layered, independent ribbon and hyperbolic metamaterial structures have the drawback of incident angle or polarization dependence [16].Meanwhile, the absorbers with complicated multi-resonator, multi-layered structures not only demand extremely fine device fabrication technique but also result in absorption tuning difficulty via voltage gating structures.Therefore, despite recent progress, novel polarization insensitive and wide-angle broadband absorbers with continuous single-layered graphene still remain to be further investigated.
In this paper, a new net-shaped periodically sinusoidally-patterned single-layered graphene-based absorber is proposed to achieve nearly 100% broadband terahertz absorption.By introducing such a unique gradient width modulation of the unit graphene sheet structure, the continuous plasmon resonances of the absorber can be directly excited and broadband terahertz absorption can be achieved.Under normal incidence in both TE and TM polarizations, over 65% normalized bandwidth of 90% terahertz absorbance can be obtained.As one of the most exciting characteristics, the broadband absorption spectra of this absorber are insensitive to the incident angles and the polarizations.The absorbance remains more than 70% even the incident angles reach 60° for both polarizations.Furthermore, with respect to conventional multi-resonator or multi-layered structures, the continuous net-shaped singlelayered graphene structure can greatly simplify the electrostatic gating structure in achieving flexible tunability.By controlling the chemical potential via electrostatic doping of the graphene sheet, the peak absorbance can be continuously tuned from 14% to 100%.This work offers a new perspective on the design of graphene-based tunable broadband terahertz absorbers.It is remarkable that this absorber design scheme can be easily scaled up to other terahertz, infrared or visible regimes for various promising applications in sensing, detecting, and optoelectronic devices.
The paper is organized as follows.Section 2 describes the design and simulation methods of the proposed absorber.Section 3 discusses the key terahertz absorption characteristics of the absorber including absorption spectra, field distributions, geometrical and electrostatic tunabilities.Finally, conclusions are drawn in Section 4.

Design and simulation methods
The proposed graphene-based broadband terahertz absorber is composed of a net-shaped periodically sinusoidally-patterned graphene sheet on the top, a lossless dielectric spacer in the middle, and a metallic reflecting plate on the bottom, as depicted in Fig. 1.A thin gating layer is placed beneath the graphene sheet to control the graphene conductivity via electrostatic doping of the graphene sheet by applying a DC voltage V g .The unit cell of the absorber is shown in Fig. 1 (b), where p x and p y are the periods in x and y directions, t p , t d and t m are the thickness of the gating layer, dielectric spacer and gold plate, respectively.And the sinusoidally modulated width W(y) in x-direction of graphene is expressed as follow: where W max ( = p x ) is the widest (at y = 0), and W min is the narrowest width (at y = ± p y /2) of the sinusoidally-patterned graphene in x-direction.It is worth mentioning that the periodically sinusoidally-patterned graphene can be produced by large-scale graphene synthesis, transfer and etching techniques, and the optical or electron beam lithography can be used to create sinusoidal patterns on graphene layer [30][31][32][33][34]. Here, we assume the material of the lossless dielectric spacer and the gating layer are polyethylene cyclic olefin copolymer (Topas) with the permittivity of ε rt = 2.35 [35,36] and the polysilicon with the permittivity of ε rp = 3 [37,38], respectively.The metallic plate is formed by gold with the relative permittivity obtained from the Drude model [39].The graphene surface conductivity can be expressed as σ g = σ intra + σ inter (Unit: S) with the intraband and interband contributions from the Kubo formula [40][41][42] below: where  In this configuration, the surface plasmon resonances of the single-layered net-shaped graphene can be excited by incident terahertz wave.A t p = 20 nm-thick polysilicon layer located at t = 20 nm beneath the graphene acts as a voltage gating layer to electrostatic dope the graphene, and the metallic plate acts as a reflecting mirror to suppress the transmission.The full terahertz absorption can be achieved by the destructive interference of the reflected fields from the graphene, the thin polysilicon layer embedded dielectric spacer, and metallic plate by adjusting the thickness t d .Because of the gradient width modulation of the sinusoidally-pattern graphene, continuous plasmon resonances over a wide frequency range can be excited, opening the possibilities to realize broadband terahertz absorption.In this work, we use the Finite Element Method (FEM) to numerically calculate and analyze the properties of the proposed absorber.In the simulations, Floquet ports in z-direction and unit cell boundaries in both x-direction and y-direction are assigned to the unit cell shown in Fig. 1(b).The initial values of the structure parameters are set to be p x = 32 µm, p y = 60 µm, t d = 26 µm, t m = 0.5 µm, W max = 32 µm, and W min = 1 µm.The single layered graphene sheet is modeled as an equivalent 2D surface impedance layer without thickness with Z g = 1/σ g .Here, we assume the initial values of the graphene chemical potential, relaxation time, and temperature to be μ c = 0.7 eV, τ = 0.1 ps, and T = 300 K.The absorbance In addition, due to the narrowest width of the sinusoidally-patterned graphene W min >> 50 nm, thus the curved edge and nanoscale effect of the graphene can be neglected [38,44].To study the absorption properties of the proposed net-shaped periodically sinusoidallypatterned single-layered graphene-based absorber, we simulate the absorption spectra and the field distributions under normal incidence.Figure 2 shows the absorption spectra in TE and TM polarizations under normal incidence when the graphene chemical potential is assumed to be μ c = 0.7 eV.As expected, broadband terahertz absorption is obtained for both polarizations.From the absorption spectra, we observe that the 90% absorbance bandwidth reaches 1.32 THz with a central frequency of 1.93 THz for TE polarization, and the 90% absorbance bandwidth reaches 1.23 THz with a central frequency of 1.78 THz for TM polarization.The normalized bandwidth with respect to the central frequency is greater than 65% for both polarizations.It is found that the absorption curve of TM polarization is close to that of TE polarization but with a small red-shift of 0.15 THz, which mainly results from the different effective resonance lengths in x and y directions and may be eliminated by further optimizing the values of t d , p x and p y .Figure 3 2.The stronger the electric field confinement is, the higher of absorbance becomes.For example, very strong electric field confinement is found at 2.0 THz corresponding to the near-unity absorbance, while the electric fields almost vanished at 3.5 THz corresponding to the absorbance of 3%.Furthermore, it is worth pointing out that most of the electric fields are confined to the curved edge of the sinusoidally-patterned graphene due to the localized surface plasmon resonance of the patterned graphene.

Results and discussion
Specifically, the extremely confined fields of the TE polarization and TM polarization are distributed between two adjacent unit cells in x-direction and y-direction, respectively.The physical origin of this phenomenon is that the electric dipole resonances between two adjacent unit cells in x and y directions are respectively excited by the x-polarized TM and ypolarized TE incident terahertz waves.As discussed above, the continuously localized plasmon resonance of the sinusoidallypatterned graphene plays a significant role in deciding the broadband absorption of the proposed absorber.The absorption bandwidth is mainly related to gradient width modulation and is expected to be weakly dependent on the incident angle θ.To investigate these characteristics, the absorbance as a function of operating frequency and incidence angle for TE polarization and TM polarization are plotted in Figs.4(a) and 4(b), respectively.It is found that the absorber exhibits excellent performances with relatively stable absorbance and bandwidth over a wide range of oblique incidence angles for both polarizations.For TE polarization, the peak absorbance decreases very slightly even if the incident angle exceeds 80°.However, the peak absorbance of TM polarization decreases much faster than TE polarization as the incident angle increases.The reason for this phenomenon is mainly related to the electric dipole resonance of the graphene, where the tangential component of the electric field for the TM polarization decreases as θ increases but that of TE polarization remains unchanged.Besides, slightly blue-shifts of the absorption for both polarizations are also observed due to some parasitic resonances occurred at the larger incident angle.Despite slightly blue-shifts and certain amount of absorption decrease, we can still find that the peak absorbance remains more than 70% with a sufficient broadband of 1.4 THz over a wide range of incidence angle up to 60° for both polarizations.From this point of view, the proposed gradient modulated structure is able to compensate the momentum mismatch between the free space terahertz waves and graphene surface plasmons, exhibiting very high terahertz wave coupling efficiency.Compared with some previously proposed broadband absorbers [24,25,28,29], it has the advantages like broader normalized bandwidth or larger incident angle insensitive at terahertz frequencies.The incident angle and polarization insensitive broadband absorption characteristics may have great potential applications in terahertz sensing, detecting, and optoelectronic devices.Furthermore, the geometrical and electrostatic tunabilities of the proposed absorber are investigated.The absorption properties of the proposed absorber directly depend on the geometry and material parameters, especially on the dielectric spacer thickness t d and the graphene conductivity σ g .To briefly demonstrate these properties, below we only discuss the absorption analysis under normal incidence for the TE polarization.Figure 5 illustrates the relation between the absorbance and the spacer thickness t d with the chemical potential μ c fixed as 0.7 eV.It is found that the absorption is related to phase-matching conditions of reflection cancellation, which is sensitive to the spacer thickness t d variation.As t d continuously increases from 16 µm to 34 µm, the absorbance enhances, the bandwidth decreases, and the central frequency red-shifts from 2.2 THz to 1.6 THz.And the absorption enhancement can be directly predicted from the stronger terahertz field confined to patterned graphene between adjacent unit cells when t d is bigger.It is remarkable that the absorption tuning via t d , is very useful in designing an absorber with specific requirement, but such tuning is no longer possible since the absorber is fabricated.However, absorption tuning via controlling the graphene conductivity can be used to solve this problem and make the fabricated absorber with flexible tunability.As shown in Kubo formulas Eq. ( 2) and Eq. ( 3), the surface conductivity of graphene is directly dependent on the chemical potential μ c , which can be easily tuned from 0 to 0.8 eV in experiments by the electrostatic doping [45][46][47].Figure 6 shows the absorption spectra as a function of terahertz frequency and the chemical potential μ c under normal incidence for the TE polarization when t d is fixed as 26 µm.It is obvious that, as μ c increases, the absorption increases without changing the operating frequency range.And the absorbance increases from 14% to nearly 100% as μ c increases from 0 to 0.8 eV.This absorber with flexible tunability may be used as a tunable broadband attenuator or spatial modulator at terahertz frequencies.In addition, unlike the conventional absorbers consisting of isolated graphene ribbons, disks and multi-resonators, the proposed absorber has net-shaped sinusoidally-patterned graphene layer with inherent continues electrical connection, which may greatly simplify the gating structure for achieving flexible tunability of the absorption properties by applying just one voltage gate, as shown in Fig. 1(a).And the design scheme of this tunable broadband terahertz absorber can be easily scalable to infrared or visible regimes.

Conclusion
In conclusion, we have demonstrated a new efficient route to achieving broadband terahertz absorber with nearly 100% absorption using a net-shaped sinusoidally-patterned graphene sheet placed on a thin polysilicon layer embedded dielectric spacer supported on a metallic reflecting plate.It is found that, by introducing such a unique gradient width modulation of the unit graphene sheet structure, the continuous plasmon resonances of the absorber can be -Dirac distribution, ω is the radian frequency, ξ is energy, c μ is the chemical potential, Γ is the phenomenological scattering rate, T is the absolute temperature, and1 2τ − Γ =, τ is the relaxation time, e is the charge of an electron,  is the reduced Planck's constant, and k B is the Boltzmann's constant.

Fig. 1 .
Fig. 1.(a) Schematic of the proposed graphene-based broadband terahertz absorber, where the net-shaped periodically sinusoidally-patterned graphene sheet is placed on a dielectric spacer supported on a metallic reflecting plate.A thin polysilicon layer is placed beneath the graphene sheet as a gating layer to control the graphene conductivity via a DC votage V g .(b) Schematic of the unit cell of the absorber, where θ is the incident angle, φ is azimuth angle, k  is the wavevector.The initial values of the structure parameters are set to be p x = 32 µm, p y = 60 µm, t d = 26 µm, t m = 0.5 µm, W max = 32 µm, W min = 1 µm, t = t p = 20 nm, and the single-layered graphene sheet is modeled as an equivalent 2D surface impedance layer without thikness in numerical simulation.
the S parameters in the simulations[8,43].

Fig. 2 .
Fig. 2. The numerically simulated absorption spectra of the proposed absorber with the graphene chemical potential μ c = 0.7 eV under normal incidence are displayed, where the red solid curve represents the absorption spectra in TE polarization and the blue block curve represents the absorption in TM polarization.It is observed that the proposed absorber has the 90% absorbance bandwidth of 1.32 THz with a central frequency of 1.93 THz for TE polarization, and the 90% absorbance bandwidth of 1.23 THz with a central frequency of 1.78 THz for TM polarization.The normalized bandwidth with respect to the central frequency is greater than 65% for both polarizations.
displays the simulated electric field amplitude (|E|) distributions of the proposed absorber for both polarizations, where Figs.3(a) and 3(b) are the |E| distributions for the TE and TM polarizations on the xoz and yoz planes cut in the middle of the unit cell at 2 THz, and Figs.3(c) and 3(d) are the |E| distributions for the TE and TM polarizations on the xoy plane with z = 0 at the interface between graphene and spacer at 0.6 THz, 2 THz, and 3.5 THz, respectively.It is observed that the absorber exhibits tight field confinement around the graphene sheet on the top layer, leading to strong terahertz trapping and absorption.The electric field confinement characteristics are consistent with the absorption spectra shown in Fig.

Fig. 3 .
Fig. 3.The simulated electric field amplitude (|E|) distributions of the proposed absorber with the graphene chemical potential μ c = 0.7 eV under normal incidence: (a) the |E| distributions in TE polarization on xoz plane with y = 0 and yoz plane with x = 0 at 2 THz; (b) the |E| distributions in TM polarization on xoz plane with y = 0 μm and yoz plane with x = 0 μm at 2 THz; the |E| distributions (c) in TE polarization and (d) in TM polarization on the xoy plane with z = 0 at the interface between the graphene and the spacer at 0.6 THz, 2 THz, and 3.5 THz, respectively.

Fig. 4 .
Fig. 4. Absorbance of the proposed absorber as a function of operating frequency and incident angle with the graphene chemical potential μ c = 0.7 eV for (a) the TE polarization and (b) TM polarization.The absorber exhibits excellent performances with relatively stable absorbance and bandwidth over a wide range of oblique incidence angles for both polarizations.Its peak absorbance remains more than 70% with a sufficient broadband of 1.4 THz over a wide range of incident angle up to 60° for both polarizations.

Fig. 5 .
Fig. 5. Normal-incidence absorbance in TE polarization of the graphene-based absorber as a function of operating frequency and dielectric thickness t d with the graphene chemical potential μ c = 0.7 eV.The normal-incidence absorbance is sensitive to the spacer thickness t d .As t d increases from 16 µm to 34 µm, the absorbance enhances, the bandwidth decreases, and the central frequency red-shifts from 2.2 THz to 1.6 THz.

Fig. 6 .
Fig. 6.Normal-incidence absorbance in the TE polarization of the graphene-based absorber for various values of the graphene chemical potential μ c with t d = 26 μm, where the peak absorbance increases from 14% to nearly 100% when the chemical potential is tuned from 0 to 0.8 eV.