# Design and Simulation of Terahertz Perfect Absorber with Tunable Absorption Characteristic Using Fractal-Shaped Graphene Layers

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{6}nm

^{2}in a five-stage perfect absorber. Ultimately, the variations of the absorbance parameter and plasmonic mode under rotating the graphene sheet are explored for single and double fractal triangle-shaped perfect configurations on the absorption band. The presented mechanism demonstrates the tunability of the absorption spectrum in terms of narrowing or broadening and switching the plasmonic resonance by configuring multi-stage structures that can employ a broad range of applications for sensory devices.

## 1. Introduction

_{0}, 2f

_{0}, 3f

_{0},…, the fractal structures give the possibility for the photonic devices to operate with the specific resonant frequencies, rather than multiple basic frequencies in general over the absorption band. Although some studies concerning the design of fractal absorbers have been carried out in the THz regime recently [32,33,34], there is still substantial potential for further research in this field. Accordingly, this article proposes a unique terahertz perfect absorber composed of the graphene layer, configuring triangular fractal shapes, two insulators, and a thickness substrate of gold. First, the effect of an increase in the number of fractal triangles shaped on the graphene sheet embedded in the proposed configuration is investigated in order to obtain the absorption parameter changes in the spectral response. Then, the impact of stacking fractal layers of graphene, position variations of fractal layers on the plasmonic resonance shift, and absorption peak amplitude in the absorption characteristic are studied. Further, interesting results are extracted using the DC voltage bias employed by external sources on the configuration of the proposed multilayer absorbers, which means tuning the amplitude and frequency of the absorption and narrowing or widening the absorption bandwidth of the spectral response and multiband absorption.

## 2. Theory and Background

## 3. Structural Geometry

## 4. Simulation and Discussion

_{f}) of 0.7 eV for a triangular-bow-shaped graphene layer at the beginning of the simulation. While the Fermi level is fixed at 0.7 eV, fractal architectures with shapes ii–iv (shown in Figure 1) are employed. In order to evaluate the proposed structures in terms of functionality, the absorption cross-section (ACS) parameter as a measure of the absorption process is obtained, and its relationship with the absorption efficiency is defined as follows [39]:

^{2}at E

_{f}= 0.3 eV, $2.5998\times {10}^{5}$ nm

^{2}at E

_{f}= 0.9 eV, and 1.785$\times {10}^{5}$ nm

^{2}at E

_{f}= 1.5 eV. The plasmonic frequency also shifts from 3.47 to 5.932 THz and 7.6513 THz, respectively, without any geometric manipulation. It is interesting to note that, after applying 1.4 eV of the Fermi potential, the spectral response is widened with a dramatic drop in the absorption peak, which can be due to the nature of this kind of fractal shape, and we focus further on this issue in the following. In fact, changing the Fermi energy leads to altering the graphene’s optical properties, such as its refractive index and permittivity, resulting in the variation of plasmonic frequency on the spectral response. In detail, the resonant frequency of the proposed absorber structure can be approximately expressed as $\omega =1\u2215\sqrt{Lc}$, in which L and C are the inductance and capacitance, respectively. The total inductance is equal to the summation of the kinetic inductance (L

_{k}) and standard inductance (L

_{g}). In [43], the kinetic inductance (L

_{k}) is described as ${L}_{k}=\alpha ({m}_{e}/{\left({N}_{d}e\right)}^{2}$), where $\alpha $ is related to the unit cell’s structure, and e and m

_{e}are the electron charge and mass. N

_{d}also shows the carrier concentration. By increasing the graphene’s Fermi level, the kinetic inductance is reduced; consequently, the total inductance decreases. Therefore, the resonant frequency increases, which are associated with the absorption amplitude amplification, move in an upward trend, as shown in Figure 3 [44]. Table 2 presents the quantitive variation of plasmonic resonance associated with the corresponding absorption amplitude under the impact of Fermi level changes in the single-layer fractal absorber proposed.

^{2}at 6.5962 THz, whereas that of the initial structure was equal to $2.0892\times {10}^{5}$ nm

^{2}at 5.2285 THz. Adding another graphene layer to the initial structure leads to enhancing the plasmonic modes, resulting in a sharper absorption response due to the constructive interference of the electromagnetic field components. The absorption bandwidth in the new configuration also slightly increases. These phenomena can be described by the circuit theory, in which the graphene sheet is modeled by a shunt admittance [45]. Following this, the equivalent circuit of the configuration is approximated by the transmission line and graphene admittance. Based on this established concept, a near-perfect absorption occurs at the specific frequency when the input admittance of the structure matches with the free space admittance. Hence, in order to realize a broadband spectrum, the designers need to achieve plasmonic peaks close to each other merged under the admittance matching over the absorption band, resulting in a broadening absorption response [46]. Founded by this, the same graphene layers are used to obtain stronger plasmonic resonances. In our proposed model, due to the admittance matching close to each other related to the graphene sheets, the amplitude of the absorption peak experiences a considerable amplification, as seen in Figure 4c.

^{2}, and 16.285 THz with an amplitude of $18.7564\times {10}^{4}$ nm

^{2}, under this rotation, resulting from admittance mismatching, which creates a specific distance between the plasmonic peaks that occur in this state. Figure 5 shows the profile of the electromagnetic fields for the TE and TM modes related to the plasmonic resonance in both configurations, in which variations of electromagnetic modes under the rotation of the graphene layer in plasmonic frequencies are well observed.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Shen, G.; Zhang, M.; Ji, Y.; Huang, W.; Yu, H.; Shi, J. Broadband terahertz metamaterial absorber based on simple multi-ring structures. AIP Adv.
**2018**, 8, 075206. [Google Scholar] [CrossRef] [Green Version] - Carranza, I.E.; Grant, J.P.; Gough, J.; Cumming, D. Terahertz metamaterial absorbers implemented in CMOS technology for imaging applications: Scaling to large format focal plane arrays. IEEE J. Sel. Top. Quantum Electron.
**2017**, 23, 1–8. [Google Scholar] [CrossRef] [Green Version] - Zhong, S. Progress in terahertz nondestructive testing: A review. Front. Mech. Eng.
**2019**, 14, 273–281. [Google Scholar] [CrossRef] - Lewis, R.A. A review of terahertz detectors. J. Phys. D Appl. Phys.
**2019**, 52, 433001. [Google Scholar] [CrossRef] - Haxha, S.; AbdelMalek, F.; Ouerghi, F.; Charlton, M.D.B.; Aggoun, A.; Fang, X. Metamaterial superlenses operating at visible wavelength for imaging applications. Sci. Rep.
**2018**, 8, 16119. [Google Scholar] [CrossRef] [Green Version] - Asl, A.B.; Rostami, A.; Amiri, I.S. Terahertz band pass filter design using multilayer metamaterials. Opt. Quantum Electron.
**2020**, 52, 155. [Google Scholar] [CrossRef] - Ghosh, S.K.; Yadav, V.S.; Das, S.; Bhattacharyya, S. Tunable graphene-based metasurface for polarization-independent broadband absorption in Lower Mid-Infrared (MIR) range. IEEE Trans. Electromagn. Compat.
**2020**, 62, 346–354. [Google Scholar] [CrossRef] - Cui, Z.; Zhu, D.; Yue, L.; Hu, H.; Chen, S.; Wang, X.; Wang, Y. Development of frequency-tunable multiple-band terahertz absorber based on control of polarization angles. Opt. Express
**2019**, 27, 22190–22197. [Google Scholar] [CrossRef] - Cai, Y.; Li, S.; Zhou, Y.; Wang, X.; Xu, K.-D.; Guo, R.; Joines, W.T. Tunable and anisotropic dual-band metamaterial absorber using elliptical graphene-black phosphorus pairs. Nanoscale Res. Lett.
**2019**, 14, 346. [Google Scholar] [CrossRef] [Green Version] - Li, H.; Ji, C.; Ren, Y.; Hu, J.; Qin, M.; Wang, L. Investigation of multiband plasmonic metamaterial perfect absorbers based on graphene ribbons by the phase-coupled method. Carbon
**2019**, 141, 481–487. [Google Scholar] [CrossRef] - Venkatachalam, S.; Zeranska-Chudek, K.; Zdrojek, M.; Hourlier, D. Carbon-based terahertz absorbers: Materials, applications, and perspectives. Nano Sel.
**2020**, 1, 471–490. [Google Scholar] [CrossRef] - Yi, Z.; Liang, C.; Chen, X.; Zhou, Z.; Tang, Y.; Ye, X.; Yi, Y.; Wang, J.; Wu, P. Dual-band plasmonic perfect absorber based on graphene metamaterials for refractive index sensing application. Micromachines
**2019**, 10, 443. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Huang, H.; Xia, H.; Xie, W.; Guo, Z.; Li, H.; Xie, D. Design of broadband graphene-metamaterial absorbers for permittivity sensing at mid-infrared regions. Sci. Rep.
**2018**, 8, 4183. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Seren, H.R.; Keiser, G.R.; Cao, L.; Zhang, J.; Strikwerda, A.C.; Fan, K.; Metcalfe, G.D.; Wraback, M.; Zhang, X.; Averitt, R.D. Optically modulated multiband terahertz perfect absorber. Adv. Opt. Mater.
**2014**, 2, 1221–1226. [Google Scholar] [CrossRef] - Cheng, X.; Huang, R.; Xu, J.; Xu, X. Broadband terahertz near-perfect absorbers. ACS Appl. Mater. Interfaces
**2020**, 12, 33352–33360. [Google Scholar] [CrossRef] [PubMed] - Hossain, M.J.; Faruque, M.R.I.; Islam, M.T. Perfect metamaterial absorber with high fractional bandwidth for solar energy harvesting. PLoS ONE
**2018**, 13, e0207314. [Google Scholar] [CrossRef] [Green Version] - Mulla, B.; Sabah, C. Perfect metamaterial absorber design for solar cell applications. Waves Random Complex Media
**2015**, 25, 382–392. [Google Scholar] [CrossRef] - Wang, Y.; Sun, T.; Paudel, T.; Zhang, Y.; Ren, Z.; Kempa, K. Metamaterial-plasmonic absorber structure for high efficiency amorphous silicon solar cells. Nano Lett.
**2012**, 12, 440–445. [Google Scholar] [CrossRef] - Wallace, G.Q.; Lagugné-Labarthet, F. Advancements in fractal plasmonics: Structures, optical properties, and applications. Analyst
**2019**, 144, 13–30. [Google Scholar] [CrossRef] - Ullah, Z.; Witjaksono, G.; Nawi, I.; Tansu, N.; Irfan Khattak, M.; Junaid, M. A review on the development of tunable graphene nanoantennas for terahertz optoelectronic and plasmonic applications. Sensors
**2020**, 20, 1401. [Google Scholar] [CrossRef] [Green Version] - Guo, C.; Zhang, J.; Xu, W.; Liu, K.; Yuan, X.; Qin, S.; Zhu, Z. Graphene-based perfect absorption structures in the visible to terahertz band and their optoelectronics applications. Nanomaterials
**2018**, 8, 1033. [Google Scholar] [CrossRef] [Green Version] - Qi, Y.; Zhang, Y.; Liu, C.; Zhang, T.; Zhang, B.; Wang, L.; Deng, X.; Wang, X.; Yu, Y. A tunable terahertz metamaterial absorber composed of hourglass-shaped graphene arrays. Nanomaterials
**2020**, 10, 533. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Mishra, R.; Panwar, R. Investigation of graphene fractal frequency selective surface loaded terahertz absorber. Opt. Quantum Electron.
**2020**, 52, 317. [Google Scholar] [CrossRef] - Nourbakhsh, M.; Zareian-Jahromi, E.; Basiri, R. Ultra-wideband terahertz metamaterial absorber based on Snowflake Koch Fractal dielectric loaded graphene. Opt. Express
**2019**, 27, 32958–32969. [Google Scholar] [CrossRef] - Bao, Z.; Tang, Y.; Hu, Z.-D.; Zhang, C.; Balmakou, A.; Khakhomov, S.; Semchenko, I.; Wang, J. Inversion method characterization of graphene-based coordination absorbers incorporating periodically patterned metal ring metasurfaces. Nanomaterials
**2020**, 10, 1102. [Google Scholar] [CrossRef] [PubMed] - Shen, H.; Liu, F.; Liu, C.; Zeng, D.; Guo, B.; Wei, Z.; Wang, F.; Tan, C.; Huang, X.; Meng, H. A Polarization-insensitive and wide-angle terahertz absorber with ring-porous patterned Graphene METASURFACE. Nanomaterials
**2020**, 10, 1410. [Google Scholar] [CrossRef] [PubMed] - Zhu, H.; Zhang, Y.; Ye, L.; Li, Y.; Xu, Y.; Xu, R. Switchable and tunable terahertz metamaterial absorber with broadband and multi-band absorption. Opt. Express
**2020**, 28, 38626–38637. [Google Scholar] [CrossRef] - Cai, Y.; Guo, Y.; Zhou, Y.; Huang, X.; Yang, G.; Zhu, J. Tunable dual-band terahertz absorber with all-dielectric configuration based on graphene. Opt. Express
**2020**, 28, 31524–31534. [Google Scholar] [CrossRef] [PubMed] - Xu, K.-D.; Li, J.; Zhang, A.; Chen, Q. Tunable multi-band terahertz absorber using a single-layer square graphene ring structure with T-shaped graphene strips. Opt. Express
**2020**, 28, 11482–11492. [Google Scholar] [CrossRef] - Xu, K.-D.; Cai, Y.; Cao, X.; Guo, Y.; Zhang, Y.; Chen, Q. Multiband terahertz absorbers using T-shaped slot-patterned graphene and its complementary structure. J. Opt. Soc. Am. B
**2020**, 37, 3034–3040. [Google Scholar] [CrossRef] - Xie, T.; Chen, D.; Yang, H.; Xu, Y.; Zhang, Z.; Yang, J. Tunable broadband terahertz waveband absorbers based on fractal technology of graphene metamaterial. Nanomaterials
**2021**, 11, 269. [Google Scholar] [CrossRef] - Zubair, A.; Zubair, M.; Danner, A.; Mehmood, M.Q. Engineering multimodal spectrum of Cayley tree fractal meta-resonator supercells for ultrabroadband terahertz light absorption. Nanophotonics
**2020**, 9, 633–644. [Google Scholar] [CrossRef] - Zubair, A.; Mehmood, M.Q.; Zubair, M. Design of a fractal metasurface based terahertz broadband absorber. In 2019 PhotonIcs & Electromagnetics Research Symposium-Spring (PIERS-Spring); IEEE: Piscataway Township, NJ, USA, 2019; pp. 663–666. [Google Scholar]
- Kenney, M.; Grant, J.; Shah, Y.D.; Escorcia-Carranza, I.; Humphreys, M.; Cumming, D.R.S. Octave-spanning broadband absorption of terahertz light using metasurface fractal-cross absorbers. ACS Photonics
**2017**, 4, 2604–2612. [Google Scholar] [CrossRef] - Arik, K.; Abdollahramezani, S.; Farajollahi, S.; Khavasi, A.; Rejaei, B. Design of mid-infrared ultra-wideband metallic absorber based on circuit theory. Opt. Commun.
**2016**, 381, 309–313. [Google Scholar] [CrossRef] - Andryieuski, A.; Lavrinenko, A.V. Graphene metamaterials based tunable terahertz absorber: Effective surface conductivity approach. Opt. Express
**2013**, 21, 9144–9155. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zhang, Y.; Li, T.; Chen, Q.; Zhang, H.; O’Hara, J.F.; Abele, E.; Taylor, A.J.; Chen, H.-T.; Azad, A.K. Independently tunable dual-band perfect absorber based on graphene at mid-infrared frequencies. Sci. Rep.
**2015**, 5, 18463. [Google Scholar] [CrossRef] [Green Version] - Piper, J.R.; Fan, S. Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance. ACS Photonics
**2014**, 1, 347–353. [Google Scholar] [CrossRef] - Bohren, C.F.; Huffman, D.R. Absorption and Scattering of Light by Small Particles; John Wiley & Sons: Hoboken, NJ, USA, 2008. [Google Scholar]
- Alaee, R. Optical Nanoantennas and Their Use as Perfect Absorbers; Karlsruher Institut für Technologie: Karlsruhe, Germany, 2015. [Google Scholar]
- Alaee, R.; Albooyeh, M.; Rockstuhl, C. Theory of metasurface based perfect absorbers. J. Phys. D Appl. Phys.
**2017**, 50, 503002. [Google Scholar] [CrossRef] [Green Version] - Jabbarzadeh, F.; Heydari, M.; Habibzadeh-Sharif, A. A comparative analysis of the accuracy of Kubo formulations for graphene plasmonics. Mater. Res. Express
**2019**, 6, 086209. [Google Scholar] [CrossRef] - Linden, S.; Enkrich, C.; Dolling, G.; Klein, M.W.; Zhou, J.; Koschny, T.; Soukoulis, C.M.; Burger, S.; Schmidt, F.; Wegener, M. Photonic metamaterials: Magnetism at optical frequencies. IEEE J. Sel. Top. Quantum Electron.
**2006**, 12, 1097–1105. [Google Scholar] [CrossRef] [Green Version] - Xiao, B.; Gu, M.; Xiao, S. Broadband, wide-angle and tunable terahertz absorber based on cross-shaped graphene arrays. Appl. Opt.
**2017**, 56, 5458–5462. [Google Scholar] [CrossRef] [PubMed] - Arik, K.; AbdollahRamezani, S.; Khavasi, A. Polarization insensitive and broadband terahertz absorber using graphene disks. Plasmonics
**2017**, 12, 393–398. [Google Scholar] [CrossRef] - Xu, Z.; Wu, D.; Liu, Y.; Liu, C.; Yu, Z.; Yu, L.; Ye, H. Design of a tunable ultra-broadband terahertz absorber based on multiple layers of graphene ribbons. Nanoscale Res. Lett.
**2018**, 13, 143. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bott, A.W. Electrochemistry of semiconductors. Curr. Sep.
**1998**, 17, 87–92. [Google Scholar] - Stoliar, P.; Calò, A.; Valle, F.; Biscarini, F. Fabrication of fractal surfaces by electron beam lithography. IEEE Trans. Nanotechnol.
**2010**, 9, 229–236. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) The schematic diagram of perfect absorber based on the fractal graphene layer; (

**b**) triangular fractal shapes on the graphene layer.

**Figure 2.**(

**a**) Absorption cross−section (ACS) spectra for different fractal triangle−shaped graphene layers embedded into perfect absorbers; (

**b**) the TE and TM electromagnetic field distribution and surface current over the fractal triangle−shaped graphene layer selected in its plasmonic resonant frequency.

**Figure 3.**The variation of ACS spectrum under changing the Fermi energy in a single fractal graphene layer.

**Figure 4.**(

**a**) Double fractal graphene layers embedded in the structure with the similar-state positioning; (

**b**) Double fractal graphene layers embedded in the structure with the cross-state positioning; (

**c**) ACS spectra of double fractal graphene layers inserted in the two states of the perfect absorber.

**Figure 5.**The electromagnetic fields distribution for TE and TM modes in plasmonic resonant frequencies of (

**a**) the same−state and (

**b**,

**c**) cross−state configurations.

**Figure 6.**(

**a**) The variations of ACS spectrum under the lower fractal layer’s Fermi level change, (

**b**) the variations of ACS under the upper fractal layer’s Fermi level change.

**Figure 7.**The variations of ACS spectrum under the simultaneous change of Fermi energy in both fractal graphene layers.

**Figure 8.**(

**a**) A schematic of multi-stage absorber structure with the fractal graphene layers inserted in dielectrics at the same-state positioning; (

**b**) a schematic of multi-stage absorber structure with the fractal graphene layers inserted in dielectrics at the cross-state positioning; (

**c**) ACS spectra achieved as an effect of adding fractal graphene layers at the same-state positioning; (

**d**) ACS spectra achieved as an effect of adding fractal graphene layers at the cross-state.

**Figure 9.**(

**a**) A schematic of monolayer fractal graphene structure under angular rotation of graphene sheet; (

**b**) the variation of ACS spectra achieved under changing angular rotation.

**Figure 10.**(

**a**) The variation of ACS spectra achieved by changing the angular rotation of lower graphene sheet in a double-layer structure at the same-state positioning; (

**b**) the variation of ACS spectra achieved by changing the angular rotation of upper graphene layer in a double-layer structure at the same-state positioning; (

**c**) the variation of ACS spectra achieved by a simultaneous change of the angular rotation of lower and upper graphene sheets in a double-layer structure at the same-state positioning.

h1 | h2 | h3 | L | W |
---|---|---|---|---|

3 μm | 1.5 μm | 50 nm | 0.4 μm | 0.4 μm |

**Table 2.**The variations of plasmonic resonance and absorption peak under Fermi level change for a single fractal graphene layer.

Fermi Potential (eV) | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 | 1.1 | 1.2 |
---|---|---|---|---|---|---|---|---|---|---|

Plasmonic resonant frequency (THz) | 3.47 | 3.978 | 4.447 | 4.8768 | 5.2285 | 5.6192 | 5.932 | 6.2445 | 6.5571 | 6.8307 |

Amplitude of absorption peak (×10^{5} nm^{2}) | 1.011 | 1.2775 | 1.529 | 1.7922 | 2.0892 | 2.2945 | 2.5998 | 2.898 | 3.186 | 3.3675 |

Absorbers with Double Fractal Graphene Layers | Plasmonic Frequency (THz) | The Amplitude of Absorption Peak (×10 ^{5} nm^{2}) |
---|---|---|

In the same-state positioning | 6.5962 | 3.7326 |

In the cross-state positioning | 16.285 4.52 | 1.87564 0.66911 |

**Table 4.**The achieved quantities related to absorption parameters under the change of Fermi energy of lower graphene sheet.

Fermi Potential (eV) | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 | 1.1 | 1.2 |
---|---|---|---|---|---|---|---|---|---|

Plasmonic Frequency (THz) | 5.9319 | 6.12725 | 6.36172 | 6.5962 | 6.83066 | 6.987 | 7.26052 | 7.495 | 7.7295 |

The Amplitude of Absorption Peak (×10 ^{5} nm^{2}) | 3.2249 | 3.13688 | 3.57054 | 3.7326 | 3.94542 | 1.63982 | 1.8853 | 2.16426 | 2.42533 |

Beamwidth of Absorption Response (GHz)| (Approximately) | 120 | 120.1 | 123.9 | 116.2 | 116 | 540.3 | 482.2 | 427.8 | 397.3 |

**Table 5.**The achieved quantities related to absorption parameters under the change of Fermi energy of upper graphene sheet.

Fermi Potential (eV) | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 | 1.1 | 1.2 |
---|---|---|---|---|---|---|---|---|---|

Plasmonic Frequency (THz) | 5.893 | 6.1237 | 6.3617 | 6.5962 | 6.8307 | 7.0651 | 7.3387 | 7.5731 | 7.8076 |

The Amplitude of Absorption Peak (×10 ^{5} nm^{2}) | 2.74937 | 3.33415 | 3.44014 | 3.7326 | 4.08488 | 1.70679 | 1.94734 | 2.25912 | 2.47892 |

Beamwidth of Absorption Response (GHz) (Approximately) | 125 | 118.85 | 116.1 | 116.2 | 114.9 | 542.98 | 498.5 | 440 | 415.93 |

**Table 6.**The achieved quantities related to absorption parameters under the simultaneous variation of Fermi energy of both graphene sheets.

Fermi Potential (eV) | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 | 1.1 | 1.2 | 1.3 |
---|---|---|---|---|---|---|---|---|---|

Plasmonic Frequency (THz) | 5.5802 | 6.0882 | 6.5962 | 7.0261 | 7.4559 | 7.8858 | 8.2375 | 8.6283 | 8.98 |

The Amplitude of Absorption Peak (×10 ^{5} nm^{2}) | 2.70932 | 3.16794 | 3.7326 | 1.67307 | 2.16996 | 2.65677 | 5.76659 | 6.22226 | 6.68774 |

Bandwidth of Absorption Response (GHz) (Approximately) | 119.13 | 121.61 | 116.2 | 537.6 | 441.29 | 381.9 | 115.71 | 117.28 | 118.83 |

**Table 7.**The achieved quantities related to absorption parameters for multilayer configuration in the similar positioning.

Number of Graphene Layers Embedded | Single-Layer | Double-Layer | Three Layers | Four Layers | Five Layers |
---|---|---|---|---|---|

Plasmonic Frequency (THz) | 5.2285 | 6.5962 | 7.3387 | 7.84669 | 8.2375 |

The Amplitude of Absorption Peak (×10 ^{5} nm^{2}) | 2.0892 | 3.7326 | 2.38817 | 3.64856 | 8.09279 |

Bandwidth of Absorption Response (GHz) (Approximately) | 123.9 | 116.2 | 460 | 360 | 110 |

**Table 8.**The achieved quantities related to absorption parameters for multilayer configuration in the cross-state positioning.

Number of Graphene Layers Embedded | Single-Layer | Double-Layer | Three Layers | Four Layers |
---|---|---|---|---|

Plasmonic Frequency (THz) | 5.2285 | 4.5251 16.3086 | 4.875 12.0872 16.1663 | 4.63828 11.9689 16.7575 |

The Amplitude of Absorption Peak (×10 ^{5} nm^{2}) | 2.0892 | 0.6711 1.953 | 1.2086 0.72523 2.07626 | 3.64856 0.48141 0.76625 |

The Bandwidth of Absorption Response (GHz) (Approximately) | 123.9 | 142 134 | 157 140 130 | 140 140 150 |

**Table 9.**The variations of absorption characteristics of monolayer fractal graphene structure under the impact of graphene sheet rotation.

Angular Rotation of Graphene Sheet (°) | 0 | 0.5 | 1 | 1.5 |
---|---|---|---|---|

Plasmonic Frequency (THz) | 3.19639 | 3.31363 | 3.58717 | 3.66533 |

The Amplitude of Absorption Peak (×10 ^{4} nm^{2}) | 8.43154 | 9.11228 | 10.35872 | 11.16 |

**Table 10.**The variations of absorption characteristics of double fractal graphene structure under the rotation of lower graphene sheet.

Angular Rotation of Graphene Sheet (°) | 0 | 2.5 | 5 | 7.5 | 10 |
---|---|---|---|---|---|

Plasmonic Frequency (THz) | 6.0491 | 6.16633 | 6.36172 | 6.08818 | 6.55711 |

The Amplitude of Absorption Peak (×10 ^{4} nm^{2}) | 3.83525 | 3.88302 | 4.03278 | 3.37791 | 4.23259 |

**Table 11.**The variations of absorption characteristics of double fractal graphene structure under the rotation of upper graphene sheet.

Angular Rotation of Graphene Sheet (°) | 0 | 2.5 | 5 | 7.5 | 10 |
---|---|---|---|---|---|

Plasmonic Frequency (THz) | 6.0491 | 6.20541 | 6.4008 | 6.12725 | 6.59619 |

The Amplitude of Absorption Peak (×10 ^{4} nm^{2}) | 3.83525 | 4.01656 | 4.13524 | 3.58740 | 4.18106 |

**Table 12.**The variations of absorption characteristics of double fractal graphene structure under the simultaneous rotation of graphene layers.

Angular Rotation of Graphene Sheet (°) | 0 | 2.5 | 5 | 7.5 | 10 |
---|---|---|---|---|---|

Plasmonic Frequency (THz) | 6.0491 | 6.3226 | 6.43988 | 6.0491 | 6.83066 |

The Amplitude of Absorption Peak (×10 ^{4} nm^{2}) | 3.83525 | 4.15166 | 4.01461 | 3.45296 | 4.4154 |

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**MDPI and ACS Style**

Maghoul, A.; Rostami, A.; Gnanakulasekaran, N.; Balasingham, I.
Design and Simulation of Terahertz Perfect Absorber with Tunable Absorption Characteristic Using Fractal-Shaped Graphene Layers. *Photonics* **2021**, *8*, 375.
https://doi.org/10.3390/photonics8090375

**AMA Style**

Maghoul A, Rostami A, Gnanakulasekaran N, Balasingham I.
Design and Simulation of Terahertz Perfect Absorber with Tunable Absorption Characteristic Using Fractal-Shaped Graphene Layers. *Photonics*. 2021; 8(9):375.
https://doi.org/10.3390/photonics8090375

**Chicago/Turabian Style**

Maghoul, Amir, Ali Rostami, Nilojan Gnanakulasekaran, and Ilangko Balasingham.
2021. "Design and Simulation of Terahertz Perfect Absorber with Tunable Absorption Characteristic Using Fractal-Shaped Graphene Layers" *Photonics* 8, no. 9: 375.
https://doi.org/10.3390/photonics8090375