# 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

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**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