# A Tunable Terahertz Metamaterial Absorber Composed of Hourglass-Shaped Graphene Arrays

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## Abstract

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## 1. Introduction

^{2}hybrid orbitals [1,2]. Owing to its unique optoelectronic properties, graphene is one of the most promising optoelectronic materials and is widely used in the field of batteries, materials processing, biomolecular sensing, food safety, and communications [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. Additionally, graphene also play an essential role in metadevices, such as detectors and modulators [18,19,20]. Taking the modulator as an example, the application of graphene enables the modulation depth of the modulator to reach 100%.

## 2. Geometric Structures and Methods

_{2}) spacer layer with a thickness of ${d}_{1}$. In this paper, the absorption spectra and the localized electric field distribution of the structure are studied using the Finite Difference Time Domain (FDTD) method [44]. The antisymmetric, symmetric, and perfectly matched layer (PML) boundary conditions are used in the X, Y, and Z directions, respectively. The isosceles triangle of this structure has two sides of length $0.8\text{}\mathsf{\mu}\mathrm{m}$. The semimajor (L) and semiminor (R) axis of the ellipse are both $0.4\text{}\mathsf{\mu}\mathrm{m}$ (that is the special case of an ellipse: circle). The thickness of SiO

_{2}(${d}_{1}$) and Si are $0.3\text{}\mathsf{\mu}\mathrm{m}$ and infinity. The period (

**P**) of the structure is $3\text{}\mathsf{\mu}\mathrm{m}$. The thickness of monolayer graphene is $0.34\text{}\mathrm{n}\mathrm{m}$. The uniform mesh accuracy along the X and Y directions are adopted as 20 nm, and the Z direction is 1 nm. The relative permittivity of Si and SiO

_{2}are adopted as 1.96 and 3.9 [45,46]. The entire system is illuminated by a plane wave propagating along the negative Z direction with total electric field

**E**polarizing along the X direction. The position of the electric field monitor is placed at the same position of the graphene layer and is larger than the graphene layer boundary.

_{2}layer and charge of an electron, respectively. Therefore Equation (1) can be expressed as follows:

## 3. Simulation Results and Discussions

#### 3.1. The Influence of Different Chemical Potentials on Absorption

#### 3.2. The Influence of Different Semiminor Axes on Absorption

#### 3.3. The Influence of Different Semimajor Axes of the Ellipse on Absorption

#### 3.4. The Influence of Different Periods on Absorption

#### 3.5. The Influence of Different Incident Angles on Absorption

## 4. Bilayer Graphene Arrays

_{2}layer with a thickness of ${\mathrm{d}}_{2}$. Whilst keeping other parameters unchanged (${\mu}_{c}=0.8\text{}\mathrm{eV},\mathrm{L}=0.4\text{}\mathsf{\mu}\mathrm{m},\mathrm{R}=0.4\text{}\mathsf{\mu}\mathrm{m},\mathrm{P}=3\text{}\mathsf{\mu}\mathrm{m}$), the absorption spectra of various ${\mathrm{d}}_{2}$ values from 100 to 400 nm with 100 nm intervals are illustrates in Figure 8b. When ${\mathrm{d}}_{2}$ is fixed at $100\text{}\mathrm{n}\mathrm{m}$, it can be seen form the spectra that there are dual-band absorption peaks at $21.6\text{}\mathsf{\mu}\mathrm{m}$ and $36.3\text{}\mathsf{\mu}\mathrm{m}$ with an absorption efficiency 41.7% and 11%, respectively. Moreover, when ${\mathrm{d}}_{2}=100\text{}\mathrm{n}\mathrm{m}$, the maximum absorption at the short-band can reach 41.7%, which exceeds that of the monolayer graphene arrays with the same parameters (38.2%). The shifts of the resonance wavelength are different for the two bands. For the long-band and short-band, the resonance wavelength undergoes blue shift and slight red shift, respectively. As for the maximum absorption, the maximum absorption at the short-band decreases with the increase in ${\mathrm{d}}_{2}$, but for the long-band, the maximum absorption increases with the increase in ${\mathrm{d}}_{2}$. According to our simulation results, the upper layer of the graphene structure mainly contributes to the short-band, and the lower layer mainly contributes to the long-band. Therefore, the bilayer graphene structure allows us to adjust the two absorption peaks and their bandwidths separately to achieve different absorption characteristics.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A1.**(

**a**) The monolayer perfect absorption of this structure, (

**b**) The bilayer perfect absorption of this structure.

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**Figure 1.**(

**a**) The schematic of “hourglass” graphene arrays structure with period (P), semimajor axis (L), semiminor axis (R). The two layers of substrate structure are Si and SiO

_{2}. The thickness of SiO

_{2}is ${\mathrm{d}}_{1}$. (

**b**) The side view of the structure which manipulates the chemical potential (${\mu}_{c}$) of graphene by applying a voltage (${V}_{b}$).

**Figure 2.**The real (

**a**) and imaginary part (

**b**) of ${\sigma}_{\mathrm{g}}$ as functions of ${\mu}_{c}$ and $\lambda $.

**Figure 3.**(

**a**) The graph of the graphene absorption. (

**b**) The absorption spectra corresponding to the chemical potential from 0.2 to 0.8 eV. (

**c**) The corresponding electric field intensity distribution under different ${\mu}_{c}$ values.

**Figure 4.**(

**a**) The graph of the graphene absorption corresponding to the semiminor axis from $0.1$ to $0.4\text{}\mathsf{\mu}\mathrm{m}$. (

**b**) The corresponding electric field intensity distribution under different R values.

**Figure 5.**(

**a**) The absorption spectra of the structure with different L values. (

**b**) The electric field distributions at the maximum absorption for $\mathrm{L}=0.2,0.3,0.4,0.5\text{}\mathsf{\mu}\mathrm{m}$.

**Figure 6.**(

**a**) The absorption spectra of the structure with different P values. (

**b**) The electric field distributions at the absorption peak for $\mathrm{P}=3.0,4.0,5.0,7.0\text{}\mathsf{\mu}\mathrm{m}$.

**Figure 7.**(

**a**,

**b**) The absorption spectra of the structure with different θ values. (

**c**) The electric field distributions at the absorption peak for $\theta ={0}^{\circ},{30}^{\circ},{45}^{\circ},{60}^{\circ}$.

**Figure 8.**(

**a**) The side view of the structure consisting of bilayer graphene arrays covered with two thin SiO

_{2}layers with thickness ${\mathrm{d}}_{1}$ and ${\mathrm{d}}_{2}$. (

**b**) The absorption spectra of the structure with different ${\mathrm{d}}_{2}$ values.

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/nano10030533

**AMA Style**

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(3):533.
https://doi.org/10.3390/nano10030533

**Chicago/Turabian Style**

Qi, Yunping, Yu Zhang, Chuqin Liu, Ting Zhang, Baohe Zhang, Liyuan Wang, Xiangyu Deng, Xiangxian Wang, and Yang Yu.
2020. "A Tunable Terahertz Metamaterial Absorber Composed of Hourglass-Shaped Graphene Arrays" *Nanomaterials* 10, no. 3: 533.
https://doi.org/10.3390/nano10030533