# Tunable THz Graphene Filter Based on Cross-In-Square-Shaped Resonators Metasurface

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## Abstract

**:**

## 1. Introduction

## 2. Structure Description and Numerical Investigation

#### 2.1. Conductivity Model of Graphene

#### 2.2. Numerical Simulation

## 3. Discussion

#### 3.1. Coupled Oscillators Model Explanation

#### 3.2. Influence of Graphene Cross Shift on the Transmission Spectra

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Scheme of the unit cell geometry: The graphene cross-like layer is located on the quartz substrate (with $\u03f5=3.75$) in its center and is surrounded by a square gold ring. G is the size of the unit cell, R and K is the external size and width of gold ring respectively, and L and D is the length and the width of graphene cross-like layer respectively.

**Figure 2.**On the left side: Transmittance spectra of the filter in the absence of the gold ring with a fixed graphene Fermi level of 0.5 eV (

**a**), in the absence of the graphene layer (

**b**), and in case of the full Fano-resonant structure under electrostatic doping of 0.5 eV (

**c**). On the right side: Corresponding electric field distributions.

**Figure 3.**Transmission spectra of the filter for the different graphene Fermi level values from 0 eV to 0.5 eV (different gate voltage values).

**Figure 4.**Transmission spectra for theoretical and numerical calculations with increasing graphene Fermi level values from 0 eV to 0.5 eV (different gate voltage values) for graphene-based filter.

**Figure 5.**Transmission spectra of the filter with different unit cell structure: Original designed filter structure (

**a**), structure with shifted graphene cross along one direction up to 100 $\mathsf{\mu}$m (

**b**), structure with shifted graphene cross along two directions up to 100 $\mathsf{\mu}$m, and (

**c**) graphene Fermi energy fixed at 0.5 eV.

${\mathit{E}}_{\mathit{f}}$, eV | ${\mathit{\omega}}_{\mathit{g}}$, THz | ${\mathit{\gamma}}_{\mathit{g}}$, THz | Q | A${}_{1}$ | A${}_{2}$ | ${\mathit{\phi}}_{1}$ | ${\mathit{\phi}}_{2}$ | ${\mathit{f}}_{\mathit{m}1}$ | ${\mathit{f}}_{\mathit{m}2}$ | ${\mathit{f}}_{\mathit{g}}$ |
---|---|---|---|---|---|---|---|---|---|---|

0 | 0.2192 | 0.0385 | 5.7 | 0.9 | −0.8 | 1.62$\pi $ | 0.08$\pi $ | 1 | 0.1 | 0 |

0.1 | 0.2632 | 0.0387 | 6.8 | 0.47 | −0.7 | 1.85$\pi $ | 0.27$\pi $ | 1 | 0.1 | 0.03 |

0.2 | 0.2680 | 0.0112 | 24 | 0.47 | −0.44 | 1.92$\pi $ | 0.3$\pi $ | 1 | 0.1 | 0.05 |

0.3 | 0.2692 | 0.0088 | 30.6 | 0.47 | −0.34 | 1.93$\pi $ | 0.32$\pi $ | 1 | 0.1 | 0.08 |

0.4 | 0.2701 | 0.005 | 54 | 0.47 | −0.3 | 1.94$\pi $ | 0.33$\pi $ | 1 | 0.1 | 0.1 |

0.5 | 0.2712 | 0.0037 | 85 | 0.47 | −0.28 | 1.94$\pi $ | 0.34$\pi $ | 1 | 0.1 | 0.12 |

Offset, $\mathsf{\mu}$m | ${\mathit{A}}_{1}$ | ${\mathit{A}}_{2}$ | ${\mathit{\phi}}_{1}$ | ${\mathit{\phi}}_{2}$ |
---|---|---|---|---|

0–0 | 0.47 | −0.28 | 1.94$\pi $ | 0.34$\pi $ |

0–100 | 0.3 | −0.32 | 1.94$\pi $ | 0.51$\pi $ |

100–100 | 0.3 | −0.35 | 1.94$\pi $ | 0.52$\pi $ |

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**MDPI and ACS Style**

Zaitsev, A.; Grebenchukov, A.; Khodzitsky, M.
Tunable THz Graphene Filter Based on Cross-In-Square-Shaped Resonators Metasurface. *Photonics* **2019**, *6*, 119.
https://doi.org/10.3390/photonics6040119

**AMA Style**

Zaitsev A, Grebenchukov A, Khodzitsky M.
Tunable THz Graphene Filter Based on Cross-In-Square-Shaped Resonators Metasurface. *Photonics*. 2019; 6(4):119.
https://doi.org/10.3390/photonics6040119

**Chicago/Turabian Style**

Zaitsev, Anton, Alexander Grebenchukov, and Mikhail Khodzitsky.
2019. "Tunable THz Graphene Filter Based on Cross-In-Square-Shaped Resonators Metasurface" *Photonics* 6, no. 4: 119.
https://doi.org/10.3390/photonics6040119