# Design of a Reconfigurable THz Filter Based on Metamaterial Wire Resonators with Applications on Sensor Devices

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Filter Theory and Design Decisions

#### 2.1. Working Principle

#### 2.2. Circuit Theory

#### 2.2.1. Equivalent Circuit Admittance for the Wire Arrays

#### 2.2.2. Transmission Matrix of the Filter

#### 2.3. Parameters’ Choice

- Length ($l$) = 1.42 mm;
- Radius of the wires ($a$) = 0.2 μm;
- Distance between wires ($d$) ∈ [15; 20] μm.

## 3. Mechanical Simulations

#### 3.1. Device’s Modelling

#### 3.2. Generation of the Required Force to Compress the Device

**B**and the magnetic field

**H**is not linear. Since the FEMM solver is based on the principle of symmetry, we only draw part of the device (as shown in the Figure 4) [32]. The core of the plunger is made of iron and it is surrounded by a coil (1000 turns of copper wire), which will induce the movement of the core. The base (wood 1) and the surface (wood 2) that contacts with the device would ideally consist of wood, which in turn has air-like magnetic properties.

_{c}is the coil length, W

_{c}is the coil width, L

_{p}is the plunger length, W

_{p}is the plunger width, σ is the electrical conductivity of the iron, g is the length of the gap between the coil and the plunger, N

_{turns}is the number of turns of the coil, L

_{wood}

_{1}is the length of the base of the plunger, W

_{wood}

_{1}is the width of the base of the plunger, L

_{wood}

_{2}is the length of the surface of the plunger and W

_{wood}

_{2}is the width of the surface of the plunger, respectively.

## 4. Results

#### 4.1. Return Loss and Insertion Loss in the Frequency Domain as a Function of Distance between Wires

_{r}= 2.4 and PTFE posseses ε

_{r}= 2.1 [26]. The losses were not considered due to the characteristics of these materials, as highlighted in Section 2.

#### 4.1.1. HDPE

#### 4.1.2. PTFE

#### 4.2. Reduction in the Distance between Wires as a Function of Required Current

#### 4.2.1. HDPE

#### 4.2.2. PTFE

#### 4.3. Reflectance and Transmittance as a Function of Applied Force

#### 4.3.1. HDPE

#### 4.3.2. PTFE

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Xu, W.; Xie, L.; Ying, Y. Mechanisms and applications of terahertz metamaterial sensing: A review. Nanoscale
**2017**, 9, 13864–13878. [Google Scholar] [CrossRef] [PubMed] - Salim, A.; Lim, S. Review of Recent Metamaterial Microfluidic Sensors. Sensors
**2018**, 18, 232. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Gerislioglu, B.; Ahmadivand, A.; Pala, N. Tunable plasmonic toroidal terahertz metamodulator. Phys. Rev. B
**2018**, 97, 161405. [Google Scholar] [CrossRef] [Green Version] - Ahmadivand, A.; Gerislioglu, B.; Ahuja, R.; Kumar Mishra, Y. Terahertz plasmonics: The rise of toroidal metadevices towards immunobiosensings. Mater. Today
**2020**, 32, 108–130. [Google Scholar] [CrossRef] - Ahmadivand, A.; Gerislioglu, B.; Ramezani, Z. Gated graphene island-enabled tunable charge transfer plasmon terahertz metamodulator. Nanoscale
**2019**, 11, 8091–8095. [Google Scholar] [CrossRef] [PubMed] - Ferraro, A.; Zografopoulos, D.; Caputo, R.; Beccherelli, R. Periodical Elements as Low-Cost Building Blocks for Tunable Terahertz Filters. IEEE Photonics Technol. Lett.
**2016**, 28, 2459–2462. [Google Scholar] [CrossRef] - Ferraro, A.; Tanga, A.; Zografopoulos, D.; Messina, G.; Ortolani, M.; Beccherelli, R. Guided mode resonance flat-top bandpass filter for terahertz telecom applications. Opt. Lett.
**2019**, 44, 4239. [Google Scholar] [CrossRef] - Sun, D.; Qi, L.; Liu, Z. Terahertz broadband filter and electromagnetically induced transparency structure with complementary metasurface. Results Phys.
**2020**, 16, 102887. [Google Scholar] [CrossRef] - Sanphuang, V.; Ghalichechian, N.; Nahar, N.; Volakis, J. Reconfigurable THz Filters Using Phase-Change Material and Integrated Heater. IEEE Trans. Terahertz Sci. Technol.
**2016**, 6, 583–591. [Google Scholar] [CrossRef] - Chang, C.; Huang, L.; Nogan, J.; Chen, H. Invited Article: Narrowband terahertz bandpass filters employing stacked bilayer metasurface antireflection structures. APL Photonics
**2018**, 3, 051602. [Google Scholar] [CrossRef] - Zaitsev, A.; Grebenchukov, A.; Khodzitsky, M. Tunable THz Graphene Filter Based on Cross-In-Square-Shaped Resonators Metasurface. Photonics
**2019**, 6, 119. [Google Scholar] [CrossRef] [Green Version] - Ferraro, A.; Zografopoulos, D.; Caputo, R.; Beccherelli, R. Guided-mode resonant narrowband terahertz filtering by periodic metallic stripe and patch arrays on cyclo-olefin substrates. Sci. Rep.
**2018**, 8, 1–8. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cong, L.; Tan, S.; Yahiaoui, R.; Yan, F.; Zhang, W.; Singh, R. Experimental demonstration of ultrasensitive sensing with terahertz metamaterial absorbers: A comparison with the metasurfaces. Appl. Phys. Lett.
**2015**, 106, 031107. [Google Scholar] [CrossRef] - Zhang, N.; Song, R.; Hu, M.; Shan, G.; Wang, C.; Yang, J. A Low-Loss Design of Bandpass Filter at the Terahertz Band. IEEE Microw. Wirel. Compon. Lett.
**2018**, 28, 573–575. [Google Scholar] [CrossRef] - Němec, H.; Duvillaret, L.; Garet, F.; Kužel, P.; Xavier, P.; Richard, J.; Rauly, D. Thermally tunable filter for terahertz range based on a one-dimensional photonic crystal with a defect. J. Appl. Phys.
**2004**, 96, 4072–4075. [Google Scholar] [CrossRef] [Green Version] - Ko, Y.; Magnusson, R. Flat-top bandpass filters enabled by cascaded resonant gratings. Opt. Lett.
**2016**, 41, 4704. [Google Scholar] [CrossRef] [PubMed] - Yamada, K.; Lee, K.; Ko, Y.; Inoue, J.; Kintaka, K.; Ura, S.; Magnusson, R. Flat-top narrowband filters enabled by guided-mode resonance in two-level waveguides. Opt. Lett.
**2017**, 42, 4127. [Google Scholar] [CrossRef] - Melo, A.; Gobbi, A.; Piazzetta, M.; da Silva, A. Cross-Shaped Terahertz Metal Mesh Filters: Historical Review and Results. Adv. Opt. Technol.
**2012**, 2012, 1–12. [Google Scholar] [CrossRef] - Ozbey, B.; Unal, E.; Ertugrul, H.; Kurc, O.; Puttlitz, C.; Erturk, V.; Altintas, A.; Demir, H. Wireless Displacement Sensing Enabled by Metamaterial Probes for Remote Structural Health Monitoring. Sensors
**2014**, 14, 1691–1704. [Google Scholar] [CrossRef] [Green Version] - Chen, J.; Kaushik, S. Terahertz Interferometer That Senses Vibrations Behind Barriers. IEEE Photonics Technol. Lett.
**2007**, 19, 486–488. [Google Scholar] [CrossRef] - Pavia, J.P.; Ribeiro, M.; Souto, N. Design of Frequency Selective Devices for the THz Domain with Applications on Structural Health Monitoring. In Proceedings of the 2019 Thirteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials), Rome, Italy, 16–21 September 2019. [Google Scholar]
- Pozar, D. Microwave Engineering; John Wiley & Sons: Hoboken, NJ, USA, 2012. [Google Scholar]
- Naftaly, M.; Vieweg, N.; Deninger, A. Industrial Applications of Terahertz Sensing: State of Play. Sensors
**2019**, 19, 4203. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cunningham, P.; Valdes, N.; Vallejo, F.; Hayden, L.; Polishak, B.; Zhou, X.; Luo, J.; Jen, A.; Williams, J.; Twieg, R. Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials. J. Appl. Phys.
**2011**, 109, 043505–043510. [Google Scholar] [CrossRef] [Green Version] - Madhu, G.; Bhunia, H.; Bajpai, P.; Chaudhary, V. Mechanical and morphological properties of high density polyethylene and polylactide blends. J. Polym. Eng.
**2014**, 34, 813–821. [Google Scholar] [CrossRef] - Dhanumalayan, E.; Joshi, G. Performance properties and applications of polytetrafluoroethylene (PTFE)—A review. Adv. Compos. Hybrid Mater.
**2018**, 1, 247–268. [Google Scholar] [CrossRef] - Reddy, J. Introduction to the Finite Element Method; McGraw-Hill: New York, NY, USA, 2006. [Google Scholar]
- Gmsh. Available online: http://gmsh.info/doc/texinfo/gmsh.html (accessed on 23 March 2020).
- Råback, P.; Byckling, M.; Pursula, A.; Ruokolainen, J.; Zwinger, T.; Malinen, M. CSC-Documentation-Elmer Sover. Available online: https://www.csc.fi/web/elmer/documentation (accessed on 23 March 2020).
- Abazari, A.; Safavi, S.; Rezazadeh, G.; Villanueva, L. Modelling the Size Effects on the Mechanical Properties of Micro/Nano Structures. Sensors
**2015**, 15, 28543–28562. [Google Scholar] [CrossRef] [PubMed] - Engineering ToolBox. Available online: https://www.engineeringtoolbox.com (accessed on 23 March 2020).
- Finite Element Method Magnetics: Documentation. Available online: http://www.femm.info/wiki/Documentation/ (accessed on 23 March 2020).

**Figure 4.**Scheme of the magnetic circuit to be modeled on a finite element method magnetics (FEMM) solver.

**Figure 5.**Return loss in the frequency domain as a function of applied compression for high-density polyethylene (HDPE) host medium.

**Figure 6.**Insertion loss in the frequency domain as a function of applied compression for HDPE host medium.

**Figure 7.**Return loss in the frequency domain as a function of applied compression for polytetrafluoroethylene (PTFE) host medium.

**Figure 8.**Insertion loss in the frequency domain as a function of applied compression for PTFE host medium.

**Figure 9.**Reduction in the distance between wires as a function of applied force and current for 10, 30, 50 and 70 wires and a filter assembled with HDPE.

**Figure 10.**Reduction in the distance between wires as a function of applied current for 10, 30, 50 and 70 wires and a device assembled with HDPE.

**Figure 11.**Reduction in the distance between wires as a function of applied force and current for 10, 30, 50 and 70 wires and a filter assembled with PTFE.

**Figure 12.**Reduction in the distance between wires as a function of applied current for 10, 30, 50 and 70 wires and a device assembled with PTFE.

**Figure 13.**Reflectance as a function of applied force for 10, 30, 50 and 70 wires and a filter assembled with HDPE.

**Figure 14.**Transmittance as a function of applied force for 10, 30, 50 and 70 wires and a filter assembled with HDPE.

**Figure 15.**Reflectance as a function of applied force for 10, 30, 50 and 70 wires and a filter assembled with PTFE.

**Figure 16.**Transmittance as a function of applied force for 10, 30, 50 and 70 wires and a filter assembled with PTFE.

Material | Density (Kg/m^{3}) | Young’s Modulus (GPa) | Poisson’s Ratio |
---|---|---|---|

Gold | 19300 | 78 | 0.44 |

HDPE | 641 | 0.8 | 0.46 |

PTFE | 2100 | 0.3 | 0.46 |

L_{c} | W_{c} | L_{p} | Wp | σ | g | N_{turns} | L_{wood}_{1} | W_{wood}_{1} | L_{wood}_{2} | W_{wood}_{2} |
---|---|---|---|---|---|---|---|---|---|---|

0.27 mm | 0.1 mm | 0.05 mm | 0.37 mm | 10.44 MS/m | 0.005 mm | 1000 | 0.03 mm | 0.079 mm | 0.03 mm | 0.71 mm |

**Table 3.**Filter quality and performance parameters considering a distance between wires d = 17.5 µm.

FWHM (GHz) | Q | t_{d} (µs) |
---|---|---|

0.9 | 455 | 1.1848 |

**Table 4.**Calculation of the sensitivity of the filter considering a distance between wires d = 17.5 µm.

Number of Wires | $\Delta \mathit{F}$ (mN) | Sensitivity (N) |
---|---|---|

10 | 4.09 | 26.87 |

30 | 5.68 | 19.35 |

50 | 6.68 | 16.45 |

70 | 8 | 13.74 |

**Table 5.**Filter quality and performance parameters considering a distance between wires d = 18.5 µm.

FWHM (GHz) | Q | t_{d} (µs) |
---|---|---|

1.1 | 399 | 1.4481 |

**Table 6.**Calculation of the sensitivity of the filter considering a distance between wires d = 18.5 µm a reflectance ${S}_{11}$ = 0.6553.

Number of Wires | $\Delta \mathit{F}$ (mN) | Sensitivity (N) |
---|---|---|

10 | 0.657 | 524.66 |

30 | 0.821 | 419.85 |

50 | 0.965 | 357.2 |

70 | 1.2 | 287.25 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pavia, J.P.; Souto, N.; Ribeiro, M.A.
Design of a Reconfigurable THz Filter Based on Metamaterial Wire Resonators with Applications on Sensor Devices. *Photonics* **2020**, *7*, 48.
https://doi.org/10.3390/photonics7030048

**AMA Style**

Pavia JP, Souto N, Ribeiro MA.
Design of a Reconfigurable THz Filter Based on Metamaterial Wire Resonators with Applications on Sensor Devices. *Photonics*. 2020; 7(3):48.
https://doi.org/10.3390/photonics7030048

**Chicago/Turabian Style**

Pavia, João Pedro, Nuno Souto, and Marco Alexandre Ribeiro.
2020. "Design of a Reconfigurable THz Filter Based on Metamaterial Wire Resonators with Applications on Sensor Devices" *Photonics* 7, no. 3: 48.
https://doi.org/10.3390/photonics7030048