**Author details**

Channam Venkat Sunil Kumar1 \*, Francis Maury2 and Naoufal Bahlawane3

\*Address all correspondence to: sunilc\_kumar@live.com

1 SPIN Laboratory, Department of Physics, University of Liege, Liège, Belgium

2 CIRIMAT, ENSIACET, Toulouse, France

3 Luxembourg Institute of Science and Technology (LIST), Belvaux, Luxembourg

#### **References**


[3] Rudé M, Mkhitaryan V, Cetin AE, Miller TA, Carrilero A, Wall S, de Abajo FJ, Altug H, Pruneri V. Ultrafast and broadband tuning of resonant optical nanostructures using phase-change materials. Advanced Optical Materials. 2016;**4**(7):1060-1066

**5. Conclusions**

166 Metamaterials and Metasurfaces

which VO2

multiple applications. VO2

**Conflict of interest**

**Author details**

**References**

Channam Venkat Sunil Kumar1

2 CIRIMAT, ENSIACET, Toulouse, France

improved multifold by incorporating a VO2

optically contrasting media, makes VO2

optoelectronic devices and smart responsive metasurfaces.

sibilities new generation of semiconducting devices.

The authors of this chapter indicate no conflict of interest.

\*Address all correspondence to: sunilc\_kumar@live.com

\*, Francis Maury2

1 SPIN Laboratory, Department of Physics, University of Liege, Liège, Belgium

3 Luxembourg Institute of Science and Technology (LIST), Belvaux, Luxembourg

BJ, Seo G, Kim HT, Ventra MD. Reconfigurable gradient index using VO<sup>2</sup>

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occurring disordered state can be controlled with accurate temperature inputs and the ratio of the semiconducting to metallic parts can be configured spatially over the whole surface or selectively on a part of the metasurface. The rich physics involved in this phenomenon will help to further understand the mechanisms of phase transitions in the fundamental point of view whereas, the unique properties displayed by the material will inspire application pos-

layers can be integrated to metamaterial makes it an ideal candidate for future

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[45] Sohn JI, Joo HJ, Ahn D, Lee HH, Porter AE, Kim K, et al. Surface-stress-induced Mott transition and nature of associated spatial phase transition in single crystalline VO2

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[18] Liu PQ, Luxmoore IJ, Mikhailov SA, Savostianova NA, Valmorra F, Faist J, Nash GR. Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled

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tion using a split-ring resonator metamaterial. Nano Letters. 2011;**11**(3):1025-1031 [23] Dicken MJ, Aydin K, Pryce IM, Sweatlock LA, Boyd EM, Walavalkar S, et al. Frequency

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1750-1753


**Chapter 9**

Provisional chapter

**Design of Graphene-Based Metamaterial Absorber and**

DOI: 10.5772/intechopen.78608

Graphene is a monolayer of carbon atoms arranged in a honeycomb structure which exhibits remarkable properties including high electron mobility, mechanical flexibility, and saturable absorption. In this chapter, the conductivity model of the graphene is first reviewed. Based on the conductivity model of graphene, the equivalent circuit model of graphene is discussed. By varying graphene's chemical potential via external biasing voltage, graphene conductivity can be flexibly tuned in the terahertz and infrared frequencies. With the tunable characteristic, graphene-based metamaterial absorber and reflectarray have been designed. Good performance in these examples illustrates that

Metamaterial [1–6] has attracted much attention in the scientific communities over the past 20 years. The metamaterial is a macroscopic composite of periodic or non-periodic structures whose scale is smaller than the wavelength. Metamaterials derive their properties not from the properties of base materials but from their newly designed structures. The property of the subwavelength structure in the metamaterial can be described by effective medium parameters [7–12] including electric permittivity and magnetic permeability. The design of the structure allows effective medium parameters to be tailored to special parameters, for example, near-zero values and negative values, and the resultant metamaterials could flexibly manipulate the behavior of electromagnetic waves in ways that have not been conventionally possible

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

graphene promises sufficient flexibility in the design of metamaterial devices. Keywords: graphene, conductivity model, equivalent circuit model, tunable,

Design of Graphene-Based Metamaterial Absorber and

**Antenna**

Antenna

Yan Shi and Ying Zhang

Abstract

1. Introduction

Yan Shi and Ying Zhang

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78608

metamaterial, absorber, reflectarray

#### **Design of Graphene-Based Metamaterial Absorber and Antenna** Design of Graphene-Based Metamaterial Absorber and Antenna

DOI: 10.5772/intechopen.78608

Yan Shi and Ying Zhang Yan Shi and Ying Zhang

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.78608

#### Abstract

Graphene is a monolayer of carbon atoms arranged in a honeycomb structure which exhibits remarkable properties including high electron mobility, mechanical flexibility, and saturable absorption. In this chapter, the conductivity model of the graphene is first reviewed. Based on the conductivity model of graphene, the equivalent circuit model of graphene is discussed. By varying graphene's chemical potential via external biasing voltage, graphene conductivity can be flexibly tuned in the terahertz and infrared frequencies. With the tunable characteristic, graphene-based metamaterial absorber and reflectarray have been designed. Good performance in these examples illustrates that graphene promises sufficient flexibility in the design of metamaterial devices.

Keywords: graphene, conductivity model, equivalent circuit model, tunable, metamaterial, absorber, reflectarray

### 1. Introduction

Metamaterial [1–6] has attracted much attention in the scientific communities over the past 20 years. The metamaterial is a macroscopic composite of periodic or non-periodic structures whose scale is smaller than the wavelength. Metamaterials derive their properties not from the properties of base materials but from their newly designed structures. The property of the subwavelength structure in the metamaterial can be described by effective medium parameters [7–12] including electric permittivity and magnetic permeability. The design of the structure allows effective medium parameters to be tailored to special parameters, for example, near-zero values and negative values, and the resultant metamaterials could flexibly manipulate the behavior of electromagnetic waves in ways that have not been conventionally possible

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[13–22]. For example, the well-known double negative materials, which was proposed by Veselago [23], can support the backward propagating waves [24], and near-zero material can tunnel electromagnetic waves through very narrow channels [25].

In recent years, metasurfaces have caused huge research interest [26–30]. Metasurfaces may be considered as the two-dimensional counterparts of metamaterials. Due to its subwavelength thickness, metasurfaces are easier to fabricate by using planar fabrication technology. Different from the effective medium characterization of the volume metamaterial, metasurfaces modulate the behaviors of electromagnetic waves through specific boundary conditions. By designing subwavelength-scaled patterns in horizontal dimensions, characteristics of electromagnetic waves including phase, magnitude, and polarization can be flexibly manipulated. One of the most important applications by means of the metasurface is to control the wavefront of the electromagnetic waves by imparting local, gradient phase shift to the incoming waves, which results in generalized Snell's transmission and reflection laws [26].

Graphene [31, 32] consisting of a single layer of carbon atoms arranged in a hexagonal lattice has attracted increasingly attention of the research community due to its extraordinary mechanical, electric, optical, and heating properties. Intrinsic graphene is a zero band-gap semiconductor which is very promising for nanoelectronics applications, because its conduction and valence bands meet at Dirac points. Graphene's transport characteristic and conductivity can be tuned by either electrostatic or magnetostatic gating or via chemical doping [31, 33]. The Fermi level of intrinsic graphene can be engineered to support surface plasmons polariton (SPP) [34, 35]. These fascinating characteristics promise graphene a nature candidate in the metamaterial/metasurface-based devices including absorbers [36–39], cloaks [40], filters [41], antennas [42, 43], nonlinear optical devices [44], etc. In this chapter, we first review the conductivity model and equivalent circuit model of graphene, respectively. Next, a graphenebased metamaterial absorber with good performance including tunable absorbing bandwidth, wide angle, and polarization insensitive characteristic is developed at mid-infrared frequencies. Finally, a wideband tunable graphene-based metamaterial reflectarray is proposed to generate an orbital angular momentum (OAM) vortex wave in terahertz.

field force F

in which

⇀

current becomes J

<sup>m</sup> ¼ �e v⇀ � <sup>B</sup>

ilarly, in the case of an electric field E

⇀

<sup>σ</sup>yx ¼ � <sup>e</sup><sup>2</sup>v<sup>2</sup>

þ

⇀

Figure 1. A graphene sheet biased with a static magnetic field.

Therefore, the induced current has two components, i.e., J

expressions of σxx and σxy for zero energy gap are [45, 46]:

<sup>F</sup>eB<sup>0</sup> π

X∞ n¼0

8 < : ⇀

J ⇀ ¼ σ� E ⇀

<sup>σ</sup> <sup>¼</sup> <sup>σ</sup>xx �σyx

The conductivity tensor in Eq. (2) can be determined from Kubo formalism, and the explicit

nFð Þ� Mn nFð Þ� Mnþ<sup>1</sup> nFð Þþ �Mnþ<sup>1</sup> nFð Þ �Mn

ð Þ <sup>ω</sup> � <sup>j</sup>2<sup>Γ</sup> <sup>2</sup> h i ,

ð Þ Mnþ<sup>1</sup> <sup>þ</sup> Mn <sup>2</sup> � <sup>ℏ</sup><sup>2</sup>

graphene is magnetically induced gyrotropy which can be stated as

¼ �byeB0<sup>v</sup> is generated to deflect the electron toward �y direction.

<sup>¼</sup> <sup>b</sup>xJx <sup>þ</sup> <sup>b</sup>yJy <sup>¼</sup> <sup>b</sup>xσxxEx <sup>þ</sup> <sup>b</sup>yσyxEx. Sim-

<sup>0</sup> <sup>¼</sup> <sup>b</sup>zB0, the induced

ð3Þ

(4)

⇀

Design of Graphene-Based Metamaterial Absorber and Antenna

http://dx.doi.org/10.5772/intechopen.78608

173

, (1)

<sup>σ</sup>yx <sup>σ</sup>xx � �: (2)

⇀

<sup>¼</sup> <sup>b</sup>xJx <sup>þ</sup> <sup>b</sup>yJy ¼ �bxσyxEy <sup>þ</sup> <sup>b</sup>yσxxEy. Hence, an interesting property of

nFð Þ� Mn nFð Þ� Mnþ<sup>1</sup> nFð Þþ �Mnþ<sup>1</sup> nFð Þ �Mn ð Þ Mnþ<sup>1</sup> � Mn <sup>2</sup> � <sup>ℏ</sup><sup>2</sup>ð Þ <sup>ω</sup> � <sup>j</sup>2<sup>Γ</sup> <sup>2</sup> h i

<sup>¼</sup> <sup>b</sup>yEy and a static magnetic field <sup>B</sup>
