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Pramana

, 90:65 | Cite as

Investigation of graphene-integrated tunable metamaterials in THz regime

  • S Mahircan Demir
  • Yahya Yüksek
  • Cumali Sabah
Article
  • 229 Downloads

Abstract

A metallic fishnet metamaterial structure in sub-THz region is presented. The proposed structure is based on hexagonal resonators. Simulations have been performed by a 3D full-wave electromagnetic simulator and a negative refractive index has been observed at the frequency range between 0.55 and 0.70 THz with the help of the graphene layer. In order to observe the effect of the graphene layer, the metamaterial structure has been simulated and examined before and after graphene integration. Significant modification in the propagation properties has been observed after the graphene integration. Change in S-parameters with the size variation of hexagonal resonators and alteration in graphene thickness are also presented as a parametric study to show the tunability of the structure. Suitability of the metamaterial for sensor applications has been investigated. The proposed metamaterial structure is promising to be effectively used for tunability and sensor applications.

Keywords

Graphene-integrated metamaterials fishnet sensor applications tunability 

PACS Nos

81.05.Xj 78.67.Pt 41.20.-q 73.22.Pr 

1 Introduction

In recent years, unusual and unnatural electromagnetic properties of metamaterials (MTMs) have attracted a great deal of attention. Unusual electromagnetic properties of MTMs, such as simultaneous negative permittivity and permeability, which are not seen in nature, were first examined by Veselago by theoretically explaining the differences between right-handed (RH) and left-handed (LH) substances in terms of Doppler effect, Vavilov–Cerenkov effect and Snell’s law [1]. Nowadays, it is possible to have LH MTMs not only in theory, but also in experiment with some special arrangement of the materials. Mainly, composites are constructed by using dielectric materials which are periodically arranged and combined with metal layers to observe negative permittivity and permeability [2]. These composites were investigated in different frequency ranges such as gigahertz [3, 4, 5], terahertz [6, 7, 8, 9] and optical [10, 11, 12] for many purposes.
Fig. 1

The geometry of the proposed MTM design. (a) Front and back views of the structure without graphene, (b) perspective view of the structure with graphene and (c) top view of the structure with graphene.

Recently, graphene has drawn significant attention not only because it is the thinnest (2D) nanomaterial in nature, but also due to its perfect electrical and optical transparency properties [13, 14]. Graphene, which is known as the thinnest and the strongest material in the Universe, is a single layer of carbon atoms arranged in two dimensions [14, 15]. Graphene in MTM composites can provide ultra-wideband tunability, and it can modulate MTM structures [16]. Therefore, a graphene layer can be integrated into MTM structures to obtain tunable devices, especially in THz frequencies to develop new sensor structures, modulators, antennas and filters [17, 18, 19, 20].

In this study, a graphene-integrated fishnet MTM comprising hexagonal resonators is presented. Since THz science is a relatively new field of study and new structures and materials are needed to be discovered for this frequency regime, the proposed material has been investigated in sub-THz region. S-parameters, permittivity (\(\varepsilon \)), permeability (\(\mu \)), surface current and electric field distributions obtained by using a 3D full-wave electromagnetic simulator are presented for tunability and sensing applications. In order to understand the effect of graphene in MTM structures, the S-parameters and the effective constitutive parameters of the structure are discussed and examined in detail. Furthermore, the differences in S-parameters with respect to the alteration of the size of the hexagonal resonators and the thickness of the graphene layer are also presented as a parametric study for tunability applications. By adding a single layer and double layers respectively, the proposed structure is tested for sensor applications.

This paper is organised as follows. Section 2 of the paper provides the simulation results of the proposed MTM structure with and without graphene integration. In order to understand the effect of the graphene layer, S-parameters and the obtained constitutive parameters for the structure will be demonstrated in this section. Moreover, electric field and surface current distributions will be presented for further demonstration. Change in S-parameters with the variation on the dimension of the hexagonal resonators and the thickness of the graphene layer is discussed in §3 of the paper for tunability applications. The importance of the structure for sensing application is investigated in §4. Finally, the study is summarised and concluded in §5.
Fig. 2

Simulation results for the structure without graphene. (a) Magnitude spectra of the reflection (\(S_{11})\) and transmission (\(S_{21})\) and (b) phase spectra of the reflection (\(S_{11})\) and transmission (\(S_{21})\).

2 Design and simulation results

Figure 1 shows the geometry of the structure. The structure is composed of hexagonal resonators. The metallic part is shown in yellow in figure 1a, and it is aluminum, the electrical conductivity of which is \(3.56 \times 10^{7}\hbox { S}/\hbox {m}\). The thickness of aluminum is 0.5 um. A small hexagonal gap is created on the metallic part and the height (r) of the gap is set as 40 um. This procedure is done for both sides of the structure to create a fishnet MTM. Quartz (\(\varepsilon = 3.75\)) is selected as a dielectric material between the metallic layers. The effective thickness of the dielectric material is 20 um. The length (l) and width (w) of the dielectric substrate are adjusted as 337.75 um and 390 um, respectively. Graphene-integrated version of the structure is shown in figure 1b. The effective thickness of graphene is 0.33 nm. Figure 1c presents the top view of the structure after the graphene integration. Simulations have been performed by a 3D full-wave electromagnetic solver based on finite integration technique to obtain reflection parameter (\(\Gamma =\left| {S_{11} } \right| )\), transmission parameter (\(\tau =\left| {S_{21} } \right| )\), permittivity (\(\varepsilon )\) and permeability ( \(\mu \)) of the composite. Furthermore, the surface current distributions and electric field distributions are obtained and presented as a result of simulations.

Two ports are placed opposite to each other for the excitation and detection of the electromagnetic waves. Periodic boundary conditions are utilised in the x and y directions and open boundary conditions are utilised along the z direction. Therefore, symmetry can be observed in the x and y directions, and the wave propagates perpendicular to the z direction. The structure is examined in a frequency band extending up to 1 THz and scattering parameters are obtained from the simulations.

The simulation results for the structure before graphene integration is presented in figure 2. As one can see in figure 2, the transmission peaks around 0.48 THz, while the reflection dips at the same frequency. Moreover, the phase of the transmission dips around the same frequency. These findings verify the fact that there is a resonance in these frequencies [21, 22]. In order to understand whether the structure has a negative permittivity and permeability values, detailed constitutive parameter analysis is needed. Figure 3 shows the real part of the permittivity (\(\varepsilon \)) and permeability (\(\mu \)) of the structure without graphene layer. From figure 3, it is certain that the permittivity and permeability of the composite are negative between the frequencies 0.28 THz and 0.3 THz. For more information, the surface current distributions and electric field distributions of the composite at 0.297 and 0.7345 THz are presented in figures 4 and 5, respectively.
Fig. 3

Constitutive parameters of the structure without graphene. (a) Permittivity (\(\varepsilon \)) and (b) permeability (\(\mu \)).

Fig. 4

(a) Surface current distribution of the structure without graphene at 0.297 THz and (b) electric field distribution of the structure without graphene at 0.297 THz.

Fig. 5

(a) Surface current distribution of the structure without graphene at 0.7345 THz and (b) electric field distribution of the structure without graphene at 0.7345 THz.

Figure 4 represents the surface current distribution at the metallic parts of the structure and the electric field distribution of the whole structure at 0.297 THz, where both the permittivity and permeability of the composite are negative. Figure 5 shows the surface current distribution at the metallic parts of the structure and the electric field distribution of the whole structure at 0.7345 THz, where the permeability of the composite is negative. The surface current distributions at both the frequencies show antisymmetric response due to a magnetic resonance [23]. The directions of the current flow change at the opposing metallic areas, and they are opposite to each other. A virtual current loop occurs in these regions due to the displacement current [24, 25, 26, 27]. The electric fields concentrate at the outer side of the metallic region for both the samples.

Graphene-integrated version of the composite, which is investigated above, is constructed and simulation results of the structure are presented in figure 6 with the indication of the S-parameters and phase spectra. Moreover, permittivity and permeability of the composite are provided in figure 7 to understand the effect of graphene layer for proposed structure.
Fig. 6

Simulation results for the structure with graphene. (a) Magnitude spectra of the reflection (\(S_{11})\) and transmission (\(S_{21})\) and (b) phase spectra of the reflection (\(S_{11})\) and transmission (\(S_{21})\).

Fig. 7

Constitutive parameters of the structure with graphene. (a) Permittivity (\(\varepsilon \)) and (b) permeability (\(\mu \)).

Fig. 8

(a) Surface current distribution of the structure with graphene at 0.553 THz and (b) electric field distribution of the structure with graphene at 0.553 THz.

When figures 2 and 6 are compared, it is seen that there is an improvement in the graphene-integrated version of the composite in terms of S-parameters and phase spectra. The high conductivity of the graphene layer is the main reason for this improvement. Furthermore, when the two constitutive parameters are compared, it can be interpreted that the permittivity of the structure with the graphene stays negative for a larger frequency. Therefore, graphene integration provides a negative refractive index for a larger frequency range for this structure. In figure 7, the composite has negative permittivity and permeability for the frequency range between 0.55 and 0.7 THz. In addition, the permeability falls below zero after 0.73 THz and another negative refractive index is observed between 0.73 and 0.8 THz. Moreover, Lorentz- and Drude-like behaviours are observed for the permittivity and permeability of the structure for both cases before and after graphene integration [28].

Surface current distribution of the metallic part with the graphene layer and the electric field distribution of the whole structure at 0.553 THz, where the permittivity and permeability of the structure are both negative, are given in figure 8. As the metallic region is covered with a graphene layer which has high electron mobility and conductivity, the density of the surface current is higher compared to the structure without graphene. As observed in figures 4 and 5, virtual current loops are formed at the opposing metallic regions for the graphene-integrated composite as well. The difference of the electric field distribution from figures 4 and 5 is that the field is concentrated on the centre of the composite rather than the sides of the hexagonal metallic layer. In addition, the electric field is also distributed to the metallic parts and it is more intense compared to the structure without graphene.

3 Tunability

The proposed structure is examined with and without graphene layer between 0 and 1 THz region. For using and achieving the full potential of MTMs, it is required to have the ability of tuning or controlling their material properties [29]. In this study, two types of tuning methods will be investigated. In order to tune the material properties of the MTM composite, mechanical and electromechanical methods are examined in detail. First, the mechanical method is implemented by changing the dimension of the hexagonal gap. As shown in figure 1a, the height of the hexagonal gap (r) is changed to observe the effect in the simulation results. This method is used for the structure with and without the graphene layer. Since the proposed structure is a fishnet MTM, the height of the hexagonal gaps at both sides is tuned. Figure 9 represents \(S_{11}\) (reflection) and figure 10 represents \(S_{21}\) (transmission) for the structure without graphene layer.
Fig. 9

Magnitude change of the reflection (\(S_{11})\) spectra for the structure without graphene.

Fig. 10

Magnitude change of the transmission (\(S_{21})\) spectra for the structure without graphene.

Fig. 11

Magnitude change of the reflection (\(S_{11})\) spectra for the structure with graphene.

Fig. 12

Magnitude change of the transmission (\(S_{21})\) spectra for the structure with graphene.

Fig. 13

(a) Real part of the graphene permittivity between 0 and 0.02 THz, (b) real part of the graphene permittivity between 0.02 and 1 THz and (c) imaginary part of the graphene permittivity between 0 and 1 THz.

As can be seen from figures 9 and 10, by changing the height (r) of the hexagonal gaps, material properties of the composite can be dynamically controlled. The height (r) of the hexagonal gaps changes from 20 um to 60 um, and five samples are taken by linearly increasing the parameter. It is observed that if the height of the hexagonal gaps increases, the reflection and transmission parameters around 0.3 THz are shifted to the left. Additionally, the magnitude of the reflection and transmission parameters are affected by changing r. Change in reflection and transmission spectra with change in r for the structure with graphene layer is presented in figures 11 and 12, respectively. Parameter r changes from 30 um to 60 um, and four samples are taken by linearly increasing the parameter. As graphene layer is integrated into the structure, it is expected to have the change in the magnitude of the reflection and transmission parameters, and it is observed in the simulation results, clearly. It can be interpreted that with the increase in r, there is a left shift in the reflection and transmission spectra around 0.3 THz. This result is exactly the same with the first case in which the composite without graphene is investigated. As a result, the simulation results show that the proposed structure is mechanically tunable and the material properties of the structure can be dynamically controlled by changing the physical parameter of the composite.

The second type of tuning method is electromechanical tunability method. For this method, the electrical properties of the graphene monolayer are to be understood. Kubo formula can be used to obtain the conductivity (\(\sigma _{\mathrm{g}})\) of the graphene monolayer [16, 22]:
$$\begin{aligned}&\sigma _{\mathrm{g}} (\omega , \mu _{c}, \tau , T) = \sigma _{\mathrm{intra}}+ \sigma _{\mathrm{inter}}= \frac{j\hbox {e}^{2}\left( {\omega -j\tau ^{-1}} \right) }{\pi \hbar ^{2}}\nonumber \\&\quad \times \left[ \frac{1}{\left( {\omega -j\tau ^{-1}} \right) ^{2}}\mathop \int \nolimits _0^\infty \frac{\partial fd\left( \varepsilon \right) }{\partial \varepsilon }-\frac{\partial fd\left( {-\varepsilon } \right) }{\partial \varepsilon }\hbox {d}\varepsilon \right. \nonumber \\&\qquad \left. -\mathop \int \nolimits _0^\infty \frac{fd\left( {-\varepsilon } \right) -fd\left( \varepsilon \right) }{\left( {\omega -j\tau ^{-1}} \right) ^{2}-4\left( {\varepsilon /\hbar } \right) }\hbox {d}\varepsilon \right] , \end{aligned}$$
(1)
where j is the imaginary unit, \(\varepsilon \) is the energy of the incident wave, \(fd\left( \varepsilon \right) \) is the Fermi–Dirac distribution, \(\hbar \) is the reduced Planck’s constant, and \(\tau \) is the scattering time.
Fig. 14

Magnitude change of the reflection (\(S_{11})\) spectra for electromechanical tunability.

Fig. 15

Magnitude change of the transmission (\(S_{21})\) spectra for electromechanical tunability.

Fig. 16

(a) Perspective view of the proposed MTM design covered with an unknown overlayer, (b) top view of the structure with single OL and (c) top view of the structure with double OL.

Correspondingly, the dielectric constant of the graphene monolayer can be expressed as follows:
$$\begin{aligned} \varepsilon _{\mathrm{g}} = 1+ j (\mathop {\sigma }\nolimits _{\mathrm{g}}{/}\omega \mathop {\varepsilon }\nolimits _{0}\!\Delta ), \end{aligned}$$
(2)
where \(\Delta \) is the graphene thickness and \(\varepsilon _{0}\) is the free space permittivity. Figure 13 shows the real and imaginary parts of the graphene permittivity in THz regime. As one can see from figure 13, the real part of graphene permittivity is very high in lower frequencies and it decreases significantly when the frequency increases. In addition, the imaginary part of the permittivity exponentially decreases when the frequency gets higher, as expected (see eq. (2)).

Now, by changing the thickness of graphene, dielectric constant of graphene monolayer is altered. Since the dielectric constant of graphene is controlled by a physical quantity, this type of tunability can be called electromechanical tunability. Figures 14 and 15 show the reflection and transmission spectra of the structure which is covered with a graphene layer, respectively. The thickness of graphene layer varies from 0.33 nm to 1.32 nm, and four samples are taken by increasing the thickness linearly. The change in magnitude for both the reflection and transmission parameters can be seen in figures 14 and 15. The simulations show that the proposed structure is electromechanically tunable as S-parameters of the structure vary when the dielectric constant of the graphene monolayer varies, and the dielectric constant of the graphene monolayer is controlled by the graphene thickness.

4 Sensor applications

In this section, the proposed MTM structure with graphene layer is used for a double-sided detection system which means both front and back sides of the structure is used for sensing application [30, 31, 32, 33]. An unknown layer is used for the analysis of the structure. The layer is treated as an overlayer (OL) which changes the reflection and the transmission characteristics of the device. The frequency response of the device is investigated when the dielectric constant of the OL is altered. Both single and double OL situations are considered. Figure 16 shows the one-sided perspective view of the structure with OL. Note that the parameters defined in figure 1 are the same and the thickness of the OL is fixed to 2 um.

The simulation results for the single- and double-OL cases are presented in figures 17 and 18, respectively. Permittivity (\(\varepsilon \)) of the OL is altered from 1 to 9 for both cases and five samples in total are taken by increasing the permittivity linearly. Figure 17 represents the transmission for the single-OL case and figure 18 represents the transmission for the double-OL case.
Fig. 17

Transmission parameters (\(S_{21})\) for the single-OL case.

Fig. 18

Transmission parameters (\(S_{21})\) for the double-OL case.

As can be seen in figures 17 and 18, the frequency shifts to the lower frequencies for both single- and double-OL cases when the permittivity (\(\varepsilon \)) of the OL is increased. Stronger shift in frequency is observed with larger permittivity values. Thus, sensitivity increases with the rising OL permittivity for both the cases. Furthermore, when the single- and double-OL cases are compared, it is clearly seen that the sensitivity of the double-OL case is enhanced. Since the hexagonal resonators are placed both in the front and back sides of the substrate, double coating enhances the sensitivity of the sensor device because it has more interaction with OLs [30]. It means that the double-sided cover provides more sensitive detection and greater sensing capability compared to the single-sided detection and sensing.

5 Conclusion

In this study, a graphene-integrated fishnet-based MTM structure comprising hexagonal resonators has been introduced for different purposes such as tunability and sensing applications. In order to show the modification of propagation properties due to the graphene integration, the structure has been simulated with and without graphene layer. The simulation results showed that significant modification can be achieved thanks to the unique properties of graphene. A negative refractive index can be observed for a larger frequency range when graphene layer is integrated. Moreover, the surface current and electric field distributions have been investigated to show the propagation properties and to verify the resonance behaviour of the structure. Parametric studies showed the possibility of tuning the frequency response of the proposed MTM structure by adjusting the physical quantities. Also, the structure has been investigated for sensor applications by adding an unknown layer and altering its permittivity to observe the sensitivity property. The results showed that as the dielectric constant of the unknown layer increases, transmission peaks also increase. Therefore, the composite can be used in antennas, filters, absorbers, sensors and imaging systems. For this study, sensor application has been selected and investigated as a potential application. The simulations indicate that the proposed structure can be effectively used in sensors and many different MTM applications.

Notes

Acknowledgements

The work reported here was carried out at Middle East Technical University-Northern Cyprus Campus (METU-NCC). It is supported by METU-NCC under grant numbers of BAP-FEN-15-D-3 and BAP-FEN-16-K-8.

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of Electrical and Electronics EngineeringMiddle East Technical University-Northern Cyprus Campus (METU-NCC)TRNC / Mersin 10Turkey
  2. 2.Kalkanli Technology Valley (KALTEV)Middle East Technical University-Northern Cyprus Campus (METU-NCC)TRNC / Mersin 10Turkey

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