# A novel tunable antenna at THZ frequencies using graphene-based Artificial Magnetic Conductor (AMC).

1. INTRODUCTIONIn recent years, artificial magnetic conductor (AMC) ground plane has been widely used in the design and implementation of high-efficient and low-profile antennas [1-6]. In comparison with perfect electric conductor (PEC) ground plane, the AMC one can significantly reduce the separation distance from the radiator to the ground plane due to the additional capacitance introduced by the periodic pattern. For some antennas based on the modes excited on the surface, the AMC can expand the bandwidth [7]. However, for other applications, especially the ultra-wide bandwidth (UWB) antennas, it may cause severe bandwidth degradation due to its relatively narrowband [1]. To achieve dynamic tuning capacity and broaden the AMC bandwidth, the capacitive lumped elements such as varactor diodes were inserted between the metallic AMC units [1, 3]. In [4], an adjustable air-gap was used in the substrate to attain the frequency band selection, which can also be realized by adopting magnetic controllable ferrite material instead of traditional dielectric [6]. Nevertheless, at very high frequencies (for example THz), all of the tuning methods mentioned above become unrealistic because of the extremely small sizes of the antennas.

On the other hand, graphene has attracted much attention due to its extraordinary electrical, thermal, mechanical and optical properties [8, 9]. The dynamic variation of its surface conductivity, which can be modulated with an external electric field or chemical doping, makes the tunability of THz devices a reality. In [10], the radiation pattern of dipole antenna array was controlled by switching between the low- and high-resistivity states of graphene ground plane. A beam reconfiguration antenna was designed using a switchable high impedance surface (HIS) [11]. In [12], graphene acts as an antenna radiator and has an active resonance frequency based on the concept of surface plasmonic resonance.

In this work, a novel tunable antenna using graphene-based AMC is proposed for THz applications. With different electric fields applied, the equivalent capacitance of the AMC is changed, and the resonance frequency shifts subsequently. Compared to other tuning structures, the graphene-based AMC can be effective used for nanoscale THz devices and is easy to process. Moreover, it can provide a wider bandwidth than previously proposed models.

2. THE REFLECTION CHARACTERISTICS OF GRAPHENE-BASED AMC

The AMC unit cell made of graphene sheet is shown in Figure 1(a), and the surface impedance of the patch array at THz band can be approximated by [6,13,14]

[Z.sub.g] = j ((D/D - g) (1/[sigma]) - (1/w[C.sub.eff])) (1)

[C.sub.eff] = 1/[pi] [[epsilon].sub.0] ([[epsilon].sub.r] + 1) D ln [csc (([pi]/2) (g/D))] (2)

where D is the period of the square patches, g is the gap between adjacent patches, [tau] is the relaxation time, [[epsilon].sub.r] is the relative permittivity of the substrate, and [C.sub.eff] is the capacity related to the patch geometry and background environment. It is known that graphene can be modeled as an infinitesimally thin surface characterized by a surface conductivity [sigma]([omega], [GAMMA], [[micro].sub.c], T). With the help of Kubo formalism, the Drude model of graphene surface conductivity in intraband can be

given by [15]

[sigma] ([omega]) = [[sigma.sub.0]/ (1 + j[omega][tau]) (3)

[[sigma].sub.0] = [e.sup.2][k.sub.B][T.sub.[tau]]/[pi][h.sup.2] [[[micro].sub.c]/[k.sub.B]T + 2ln (1 + [e.sup.- [[micro].sub.c]/[k.sub.B]T)] (4)

where [omega] is the angular frequency, [k.sub.B] the Boltzmann's constant, h the reduced Planck's constant, T the temperature, and [[micro].sub.c] the chemical potential of graphene sheet. Throughout this work, we assume T = 300K, [tau] = 1 ps, and [[micro].sub.c] is below 1 eV [16]. The relationship between the electric bias field E and [[micro].sub.c] (see Figure 2) can be calculated by [15]

E = e/[pi][h.sup.2]vf[[epsilon].sub.0] [[integral].sup.[infinity].sub.0] [epsilon] ([f.sub.d] ([epsilon]) - [f.sub.d] ([epsilon] + 2 [[micro].sub.c])) d[epsilon] (5)

where

[f.sub.d] ([epsilon]) = [(e([[epsilon]-[[micro].sub.c])/=[k.sub.B]T] + 1).sup.-1] (6)

When [omega][tau] >> 1, the grid impedance can be approximated as a pure reactance, and [Z.sup.[omega][tau]>>1.sub.g] = [(j[omega][C.sub.g]([omega])).sup.-1], where [C.sub.g]([omega]) is the equivalent capacitance of the grid pattern.

According to the transmission line theory, the impedance of the grounded substrate for normal incident wave can be written as

[Z.sub.d] = j[[eta].sub.0] tan ([k.sub.d]h) / [square root of ([[epsilon].sub.r])] = j[omega][L.sub.d] ([omega]) (7)

where [[eta].sub.0] is the wave impedance in free space, h is the substrate thickness, [k.sub.d] (= [omega] [square root of ([[micro].sub.0][[epsilon].sub.0][[epsilon].sub.r])) is the wave number of the incident wave

in substrate, and Ld(w) is the equivalent inductance of the grounded substrate.

The total surface impedance is a parallel combination of capacitance grid impedance of the array and inductive impedance of the grounded substrate [13]

[Z.sub.s] = [Z.sub.g] [Z.sub.d]/([Z.sub.g] + [Z.sub.d]) (8)

As shown in Figure 1(b), the reflection phase R can be computed using a normally incident TE wave by

R = ([Z.sub.s] - [[eta].sub.0])/([Z.sub.s] + [[eta].sub.0]) (9)

A comparison of the reflection phase obtained by analytical equations and simulation is shown in Figure 3, and good agreement is obtained.

Here, the impact of chemical potential [[micro].sub.c] on the resonance frequency of AMC surface is investigated in detail. As shown in Figure 4(a), a maximum shift of 0.75 THz (from 1.47 to 2.22 THz) can be achieved in the resonance frequency of AMC surface by varying [[micro].sub.c] from 0.15 to 1eV. In addition, the tuning capacity at low [[micro].sub.c] is more effective than that at high one. As [[micro].sub.c] increases, the phase curve becomes more flat, which means an improved bandwidth. To explain this phenomenon, Figure 5 shows the equivalent circuit model of AMC surface, and its input impedance is inductive as the substrate thickness is much smaller than the wavelength [13]. Therefore, the resonance frequency of AMC surface can be expressed as

[[omega].sub.0] = 1/ [square root of ([C.sub.g][L.sub.d])] (10)

The bandwidth of AMC is defined as the frequency range when its reflection phase changes from +90[degrees] to -90[degrees], and is proportional to [square root of ([L.sub.d]/[C.sub.g])]. As [[micro].sub.c] increases, the grid impedance becomes less capacitive, and therefore, both the resonance frequency and bandwidth increase. Figure 4(b) shows the reflection magnitude of the AMC surface, and its minimum value is about -11 dB. The AMC ground plane becomes more reflective as [[micro].sub.c] increases, which is caused by the mushroomed carrier concentration and ensuing ohmic loss in graphene patches. However, when [[micro].sub.c] < 0.15 eV, the ohmic loss in graphene becomes severe and the reflection magnitude drops rapidly. Under such circumstances, the graphene patch array should be viewed as an absorber rather than the AMC ground plane. Note that the spatial dispersion may significantly affect the waves excited on graphene transferred onto a dielectric, as demonstrated in [17]. However, it may not be important in our work due to the large [[micro].sub.c] and the relatively low [[epsilon].sub.r] of the substrate employed in our simulation. In addition, the current full-wave simulators cannot take this phenomenon into account, so the spatial dispersion is excluded in this work.

3. ANTENNA MODEL AND CHARACTERIZATION

In this section, a simple bowtie antenna made of Cu is placed above the graphene-based AMC ground plane, as shown in Figures 6(a) and (b). The potential fabrication strategy is briefly introduced as follows. A 10-[[micro]m-thick grounded Si[O.sub.2] is employed as the AMC substrate. In consideration of the feasibility in fabrication, a 300-[micro]m-thick silicon handle wafer is bounded under the quartz substrate. Above the quartz is a 50-nm-thick polycrystalline silicon layer and 10-nm-thick [Al.sub.2] [O.sub.3] film in sequence, which can be easily obtained by RF sputtering. The AMC ground plane consists of 15 x 15 graphene square patches with D = 10, [micro]m and g = 1 [micro]m, which can be patterned by high resolution e-beam lithography tool. The graphene patches can be connected by 60-nm-wide graphene nano-ribbons (GNR) to keep all patches at the same / c when applying a DC voltage between the AMC and polycrystalline silicon [18, 19]. The GNRs are excluded in our simulation due to their negligible impact on the whole device. Using the chemical vapor deposition (CVD), a 2-[micro]m-thick Si[O.sub.2] is deposited on graphene-based AMC, and the gold antenna can be finally fabricated by photolithography method.

The original resonance frequency of the bowtie antenna is optimized to be 2 THz. Figures 7(a)-(d) show the return loss of the antenna system (including the bowtie antenna and graphene-based AMC ground plane) at different [[micro].sub.c]. It is obvious that the operating frequency of the antenna will be greatly influenced when the active AMC is introduced. The best matched frequency point of the antenna system is always close to the resonance frequency of the AMC. At [[micro].sub.c] = 0.25 eV, the bandwidth of the antenna system is 11% (0.37THz), which is smaller than that of the original bowtie antenna. However, with the increase of / c, the AMC bandwidth increases and the antenna system can be best matched at several frequencies, which will expand its bandwidth greatly (from 22% to 47%). Therefore, by varying the applied voltage, the operating frequency of the antenna system shift from 1.45 to 3.21 THz.

Figures 8(a) and (b) show the gain patterns of the bowtie antenna with and without ground plane, respectively. The maximum gain of the antenna system is about 9.19dB, which is much larger than that of the bowtie antenna without the ground plane. Cbviously, both the traditional and AMC ground planes can significantly improve the gain. However, the traditional ground plane leads to mismatch, as shown in Figure 9. Further, the gain of the antenna system at different [[micro].sub.c] is plotted in Figure 10. It is found that the maximum gain reaches its peak value near the resonance frequency of AMC and decreases when deviating from this frequency.

4. CONCLUSION

In this paper, a novel tunable low-profile antenna is developed. First, the tunability of a graphene-based AMC is demonstrated by varying its chemical potential. It is shown that both the resonance frequency and bandwidth increases with the applied voltage. Then, the bowtie antenna is mounted above the graphene-based AMC ground plane to form the whole tunable antenna system. The operating frequency of the antenna system can be tuned from 1.45 to 3.21 THz when adjusting the chemical potential from 0.25 to 1 eV. Remarkable improvement of the gain can be observed, which has the peak value larger than 9 dB.

ACKNOWLEDGMENT

This work was supported by the Program of Zhejiang Leading Team of Science and Technology Innovation.

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Xu-Chen Wang *, Wen-Sheng Zhao, Jun Hu, and Tian Zhang

Centre for Opt. & EM Research, Zhejiang Provincial Key Lab for Sensing Technologies, State Key Lab of MOI, Zhejiang University, Hangzhou 310058, China

Received 2 May 2013, Accepted 31 May 2013, Scheduled 9 June 2013

* Corresponding author: Xu-Chen Wang (zjuwangxuchen@163.com).

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Author: | Wang, Xu-Chen; Zhao, Wen-Sheng; Hu, Jun; Zhang, Tian |
---|---|

Publication: | Progress In Electromagnetics Research Letters |

Article Type: | Abstract |

Geographic Code: | 9CHIN |

Date: | Jun 1, 2013 |

Words: | 2504 |

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