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Abstract
A graphene-based metamaterial transmitarray antenna is proposed to generate tunable orbital angular momentum (OAM) vortex waves in terahertz. Theoretical design of the transmitarray antenna has been developed by using the transmission line network model, and a multilayer graphene-based metamaterial element has been designed. By changing the chemical potentials of the graphene sheets, the 360° transmission phase range of the element is achieved in a broad band from 4.2 THz to 5.6 THz. By arranging the metamaterial element into a transmitarray, the OAM waves with tunable modes including l = 0, ±1, ±2 and the mode purity greater than 0.96 are generated. Simulation results are given to demonstrate good performance of the proposed design, which provides a feasible way to the efficient generation and manipulation of the OAM vortex waves in terahertz.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Orbital angular momentum (OAM) vortex waves have attracted increasing attentions in recent years due to its promising potential ability in wireless communication. Different from the conventional plane waves, the OAM vortex beam has an azimuthal phase of exp(jlφ) and its Poynting vector abides by a spiral trajectory around the optical axis, where l is the topological charge [1]. With the theoretically unlimited orthogonal eigenstates, the OAM beam has been considered to boost communication capacity.
There have been many attempts to generate the OAM beams including spiral phase plate [2], holographic diffraction gratings [3], spiral reflectors [4], and antenna arrays [5]. Recent progress in metamaterials has enabled new ways to manipulate the OAM beams in microwave and optics [6]. By properly designing sub-wavelength topology element, various the OAM waves including multiple beams and different modes [7] and non-diffractive beams [8] are generated. However, in these reported designs the OAM modes cannot be changed, once the metamaterial-based structures are designed. In recent years, graphene has caused tremendous interests owing to unique electrical and mechanical properties. The graphene has the highest mobility in known materials. By changing electrochemical potential, the conductivity of the graphene can be flexibly tuned. With the tunable feature, the graphene becomes a natural candidate for the designs of the tunable devices including the absorbers [9], reflectarrays [10], lens [11], modulation [12], etc.
The contribution of the work is to develop a graphene-based metamaterial transmitarray antenna to flexibly generate the OAM vortex beam with the tunable modes. A design method based on a transmission line network model has been proposed to design a stacked graphene-based metamaterial unit cell. By applying different external gate voltages to the graphene sheets, the transmission phase range of the designed unit cell can cover 360°, which distinguishes the proposed design from the conventional metamaterial/metasurface based designs in which the phase variation is achieved by either adjusting the dimensions of the unit cell [7] or rotating the unit cell [8]. By arranging the unit cell into an array along the azimuthal direction, the resultant transmitarray has a helical phase profile of exp(jlφ). Illuminated by a horn antenna, the transmission wave through the transmitarray becomes an OAM vortex wave. As the chemical potentials of the graphene sheets vary with the change of the applied gate voltages, the OAM wave with different modes including 0, ±1, and ± 2 can be dynamically obtained in a wide frequency band from 4.2 THz to 5.6 THz.
2. Design of metamaterial transmitarray
Figure 1 shows the proposed metamaterial unit cell and the corresponding transmission line network model. The metamaterial unit cell is a four-layer configuration, each of the four layers is same and consists of a graphene-quartz-graphene sandwich structure. The side length of the graphene sheet is 20 µm, and the thickness of the quartz hd is 5 µm. An air layer with a thickness of h0=10 µm is placed between two adjacent sandwich structures. The relative permittivity of the quartz is 3.78. Considering that the thickness of the monolayer graphene is about 0.335 nm, the monolayer graphene is regarded as an infinitesimally thin conductive sheet. The corresponding conductivity can be analytically approximated as according to Kubo formula [13–15]
in which intra-band conductivity σintra and inter-band conductivity σinter are given as, respectivelyHere e is electron charge, kB is Boltzmann constant, ℏ is reduced Planck’s constant, ω is radian frequency, T = 300 K is room temperature, μc is defined as chemical potential of graphene, and Γ=1/(2τ) is charged particle scattering rate with the momentum relaxation time τ = 2ps.
With the designed unit cell, the corresponding TL network is shown in Fig. 1. Each graphene sheet is considered as a shunt admittance Ys(i)=1/σ(i) (i = 1, 2). The quartz and the air layers, respectively, are equivalent to the TLs with the phase constants of βd and β0 and the lengths of hd and h0. Each part in the unit cell are cascaded together to achieve the whole TL network model. The transfer matrix of the whole network [A] [16] can be written as
Fig. 2. Comparison of S21 between the FW simulation and the TL network model. (a). Magnitude of S21. (b) Phase of S21.
The proposed metamaterial unit cell is arranged into an array along the azimuthal direction, as shown in Fig. 4. The OAM vortex wave can be generated by the transmitarray as the variation of the transmission phase with the azimuthal angle φ continuously covers 360°. However, it is infeasible for a continuous phase variation. A good approximation is to discretize the transmission phase of 360° into N piecewise segments, each of which covers the phase of 360°/N. Here 8 segments are used to approximately cover the transmission phase of 360°, as shown in Fig. 4. The dimensions of the transmitarray are as follows: L1 = 1400 µm, L2 = 1410 µm, and Lg = 0.5 µm. Table 1 gives the chemical potentials of 8 segments and the corresponding S21 at 4.9 THz. It can be observed that the transmission phase difference between two adjacent segments is 45° and the total phase range of the 8 segments covers 360°. Moreover, the magnitude of S21 is better than −2 dB, which means the small transmission loss of the designed transmitarray. A standard circular horn antenna as the feeding source is placed at the top of the transmitarray with a focal length to diameter ratio of 0.29. A square observation plane with a side length of 3000 µm is located at the bottom of the transmitarray with a distance of 3150 µm, on which the phase, the magnitude, the complex magnitude of the electric field are solved. The phase distribution corresponding to the OAM wave with the mode of l=+1 is observed on the observation plane at 4.9 THz, as shown in Fig. 5.
Table 1. Chemical potentials of the graphene in 8 segments and the corresponding S21.
To tune the mode of the OAM wave, the variable gate voltages Vd are applied between each graphene sheet of the transmitarray and the ground. Here the gold as a ground is placed around the transmitarray, as shown in Fig. 4. Moreover, a small gap of Ly = 0.5 µm is introduced between two adjacent graphene sheets located in the same plane to isolate different gate voltages. It is worthwhile pointing out that the use of the small gap does not affect the performance of the transmitarray. With the voltage, the chemical potential μc of the graphene can be estimated by the following formula [18]:
in which, vF≈9×105 m/s represents the Fermi velocity of the Dirac fermions, a0≈ 9×1016 m−2V−1 is estimated through a single capacitor model, and VDirac=0.8 V denotes the Dirac voltage offset caused by the natural doping.When the chemical potentials in the segments 2, 4, 6, and 8 are changed to be same as those in the segments 1, 3, 5, and 7, respectively, the OAM wave with l = 2 is generated, as shown in Fig. 5. If the chemical potentials in the 8 segments are same, the OAM wave with l = 0, i.e., the plane wave, is obtained. If we tune the gate voltages to exchange the chemical potentials of the segments 2, 3, and 4 with those of the segments 8, 7, and 6, respectively, the OAM wave with l=−1 is generated, as shown in Fig. 5. In addition, a doughnut-shaped radiation patterns characterized by the OAM wave with different modes can be observed in Fig. 5. In order to evaluate the performance of the OAM wave produced by the transmitarray, a spectral analysis of Fourier transform [19,20] is implemented. The magnitude and phase of the OAM wave are sampled along a circle with a radius of 1000 µm, as shown in the inset of Fig. 6. The mode purities for the OAM wave with l = 1 and l = 2 are larger than 96%. Furthermore, as shown in Fig. 3, the 360° transmission phase in a wide frequency band means that the OAM wave can be generated in a broad band. As the chemical potentials of the graphene sheet are chosen in the frequency band from 4.2 THz to 5.6 THz according to Fig. 3, the OAM wave with l = 1 can be achieved, as shown in Fig. 7. Similar to the case at 4.9 THz, the OAM wave with other modes can be generated in the wideband of 4.2∼5.6 THz.
3. Conclusion
In this paper, a graphene-based metamaterial transmitarray is designed to generate the tunable OAM vortex wave in a wide band covering 4.2∼5.6 THz. With the transmission line network analysis, a multilayer metamaterial element is designed and the 360° transmission phase range can be achieved in a broad band. With the proposed multilayer element, the transmitarray is designed to produce the high-purity OAM wave with the tunable modes of l = 0, ±1, ±2 in a broad band. The simulated results are given to verify the proposed design.
Funding
National Natural Science Foundation of China (61771359); Natural Science Basic Research Plan in Shaanxi Province (2018JM6006).
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