5. Graphene-based metamaterial reflectarray for orbital angular momentum (OAM) vortex wave

The electromagnetic waves carry both linear and angular momentums. Angular momentum comprises spin angular momentum (SAM) and orbital angular momentum (OAM). The SAM is associated with the circular polarization states of electromagnetic beams. The OAM arises from spatial variations of amplitude and phase that render the beam asymmetric around its propagation axis [55, 56]. In 1992, Allen et al. found that light beam with an azimuthal phase dependence of exp.(ilϕ) carries an OAM, in which ϕ represents the azimuthal angle and l is the topological charge. For any given l, the OAM vortex wave has l interwinded helical phase fronts and a phase singularity with zero intensity on the beam axis. With a theoretically unlimited range of orthogonal eigenstates, OAM offers new degrees of freedom in communication in addition to traditional linear momentum and polarization degrees of freedom [57–60].

An attractive feature of graphene is that its conductivity is changeable by controlling voltage applied to graphene via an external gate. With this characteristic, a graphene-based metamaterial reflectarray is designed for the generation of the wideband OAM vortex waves with tunable modes in this section. As shown in Figure 16, the designed reflectarray with a size of 10 10λ comprises 12 regions, each of which has the same azimuthal angle. Here, λ is wavelength in free space at the frequency of 2.3 THz. In each region, a same graphene-based metamaterial structure is designed. By tuning the conductivities of the graphene sheets in the jth region, the reflection phase of πlj/6 (j = 1, …,12) is achieved such that the whole reflectarray can generate a helical profile of exp.(ilϕ). To guarantee independently adjustable conductivities

Figure 14. Simulated variation of absorption with frequencies for different azimuth angles: (a) TM mode and (b) TE

Figure 15. Variation of the absorption with the chemical potential μc: (a) TE mode and (b) TM mode. Reprinted from

Figure 13. Simulated absorption performance at different incidence angles: (a) TM mode and (b) TE mode. Reprinted

mode. Reprinted from Zhang et al. [38], with permission from the Optical Society of America.

Zhang et al. [38], with permission from the Optical Society of America.

from Zhang et al. [38], with permission from the Optical Society of America.

182 Metamaterials and Metasurfaces

Figure 16. Schematic diagram of the designed reflectarray. (a) The whole array divided into 12 regions, each of which is filled by the same metamaterial unit cells. (b) The side view of the reflectarray. Reprinted from Shi et al. [43], with permission from the IEEE.

Figure 17. The graphene-based metamaterial unit cell and its equivalent circuit model: (a) the unit cells and (b) the equivalent circuit model. Reprinted from Shi et al. [43], with permission from the IEEE.

Figure 18. Reflection phase range for all possible chemical potentials of three graphene layers in a wide frequency band from 1.8 THz to 2.8 THz. Reprinted from Shi et al. [43], with permission from the IEEE.

Figure 19. The OAM beams with the different modes: (a) l = 1, (b) l = 2, (c) l = 3, (d) l = 1, (e) l = 2, and (f) l = 3.

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185

Reprinted from Shi et al. [43], with permission from the IEEE.

Figure 17. The graphene-based metamaterial unit cell and its equivalent circuit model: (a) the unit cells and (b) the

Figure 18. Reflection phase range for all possible chemical potentials of three graphene layers in a wide frequency band

from 1.8 THz to 2.8 THz. Reprinted from Shi et al. [43], with permission from the IEEE.

equivalent circuit model. Reprinted from Shi et al. [43], with permission from the IEEE.

184 Metamaterials and Metasurfaces

Figure 19. The OAM beams with the different modes: (a) l = 1, (b) l = 2, (c) l = 3, (d) l = 1, (e) l = 2, and (f) l = 3. Reprinted from Shi et al. [43], with permission from the IEEE.

of the graphene sheets in each region, a small height difference Δh is introduced to ensure the insulation between two adjacent regions, as shown in Figure 16(b).

vortex waves with l = 1, l = 2, and l = 3 modes and the doughnut-shaped intensity distributions. Note that the radiation patterns with singularity in the center greatly reduce the coupling between the reflectarray and the horn antenna. With the reflection phase range of

In sum, several characteristics of graphene including the conductivity model and equivalent circuit model have been presented. Two graphene-based devices, i.e., metamaterial absorber and metamaterial reflectarray, have been designed. By varying graphene's chemical potential, the wideband tunable absorption for the designed absorber and the broadband tunable OAM modes for the developed reflectarray have been demonstrated, respectively. Graphene pro-

This work is supported by National Natural Science Foundation of China under Contract 61771359 Fundamental Research Funds for the Central Universities (No. JBF180202), and

[1] Caloz C, Itoh T. Electromagnetic Metamaterials: Transmission Line Theory and Micro-

wave Applications. New Jersey: Wiley; 2005. 376 p. DOI: 10.1002/0471754323

vides more degrees of freedom for the design of the tunable metamaterial systems.

in a wide frequency band from 1.8 to 2.8 THz, as shown in Figure 18, the OAM vortex waves can be generated by the proposed reflectarray in the wide frequency band, as shown in Figure 20. It is observed that the desirable spiral phase distributions can be obtained in the

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360

whole frequency band.

Acknowledgements

Conflict of interest

Author details

References

Yan Shi\* and Ying Zhang

Technology Innovation Research Project of the CETC.

No conflict of interest was reported by the authors.

\*Address all correspondence to: shiyan@mail.xidian.edu.cn

School of Electronic Engineering, Xidian University, Xi'an, Shaanxi, China

6. Conclusion

To obtain a desirable reflection phase in each region, a metamaterial unit cell composed of a three-layer sandwich structure has been designed, as shown in Figure 17. Each sandwich structure comprises graphene/Al2O3/SiO2 materials from the top to the bottom. An insulating layer of Al2O3 material is inserted between two adjacent sandwich structures. A ground consisting of an Au material is placed at the bottom of the unit cell. The designed unit cell periodicity is P = 20 μm, and the thicknesses of SiO2, Al2O3, and Au materials are 12 μm, 10 nm, and 5 μm, respectively. In each sandwich structure, an external DC voltage is applied between the graphene layer and the SiO2 layer to control the conductivity of graphene. For convenience, the chemical potentials of the graphene layers from the top to the bottom are denoted as "μc1," "μc2," and "μc3," respectively. With the equivalent circuit model given in Figure 17(b), the maximum reflection phase range of the proposed unit cell can be obtained. As shown in Figure 18, the reflection phase range of the proposed unit cell can cover 360o in a wide frequency band from 1.8 to 2.8 THz, when three chemical potentials independently vary from 1 to 1 eV.

A wideband horn antenna as the excitation is used to generate a wave incident on the reflectarray. Figure 19 shows the OAM vortex waves with different modes generated by the reflectarray at 2.3 THz. We can clearly observe the spiral phase distributions of the OAM

Figure 20. Simulated OAM beams with l = 1 mode at different frequencies. Reprinted from Shi et al. [43], with permission from the IEEE.

vortex waves with l = 1, l = 2, and l = 3 modes and the doughnut-shaped intensity distributions. Note that the radiation patterns with singularity in the center greatly reduce the coupling between the reflectarray and the horn antenna. With the reflection phase range of 360 in a wide frequency band from 1.8 to 2.8 THz, as shown in Figure 18, the OAM vortex waves can be generated by the proposed reflectarray in the wide frequency band, as shown in Figure 20. It is observed that the desirable spiral phase distributions can be obtained in the whole frequency band.
