4. Graphene-based metamaterial absorber

With extraordinary electronic and optical properties, graphene has caused enormous research interest in recent years. The conductivity or carrier density of graphene can be tuned by the chemical potential via an external gate voltage. Various intriguing applications such as tunable cloaks [40], reflectarray [42, 43], nonlinear optical devices [44], etc., have been proposed and experimentally demonstrated. On the other hand, since Landy et al. proposed a thin and nearperfect metamaterial absorber in 2008 [52], various metamaterial absorbers have been demonstrated from microwave to optical frequencies [53, 54]. The fascinating property of the tunable conductivity promises graphene a good candidate for the design of the tunable metamaterial absorber. In this section, a broadband tunable, wide-angle, and polarization-insensitive graphene-based metamaterial absorber is designed.

Figure 11 shows the designed metamaterial absorber. The unit cell of metamaterial absorber with a periodicity of 2 μm consists of four layers from the top to the bottom: a dual ELC unit composed of Au with a thickness of 0.1 μm, a graphene sheet, a BaF2 material with a thickness of 0.24 μm, and an Au material with a thickness of 0.5 μm. Figure 12 shows the absorbing spectra of the proposed absorber for the chemical potential of μ<sup>c</sup> = 0.5 eV when TE- and TMpolarized plane waves are normally incident on the proposed absorber, respectively. It can be observed that for TE polarization, a wide absorption characteristic of 90% with a 41.12% fractional bandwidth from 27.78 to 42.16 THz is obtained. Similarly, the absorbing band for the TM polarization covers from 26.78 to 40.06 THz with a 39.74% fractional bandwidth.

from 0 to 60

for both TE and TM polarizations, the absorptions remain above 80% in the

achieved. Due to the approximate symmetry of the designed absorber, the absorption is nearly

Figure 12. Simulated absorptivity of the proposed absorber with μ<sup>c</sup> = 0.5 eV for TE and TM polarizations. Reprinted from

Figure 11. The proposed graphene-based metamaterial absorber. (a) Metamaterial unit cell. (b). Infinite periodic simulation model with periodic boundary conditions (PBC) around the unit cell. (c). A tunable gate voltage applied to the proposed absorber. All dimensions are in micrometer: w = 0.16, s = 0.2, t = 0.12, m = 0.1, d1 = 0.4, and d2 = 0.2. Reprinted

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Figure 15 demonstrates absorption variation of the proposed absorber with the chemical potential of graphene. For the TE polarization, the fractional absorbing band of the absorption of 90% with μ<sup>c</sup> = 0.2 eV is 44.8% from 25.08 to 39.56 THz. With the increase of the chemical potential, the absorption curve has a blue shift accompanied by an approximately unchanged

, the absorption over 90% can be

whole operating band. Especially, for incident angle below 50

independent of polarization, as shown in Figure 14.

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.

Figures 13 and 14 illustrate the polarization and angular dependences of the proposed absorber with μ<sup>c</sup> = 0.5 eV, respectively. As shown in Figure 13, when the incident angle varies

Figure 11. The proposed graphene-based metamaterial absorber. (a) Metamaterial unit cell. (b). Infinite periodic simulation model with periodic boundary conditions (PBC) around the unit cell. (c). A tunable gate voltage applied to the proposed absorber. All dimensions are in micrometer: w = 0.16, s = 0.2, t = 0.12, m = 0.1, d1 = 0.4, and d2 = 0.2. Reprinted from Zhang et al. [38], with permission from the Optical Society of America.

4. Graphene-based metamaterial absorber

Figure 10. Absorption of the graphene-based metasurface structure.

180 Metamaterials and Metasurfaces

graphene-based metamaterial absorber is designed.

With extraordinary electronic and optical properties, graphene has caused enormous research interest in recent years. The conductivity or carrier density of graphene can be tuned by the chemical potential via an external gate voltage. Various intriguing applications such as tunable cloaks [40], reflectarray [42, 43], nonlinear optical devices [44], etc., have been proposed and experimentally demonstrated. On the other hand, since Landy et al. proposed a thin and nearperfect metamaterial absorber in 2008 [52], various metamaterial absorbers have been demonstrated from microwave to optical frequencies [53, 54]. The fascinating property of the tunable conductivity promises graphene a good candidate for the design of the tunable metamaterial absorber. In this section, a broadband tunable, wide-angle, and polarization-insensitive

Figure 11 shows the designed metamaterial absorber. The unit cell of metamaterial absorber with a periodicity of 2 μm consists of four layers from the top to the bottom: a dual ELC unit composed of Au with a thickness of 0.1 μm, a graphene sheet, a BaF2 material with a thickness of 0.24 μm, and an Au material with a thickness of 0.5 μm. Figure 12 shows the absorbing spectra of the proposed absorber for the chemical potential of μ<sup>c</sup> = 0.5 eV when TE- and TMpolarized plane waves are normally incident on the proposed absorber, respectively. It can be observed that for TE polarization, a wide absorption characteristic of 90% with a 41.12% fractional bandwidth from 27.78 to 42.16 THz is obtained. Similarly, the absorbing band for the TM polarization covers from 26.78 to 40.06 THz with a 39.74% fractional bandwidth.

Figures 13 and 14 illustrate the polarization and angular dependences of the proposed absorber with μ<sup>c</sup> = 0.5 eV, respectively. As shown in Figure 13, when the incident angle varies

Figure 12. Simulated absorptivity of the proposed absorber with μ<sup>c</sup> = 0.5 eV for TE and TM polarizations. Reprinted from Zhang et al. [38], with permission from the Optical Society of America.

from 0 to 60 for both TE and TM polarizations, the absorptions remain above 80% in the whole operating band. Especially, for incident angle below 50 , the absorption over 90% can be achieved. Due to the approximate symmetry of the designed absorber, the absorption is nearly independent of polarization, as shown in Figure 14.

Figure 15 demonstrates absorption variation of the proposed absorber with the chemical potential of graphene. For the TE polarization, the fractional absorbing band of the absorption of 90% with μ<sup>c</sup> = 0.2 eV is 44.8% from 25.08 to 39.56 THz. With the increase of the chemical potential, the absorption curve has a blue shift accompanied by an approximately unchanged

fractional band. By adjusting the chemical potential from 0.2 to 0.8 eV, the absorbing band continuously covers from 25.08 to 44.81 THz. By comparison, for the TM polarization, the fractional absorbing bandwidth firstly increases and then decreases as the chemical potential increases. With the variation of the chemical potential from 0.2 to 0.8 eV, the absorbing band of

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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 tradi-

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 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

the absorption of 90% continuously covers from 25.74 to 40.06 THz.

tional linear momentum and polarization degrees of freedom [57–60].

momentum (OAM) vortex wave

permission from the IEEE.

5. Graphene-based metamaterial reflectarray for orbital angular

Figure 13. Simulated absorption performance at different incidence angles: (a) TM mode and (b) TE mode. Reprinted from Zhang et al. [38], with permission from the Optical Society of America.

Figure 14. Simulated variation of absorption with frequencies for different azimuth angles: (a) TM mode and (b) TE mode. Reprinted from Zhang et al. [38], with permission from the Optical Society of America.

Figure 15. Variation of the absorption with the chemical potential μc: (a) TE mode and (b) TM mode. Reprinted from Zhang et al. [38], with permission from the Optical Society of America.

fractional band. By adjusting the chemical potential from 0.2 to 0.8 eV, the absorbing band continuously covers from 25.08 to 44.81 THz. By comparison, for the TM polarization, the fractional absorbing bandwidth firstly increases and then decreases as the chemical potential increases. With the variation of the chemical potential from 0.2 to 0.8 eV, the absorbing band of the absorption of 90% continuously covers from 25.74 to 40.06 THz.
