Design of tunable biperiodic graphene metasurfaces

Periodic structures with subwavelength features are instrumental in the versatile and effective control of electromagnetic waves from radio frequencies up to optics. In this paper, we theoretically evaluate the potential applications and performance of electromagnetic metasurfaces made of periodically patterned graphene. Several graphene metasurfaces are presented, thereby demonstrating that such ultrathin surfaces can be used to dynamically control the electromagnetic wave reflection, absorption, or polarization. Indeed, owing to the graphene properties, the structure performance in terms of resonance frequencies and bandwidths changes with the variation of electrostatic bias fields. To demonstrate the applicability of the concept at different frequency ranges, the examples provided range from microwave to infrared, corresponding to graphene features with length scales of a few millimeters down to about a micrometer, respectively. The results are obtained using a full-vector semianalytical numerical technique developed to accurately model the graphene-based multilayer periodic structures under study.

Figure 1

(a) Real part and (b) imaginary part of the conductivity (${\sigma }_d$) in terms of frequency for various bias electric fields in the microwave regime.

Figure 2

(a) Schematic illustration of the graphene biperiodic structure consisting of graphene cross-shaped patches arranged in a two-dimensional lattice and under a normally incident plane wave. (b) Unit cell of the lattice. (c) Reflected and transmitted energies versus frequency. The filled circles represent the results obtained when accounting for the spatial dispersion terms in the case $E_0=20\mathrm{V}/\mathrm{nm}$.

Figure 3

Normalized induced current on the patch at $\omega =19.5\mathrm{GHz}$ for different applied electrostatic fields are plotted for a free-standing FSS consisting of a two-dimensional lattice of cross-shaped graphene patches exposed to a normal incident plane wave: (a) $E_0=0\mathrm{V}/\mathrm{nm}$, (b) $E_0=2\mathrm{V}/\mathrm{nm}$, and (c) $E_0=20\mathrm{V}/\mathrm{nm}.$

Figure 4

(a) Schematic illustration of the graphene biperiodic structure consisting of dc-connected patches on both sides of a GaAs layer residing on an infinitely thick GaAs substrate and assumed to be subjected to a normally incident plane wave. (b) The unit cell of the lattice is depicted with the dimensions; the top figure is the top view of the unit cell and the bottom figure is its side view. (c) The reflected energy versus frequency is plotted for the unbiased case as well as the biased electrostatic field with $E_0=2.2\mathrm{V}/\mathrm{nm}$.

Figure 5

Magnitude of the total electric field is shown for two resonant frequencies, namely, (a) 11.3 THz and (b) 20.0 THz. The upper figures correspond to unbiased graphene patches and the lower ones are obtained for an electrically biased graphene surface with $E=2.2\mathrm{V}/\mathrm{nm}$.

Figure 6

Schematic illustration of the absorber structure consisting of five graphene layers printed on a glass substrate: (a) the graphene patch layer, (b) the side view of the absorber and the biasing circuit. (c) Magnitude of the reflection coefficient versus frequency for different applied bias voltages ($V_g$) are plotted. In the subfigure, magnitude of the reflection coefficient at $f_0=11.2\mathrm{GHz}$ is plotted in terms of the applied bias voltages ($V_g$) for the considered absorber.

Figure 7

Schematic illustration of the polarizer designed for infrared frequencies which consists of two layers of graphene printed on a Si${}_2$N${}_3$ substrate: (a) the graphene patch layer, (b) the side view of the polarizer and the biasing circuit. (c) Power reflection coefficients $R_{xx}$ and $R_{yy}$ versus frequency for bias voltages $V_g=50$ and $0\mathrm{V}$ are plotted for the depicted multilayer periodic graphene metasurface.