This example shows how to simulate the transmission of light through a periodic array of graphene ribbons deposited on top of a glass (SiO2) substrate. The chemical potential of graphene can be tuned by applying an external biasing voltage. As illustrated in this example, this provides a mechanism for tuning the absorption resonance of the structure.
The periodic array of graphene ribbons is excited by a plane wave normally incident on the structure. The transmitted power exhibits a dip at a resonant wavelength that depends on the chemical potential of the graphene ribbons. This can be demonstrated by using the 3D FDTD simulation set up in graphene_THz_metamaterial.fsp, as shown below. The graphene ribbons are oriented along the y direction, so periodic boundary conditions are used along the y direction. Antisymmetric boundary conditions are used along the x direction.
The graphene material type (discussed in Modeling methodology) is employed to generate the surface conductivity of the graphene ribbons for the frequency range 15THz to 45THz (wavelength from about 7μm to 20μm). This model includes both intraband and interband effects. Two values of chemical potential are considered here: 0.265eV and 0.217eV. These two choices reproduce the power transmission curves presented in reference  where chemical potentials (or Fermi levels) of 0.25eV and 0.20eV are used. The slight difference between the values of chemical potential employed here and those employed in  are due to the simplified Drude-like conductivity model employed there. The following figures, obtained using the script graphene_THz_conductivity.lsf show the real and imaginary parts of the surface conductivity for the Drude-like conductivity model of reference  and the full surface conductivity model generated by the graphene material type.
In addition to considering two different chemical potential values, we also consider graphene ribbons that consist of one, two and four layers of graphene. As pointed out in Modeling methodology, this can be accomplished by scaling the surface conductivity by the number of layers.
The transmitted power vs. wavelength results, shown below, for the outlined chemical potential values (0.265eV and 0.217eV) and numbers of layers (N = 1,2,4) can be obtained by running the script graphene_THz_metamaterial.lsf. The results closely match those presented in Figure 3(a) of reference . As expected, the resonance shifts to shorter wavelengths for increasing chemical potential and increasing numbers of layers. Each of the lines in the figure was obtained using a single simulation with identical source and mesh settings. The small oscillations in the transmission spectra are caused by an early termination of the simulation due to the auto shutoff min (1e-5 in the attached simulation file); if the auto shutoff min is reduced to 1e-8 these artificial oscillations are removed.
- H. Chu and C. Gan, "Active plasmonic switching at mid-infrared wavelengths with graphene ribbon arrays," Appl. Phys. Lett. Vol. 102, 231107 (2013).
- Weilu Gao, Jie Shu, Ciyuan Qiu, and Qianfan Xu, "Excitation of plasmonic waves in graphene by guided-mode resonances", ACS Nano Vol. 6 (9), 7806-7813 (2012).