This example demonstrates how to simulate a graphene waveguide switch operating in the near infrared (30 THz). The waveguide consists of a graphene stripe deposited on a dielectric substrate. This configuration supports a surface plasmon mode that can be either suppressed or allowed to propagate depending on the biasing voltage that is applied to the graphene stripe. In the on-state, the same biasing voltage is applied to the entire graphene stripe and the surface plasmon propagates freely. In the off-state (shown below), a different biasing voltage is applied to the middle section (in red) in order to suppress the propagation of the surface plasmon mode.
Simulation setup
The project file graphene_waveguide_switch.fsp sets up the 3D FDTD simulation as shown below. The graphene waveguide is assumed to be 350nm long, and the graphene material type described in Modeling methodology is used to model the graphene stripe (with a scattering rate of 0.11meV and a temperature of 300K). Applying a biasing voltage to the graphene stripe is equivalent to modifying its chemical potential. In the on-state, a chemical potential of 0.5eV (corresponding to Von) is applied to the entire graphene stripe. In the off-state, a chemical potential of 0.1eV (corresponding to Voff) is applied to a short 50nm section in the middle of the waveguide (a chemical potential of 0.5eV is applied elsewhere). The provided project file sets up the 3D FDTD simulation in the off-state. To simulate the on-state, the chemical potential of the middle section must be changed to 0.5eV.
The electric field profile of the surface plasmon mode excited by the mode source is shown below. The surface plasmon is injected in the x direction and its effective index is estimated to be
$$ n_{\mathrm{eff}}=54.75+i 0.09 $$
Three different power monitors record the fields on the structure. For illustration purposes, the real part of Ez was extracted from the XY plane power monitor for both the on and off states. The dashed lines in the image below mark the span of the waveguide section that employs a lower chemical potential to suppress the surface plasmon mode. As expected, the surface plasmon propagates with negligible loss in the on-state and is strongly attenuated in the off-state.
Ez field in the on-state (left) and off-state (right).
The above results were obtained for a very fine grid near graphene. These plots can be obtained by running the simulation in graphene_waveguide_switch.fsp with dx=dy=dz=1nm in the mesh override region "mesh_graphene" and setting the mesh accuracy level to 4 in the FDTD settings; however, this will increase quite significantly the simulation time with respect to the original settings.
Related publications
- J. S. Gómez-Díaz and J. Perruisseau-Carrier, " Graphene-based plasmonic switches at near infrared frequencies,” OPTICS EXPRESS Vol. 21, pp. 15490- 15504 (2013)