Optical bistability of graphene in the terahertz range

We use an exact solution of the relaxation-time Boltzmann equation in a uniform ac electric field to describe the nonlinear optical response of graphene in the terahertz (THz) range. The cases of monolayer, bilayer, and $ABA$-stacked trilayer graphene are considered, and the monolayer species is shown to be the most appropriate one to exploit the nonlinear free electron response. We find that a single layer of graphene shows optical bistability in the THz range, within the electromagnetic power range attainable in practice. The current associated with the third harmonic generation is also computed.

Figure 1

Plot of the function $I\left(\kappa \right)$ vs $h=\kappa /k_F$. Function $I\left(\kappa \right)$, as computed from Eq. (10), and (dashed line) the approximation given by Eq. (12); we have taken $k_F=1$.

Figure 2

Scattering geometry. The thick line represents the graphene sheet.

Figure 3

Bistability curves of the dimensionless field $x$ as a function of $y$, for different values of the parameter $\beta$. When the power of the laser is increased the transmission through graphene follows the curve starting at zero until it reaches a point where the transmission suffers a sudden jump to higher values. The dashed-dotted straight line is the function $x=y$.