Multiplasmon Absorption in Graphene

We show that graphene possesses a strong nonlinear optical response in the form of multiplasmon absorption, with exciting implications in classical and quantum nonlinear optics. Specifically, we predict that graphene nanoribbons can be used as saturable absorbers with low saturation intensity in the far-infrared and terahertz spectrum. Moreover, we predict that two-plasmon absorption and extreme localization of plasmon fields in graphene nanodisks can lead to a plasmon blockade effect, in which a single quantized plasmon strongly suppresses the possibility of exciting a second plasmon.

Figure 1

(a) Plasmon dispersion relation. Gray area denotes the regime where a single plasmon can excite an $e\text{−}h$ pair. Red area denotes the regime where this process is forbidden but plasmons can decay via two-plasmon absorption. Similarly, the yellow area denotes the regime of three-plasmon absorption. (b) Two-plasmon damping rate ${\gamma }_p^{(2)}/\omega =F^{(2)}(\omega )$ for $E_p=E_e$, indicating that plasmons cannot oscillate when the plasmon field is equal to the intrinsic electric field. Inset shows the band structure of graphene and a two-plasmon absorption process.

Figure 2

(a) Transmission spectroscopy of a graphene nanoribbon. (b) Absorption cross section normalized to the surface area of the ribbon. The solid line stands for the low pump $I\ll I_s$, and the dashed line for the high pump intensity $I_s=24\mathrm{kW}/{\mathrm{cm}}^2$. The saturation of absorption is caused by two-plasmon absorption inside of the ribbon. The ribbon width is $D=25\mathrm{nm}$, the doping $n={10}^{12}{\mathrm{cm}}^{-2}$, and the resonance frequency ${\omega }_0=2\pi \times 28\mathrm{THz}$.

Figure 3

(a) Resonance fluorescence of a graphene nanodisk. (b) Quantized plasmon energy levels in a disk. Two-plasmon absorption induces a huge linewidth of the doubly excited state $|2⟩$, which makes it extremely difficult to populate this state and effectively turns the disk into a two-level system. (c) Absorption cross section normalized to the disk surface. The solid line stands for the low pump field ($\mathrm{\Omega }\ll \gamma$), and the dashed line for the strong pump field ($\mathrm{\Omega }=\gamma /\sqrt{2}$). (d) Scattered spectrum on resonance ($\omega ={\omega }_0$) in the strong pump regime ($\mathrm{\Omega }=4\gamma$), showing the Mollow triplet. (e) The second-order correlation function $g^{(2)}(t)$ of the scattered field for weak pump intensities, showing an antibunching effect $g^{(2)}(0)\ll 1$ characteristic of a two-level system.