Giant Optical Nonlinearity of Graphene in a Strong Magnetic Field

We calculate the nonlinear optical response of graphene in strong magnetic and optical fields, using a quantum-mechanical density-matrix formalism. We show that graphene in a magnetic field possesses a giant mid- or far-infrared optical nonlinearity, perhaps the highest among known materials. The high nonlinearity originates from unique electronic properties and selection rules near the Dirac point. As a result, even one monolayer of graphene gives rise to an appreciable nonlinear frequency conversion efficiency for incident infrared radiation.

Figure 1

(a) Landau levels near the $K$ point superimposed on the electron dispersion without the magnetic field $E=\pm {\upsilon }_F|p|$. (b) A scheme of the resonant four-wave mixing process in the four-level system of LLs with energy quantum numbers $n=-1,0,+1,+2$. The case of exact resonance is shown. Polarization of light corresponds to the allowed transitions.

Figure 2

Transition frequencies in the 4-energy level graphene system of Fig. 1. ${\omega }_{mn}$ indicates the transition frequency between level $m$ and $n$.

Figure 3

Intensity of the 4-wave mixing signal as a function of the intensity of the pump field $E_2$ normalized by $I_0=c|E_{\mathrm{sat}}{|}^2/8\pi \simeq 2.2\times {10}^5\mathrm{W}/{\mathrm{cm}}^2$. The value of $I_0$ is the saturation intensity of the transition 1–2 calculated at $B=1\mathrm{T}$ and assuming that $1/{\tau }_{mn}=\gamma =3\times {10}^{13}{\mathrm{s}}^{-1}$. $I_1$ is set to satisfy $y=0.6x$.