Quantum Theory of the Third-Harmonic Generation in Graphene

Abstract

A quantum theory of the third-harmonic generation in graphene is presented. An analytical formula for the nonlinear conductivity tensor ${\sigma }_{\alpha \beta \gamma \delta }^{(3)}(\omega ,\omega ,\omega )$ is derived. Resonant maxima of the third harmonic are shown to exist at low frequencies $\omega \ll E_F/\hslash$, as well as around the frequency $\omega =2E_F/\hslash$, where $E_F$ is the Fermi energy in graphene. At the input power of a CO${}_2$ laser ($\lambda \approx 10$ $\mu$m) of about 1 MW/cm${}^2$ the output power of the third-harmonic ($\lambda \approx 3.3$ $\mu$m) is expected to be $\simeq 50$ W/cm${}^2$.

arXiv comment5 pages, 3 figures

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