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An electrodynamic response of graphene to a strong electromagnetic radiationis considered. A hot electron model (HEM) is introduced and a correspondingsystem of nonlinear equations is formulated. Solutions of this system are foundand discussed in detail for intrinsic and doped graphene: the hot electrontemperature, non-equilibrium electron and holes densities, absorptioncoefficient and other physical quantities are calculated as functions of theincident wave frequency $\omega$ and intensity $I$, of the equilibrium chemicalpotential $\mu_0$ and temperature $T_0$, scattering parameters, as well as ofthe ratio $\tau_\epsilon/\tau_{\rm rec}$ of the intra-band energy relaxationtime $\tau_\epsilon$ to the recombination time $\tau_{\rm rec}$. The influenceof the radiation intensity on the absorption coefficient $A$ at low($\hbar\omega\lesssim 2|\mu_0|$, $dA/dI>0$) and high ($\hbar\omega\gtrsim2|\mu_0|$, $dA/dI<0$) frequencies is studied. The results are shown to be ingood agreement with recent experimental data.

Theory of the strongly nonlinear electrodynamic response of graphene: A hot electron model