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We investigate the high-order harmonic generations (HHGs) of grapheneirradiated by linearly polarized lasers with intensities in a wide range from$10^{8}$ W/cm$^2$ to $10^{13}$ W/cm$^2$. We find a striking knee structure inthe laser intensity dependence of HHGs, which consists of a linear growthregime, followed by a plateau of the saturated HHGs, and then a transition to anonlinear growth. The knee structure is rather universal for the variedharmonic orders and has been certificated by the calculations of two-banddensity-matrix equations as well as the \textit{ab initio} calculations oftime-dependent density functional theory. Based on the two-band model, wereveal the underlying mechanisms: The behavior of linear growth can be depictedanalytically by the perturbative theory of optical conductivity; While, theplateau of saturated HHGs and the transition to a nonlinear growth are causedby the quantum destructive interference and constructive interference ofharmonics generated by the electrons corresponding to the lattice momentumsaround Dirac points and M points in Brillouin zone, respectively. Inparticular, we find that tuning Fermi energy can effectively alter the kneestructure while the profile of the knee structure is not sensitive to thetemperature. Our calculations of the third-order harmonic vs. tuning Fermienergy are compared with recent experiment showing a good agreement. Ourpredicted knee structure and its associated properties are observable with thecurrent experimental techniques.

Knee structure in the laser intensity dependence of high-order harmonic generations for graphene