论文标题
石墨烯高阶谐波世代的激光强度依赖性的膝盖结构
Knee structure in the laser intensity dependence of high-order harmonic generations for graphene
论文作者
论文摘要
我们研究了线性极化激光器的辐照的石墨烯的高阶谐波世代（HHGS），其强度范围从$ 10^{8} $ w/cm $^2 $到$ 10^{13} $ w/cm $ $^2 $。我们在HHGS的激光强度依赖性中发现了一个惊人的膝盖结构，该结构由线性生长状态组成，然后是饱和HHGS的平稳，然后向非线性生长过渡。对于各种的谐波顺序，膝盖结构是普遍的，并且通过两波段密度 - 矩阵方程以及\ textIt {ab libio}计算时间依赖性密度功能理论的计算获得了认证。基于两波段模型，我们揭示了潜在的机制：可以通过光学电导率的扰动理论在分析上描述线性生长的行为；而，饱和HHG的平台和向非线性生长的过渡是由分别与布里远区域中DIRAC点和M点围绕的晶格动量产生的量子破坏性干扰和谐波的建设性干扰引起的。特别是，我们发现调整费米能量可以有效地改变膝盖结构，而膝盖结构的轮廓对温度不敏感。将我们对三阶谐波与调谐费米能量的计算与最近的实验进行了比较，显示出良好的一致性。当前的实验技术可观察到我们预测的膝盖结构及其相关特性。
We investigate the high-order harmonic generations (HHGs) of graphene irradiated 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 in the laser intensity dependence of HHGs, which consists of a linear growth regime, followed by a plateau of the saturated HHGs, and then a transition to a nonlinear growth. The knee structure is rather universal for the varied harmonic orders and has been certificated by the calculations of two-band density-matrix equations as well as the \textit{ab initio} calculations of time-dependent density functional theory. Based on the two-band model, we reveal the underlying mechanisms: The behavior of linear growth can be depicted analytically by the perturbative theory of optical conductivity; While, the plateau of saturated HHGs and the transition to a nonlinear growth are caused by the quantum destructive interference and constructive interference of harmonics generated by the electrons corresponding to the lattice momentums around Dirac points and M points in Brillouin zone, respectively. In particular, we find that tuning Fermi energy can effectively alter the knee structure while the profile of the knee structure is not sensitive to the temperature. Our calculations of the third-order harmonic vs. tuning Fermi energy are compared with recent experiment showing a good agreement. Our predicted knee structure and its associated properties are observable with the current experimental techniques.
