Trajectory analysis of high-order-harmonic generation from periodic crystals
Trajectory analysis of high-order-harmonic generation from periodic crystals
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DOI：
10.1103/physreva.95.043416
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发表时间：
2017-04-19
影响因子：
2.9
通讯作者：
Ishikawa, Kenichi L.
中科院分区：
文献类型：
--
作者：
Ikemachi, Takuya;Shinohara, Yasushi;Ishikawa, Kenichi L.
利用一维模型周期晶体理论研究了强激光脉冲驱动下固体中高次谐波的产生。通过直接在实空间网格上数值求解含时薛定谔方程，我们成功地再现了实验观察到的固态高次谐波的独特特征，如线性截止能量标度和从单平台到多平台结构的突然转变。基于模拟结果，我们提出了一个简单的模型，结合矢量势引起的带内位移，带间隧穿，并与价带空穴复合。一个关键参数是脉冲矢量势的峰谷振幅，其决定半周期期间的晶体动量位移。当最大峰谷振幅A（peak）达到布里渊区的半宽pi/a（a为晶格常数）时，HHG谱表现出从单平台结构到多平台结构的转变，并且甚至在A '（peak）= 2 pi/a，3 pi/a，.根据不同频带之间的能量差，给出了多个截止位置作为A（峰值）和第二最大值A（峰值）的函数。使用我们的方法，人们可以在动量空间中绘制电子轨迹，从中可以推导出，例如，HHG的时间-频率结构，而无需复杂的量子力学计算。最后，我们发现，截止位置不仅取决于脉冲的强度和波长，而且其持续时间，在显着的对比气相的情况下。我们的模型可以被看作是一个熟悉的三步模型，非常成功的气相HHG的固态和动量空间对应，并提供了一个统一的基础来理解HHG从固态材料和气态介质。
We theoretically study high-order-harmonic generation (HHG) from solids driven by intense laser pulses using a one-dimensional model periodic crystal. By numerically solving the time-dependent Schrodinger equation directly on a real-space grid, we successfully reproduce experimentally observed unique features of solid-state HHG such as the linear cutoff-energy scaling and the sudden transition from a single-to multiple-plateau structure. Based on the simulation results, we propose a simple model that incorporates vector-potential-induced intraband displacement, interband tunneling, and recombination with the valence-band hole. One key parameter is the peak-to-valley amplitude of the pulse vector potential, which determines the crystal momentum displacement during the half cycle. When the maximum peak-to-valley amplitude A(peak) reaches the half width pi/a of the Brillouin zone with a being the lattice constant, the HHG spectrum exhibits a transition from a single-to multiple-plateau structure, and even further plateaus appear at A'(peak) = 2 pi/a,3 pi/a,.... The multiple cutoff positions are given as functions of A(peak) and the second maximum A(peak), in terms of the energy difference between different bands. Using our recipe, one can draw electron trajectories in the momentum space, from which one can deduce, for example, the time-frequency structure of HHG without elaborate quantum-mechanical calculations. Finally, we reveal that the cutoff positions depend on not only the intensity and wavelength of the pulse, but also its duration, in marked contrast to the gas-phase case. Our model can be viewed as a solid-state and momentum-space counterpart of the familiar three-step model, highly successful for gas-phase HHG, and provide a unified basis to understand HHG from solid-state materials and gaseous media.