研究了在强中红外激光场驱动下，透明固体模型中布洛赫电子产生高次谐波辐射。我们使用速度规范方法[New J. Phys. 15，013006（2013）]求解单电子时间相关的薛定谔方程（TDSE），该方法在激光强度和能带数量增加时数值稳定。由于价带与第一导带的耦合，所得到的谐波光谱表现出一个主要的平台，具有与场强和激光波长成线性比例的截止能量。我们还发现了一个较弱的第二平台，由于耦合到更高的导带，与截止，也是近似线性的场强。为了便于分析发射的谐波的时间-频率特性，我们也解决了TDSE在一个依赖于时间的基组，休斯顿状态[物理评论B 33，5494（1986）]，这使我们能够分离带间和带内的贡献的依赖于时间的电流。我们发现，带间和带内的贡献显示非常不同的时频特性。我们表明，在这两个基地的解决方案是等价的么正变换下，但与速度计方法，休斯顿状态的治疗是数值不稳定时，使用了几个以上的低洼能带。
英文摘要：
We study the generation of high harmonic radiation by Bloch electrons in a model transparent solid driven by a strong mid-infrared laser field. We solve the single-electron time-dependent Schrödinger equation (TDSE) using a velocity-gauge method [New J. Phys. 15, 013006 (2013)] that is numerically stable as the laser intensity and number of energy bands are increased. The resulting harmonic spectrum exhibits a primary plateau due to the coupling of the valence band to the first conduction band, with a cutoff energy that scales linearly with field strength and laser wavelength. We also find a weaker second plateau due to coupling to higher-lying conduction bands, with a cutoff that is also approximately linear in the field strength. To facilitate the analysis of the time-frequency characteristics of the emitted harmonics, we also solve the TDSE in a time-dependent basis set, the Houston states [Phys. Rev. B 33, 5494 (1986)], which allows us to separate inter-band and intra-band contributions to the time-dependent current. We find that the inter-band and intra-band contributions display very different time-frequency characteristics. We show that solutions in these two bases are equivalent under an unitary transformation but that, unlike the velocity gauge method, the Houston state treatment is numerically unstable when more than a few low lying energy bands are used.
