激光驱动晶体发射高次谐波的特性研究

发布时间：2019-01-05 21:45

【摘要】：当激光与晶体相互作用时,将出现一系列的非线性光学现象,如高次谐波(HHG)、阈上电离(ATI)等。目前,研究激光晶体相互作用有两种理论模型:单电子模型和多电子模型。多电子模型基于半导体布洛赫方程(SBE),这种方法广泛的应用于固体和半导体物理中。单电子模型基于能带理论,这种方法假定固体中的每个电子的运动都是独立的,它们都受到有效势的作用。激光与原子分子相互作用在过去被广泛的研究,三步模型能够很好的描述谐波的成因,但是晶体谐波的产生机制仍在探索。目前,一些学者认为,带内和带间电流对晶体谐波起主要贡献。求解的方法都基于两种模型,多电子模型虽然求解精确,但是要考虑电子关联效应,相当费时,单电子模型求解更简单,有效势一旦被确定,相关的问题就很容易得到解决。本文的主要工作是采用单电子模型研究了激光晶体相互作用。首先采用Mathieu-type模型势数值计算了体系的能带结构,然后用B样条函数展开方法求解含时薛定谔方程,在坐标空间获得了双平台的谐波结构,之后用Bloch态和Houston态波函数作为基函数求解了含时薛定谔方程,在波矢空间得到了晶体谐波。经分析得知,晶体谐波的第一个平台来源于最高价带和最低导带间的耦合,第二个平台来源于更高的导带与价带间的耦合,且两个平台的截至能量都与激光场振幅呈线性关系。在少周期激光驱动下,谐波的第二个平台的截至位置与激光载波包络相位呈单调变化。在啁啾激光驱动下,晶体谐波谱有很大的变化,第二个平台的发射效率会随啁啾参数而改变,由此我们提出一种提高第二个平台发射效率的方法。
[Abstract]:When the laser interacts with the crystal, a series of nonlinear optical phenomena will appear, such as the high harmonic (HHG), suprathreshold ionization (ATI) and so on. At present, there are two theoretical models for studying laser crystal interaction: single electron model and multi-electron model. Multiple electron models are widely used in solid and semiconductor physics based on the (SBE), method of semiconductor Bloch equation. The single electron model is based on the energy band theory. This method assumes that each electron in a solid is independent of the motion of each electron and they are all affected by the effective potential. Laser interaction with atoms and molecules has been widely studied in the past. The three-step model can well describe the cause of harmonic, but the mechanism of crystal harmonic generation is still being explored. At present, some scholars believe that intra-band and inter-band currents play a major role in crystal harmonics. The methods are based on two kinds of models. Although the solution of multi-electron model is accurate, it is rather time-consuming to consider the electronic correlation effect. The solution of single electron model is simpler, and once the effective potential is determined, the related problems can be easily solved. The main work of this paper is to study the laser crystal interaction by single electron model. The energy band structure of the system is numerically calculated by using the Mathieu-type model potential, and then the time-dependent Schrodinger equation is solved by the B-spline function expansion method. The harmonic structure of the two platforms is obtained in the coordinate space. Then, the time-dependent Schrodinger equation is solved by using the Bloch state and Houston state wave function as the basis functions, and the crystal harmonics are obtained in the wave vector space. The results show that the first platform of crystal harmonic comes from the coupling between the highest valence band and the lowest conduction band, and the second platform comes from the higher coupling between the conduction band and the valence band, and the ending energy of the two platforms is linearly related to the amplitude of the laser field. The terminal position of the second harmonic platform and the phase of the laser carrier envelope change monotonously under the small period laser drive. The harmonic spectrum of crystal changes greatly under the driving of chirped laser, and the emission efficiency of the second platform will change with the chirp parameter. Therefore, we propose a method to improve the emission efficiency of the second platform.
【学位授予单位】：西北师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O437

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