【作者】 祁月盈；

【导师】 丁培柱；

【作者基本信息】 吉林大学 ， 原子与分子物理， 2004， 博士

【摘要】 随着强激光技术的飞速发展，理论研究强激光与物质的相互作用，解释新的实验现象，预言实验尚无法达到的更高强度激光场中物质的行为和规律，成为当前国际上极为活跃的前沿研究课题。特别是近几十年来，实验室已经可获得激光光强峰值高达1020W /cm2的激光脉冲，这极大地推进了激光与物质相互作用的理论和应用研究。强激光与物质相互作用的理论基础是强激光与原子的相互作用，在这个相互作用过程中，出现了很多由非线性作用引起的新现象，诸如激光场作用下的电子发射和光子发射：激光场作用下的多光子电离、阈上电离、隧道电离、过垒电离，激光诱导的电子复合并伴随着高次谐波的发射等。尤其是高次谐波的发射，它可能成为产生真空远紫外和软 X 射线的有效途径，还是将飞秒激光脉冲向阿秒激光脉冲转化的可能方案。在传统的量子力学中，通常将光与物质的相互作用看作是库仑场的微扰项，应用微扰理论开展研究。因为处于基态的氢原子所受的库仑电场为 E0 =e =1a.u.= 5.14×109V /cm (e为电子的电荷，a0 a0 2为玻尔半径)，相应的光强I0 = 3.51×1016W /cm2 =1a.u.，这是以往的激光器是无发达到的，微扰论的结论与实验相符。但是当激光场光强达到1013Wcm?2 时, 实验上出现了一些无法用微扰理论解释的现象，也就是说量子力学中常用的微扰理论已经不适用于描述这样的激光场与原子的相互作用了。在过去的几十年里，人们发展了多种非微扰方法，如 Floquet 理论方法、 R-矩阵方法等， 但是这些方法不适用于超短超强激光与物质的相互作用；人们开始采用直接数值求解超短超强激光与原子相互作用的含时 Schr?dinger 方程的方 1<WP=135>吉林大学博士学位论文法，这种方法采用有限差分、离散变量表象、有限元、B 样条和基函数组展开法将含时 Schr?dinger 方程离散化；采用基函数展开法时，基函数组应包含描述电离连续态的基函数——可以选择为场自由原子的本征态 、Volkov 态等。 含时 Schr?dinger 方程包容了原子、激光场以及原子与激光相互作用的全部物理内容，因此直接数值求解含时 Schr?dinger 方程以研究激光与原子的相互作用是一条合理而自然的途径。在激光与原子相互作用过程中，原子中的电子在激光电场方向上受到的作用远大于其他方向，因此强激光与 1 维原子相互作用模型很好地描述了激光与原子的相互作用，也使得问题大大简化。 Hamilton 系统具有辛结构，Hamilton 正则方程在辛变换下形式不变，它的解由辛变换群生成。基于此，80 年代初，Ruth 和冯康提出了 Hamilton 系统的辛算法，之后，人们对辛算法进行了系统的研究。冯康和他领导的小组提出了生成函数法、幂级数法构造辛格式，研究了守恒量和保体积算法，接触结构与接触算法等；孙耿、J. M. Sanz-Serna 等研究了辛 Runge-Kutta 方法；Yashida 提出了构造可分 Hamilton 系统辛格式的对称幂方法，等等。至今，辛算法已经广泛应用到天文、大气与海洋物理、地学、等离子体物理、化学反应动力学宏观模拟等领域，并在长时间、多步数的计算中较传统的非辛算法显示出明显的优越性。 量子系统是一个无穷维 Hamilton 系统，系统的波函数随时间的演化保持酉积守恒，这等价于波函数模方和辛积守恒；因此，将含时 Schr?dinger 方程离散成以波函数模方为守恒量的有限维正则方程，并采用模方守恒-辛格式数值求解是直接求解含时 Schr?dinger方程的合理途径——称为含时 Schr?dinger 方程的保结构算法。本文提出了两种将含时 Schr?dinger 方程离散成 Hamilton 正则方程的方案：1）基于空间充分远处的渐近边界条件，2）基于数值基（包括分离态和连续态波函数）展开，将含时 Schr?dinger 方程离散成以波函数模方为守恒量的有限维正则方程；讨论了保结构算法；应用于计算了强激光场中 1 维模型原子的行为，如 Rabi 共振、多光子电离、阈上电离、高次谐波发射等，还计算和讨论了 1 维类氢氦离子在双色场中高次谐波平台明显提高的物理机制。 理论研究强激光场与原子相互作用需要求解定态 Schr?dinger方程充分远空间上的本征值问题，计算连续态本征函数和正交归一化。常用的微分方程数值解法不适用于充分远空间。应用 Legendre变换可将定态Schr?dinger方程转化成形式上的Hamilton正则方程，它的解从一个空间点到另一个空间点是一个辛变换，在这种意义下定态 Schr?dinger 方程具有“辛结构”；定态 Schr?dinger 方程转化成 2<WP=136>吉林大学博士学位论文Hamilton 正则方程并采用辛格式数值求解是求解定态 Schr?dinger方程在充分远空间上的本征值问题的合理途径。因为在无穷空间上的积分发散，定态 Schr?dinger 方程的连续态本征函数不能“箱”归一化；量子系统的连续态本征函数的正交归一化是δ -函数意义下的，数值实现连续态本征函数在δ -函数意义的正交归一化是一个需要探索和完善的问题。 本文应用保结构算法计算和研究与强激光?更多还原

【Abstract】 With the rapid development of the laser technique, the theoreticalresearch on the interaction between the intense laser and matter, theexplanation for the new experimental phenomena, the prediction for thebehavior and the law of the matter in the stronger laser field, which isnot realized in the lab, are attractive. Especially in these recent years,the laser pulse with the maximum intensity about 1020W /cm2 can beobtained in the experiment, which prompt the research on theinteraction between the intense laser and matter. The theoreticalfoundation about the interaction with the intense laser and matter is theinteraction with the intense laser and atom, where many newphenomena have been generated by nonlinear interaction. Thesephenomena include the electron emission under the laser, i.e.,multiphoton ionization, above-threshold ionization, tunneling ionizationand over-barrier ionization, and the photon emission under the laser, i.e.,the high-order harmonics generation, etc. The high-order harmonicgeneration not only provides a new source of XUV and the soft X-rayradiations, but also shows a new possible way for extremely shortpulses. In the traditional quantum mechanics, the interaction with the laserand matter is regarded as the perturbation of the coulomb field and isdealt with perturbation theory. When the electron locates at the groundstate of the hydrogen atom, its coulomb electronic field isE0 = e =1a.u.=5.14×109V /cm(e is the charge of the electron, a0 is the a0 2Bohr radius), corresponding to the light intensity 5<WP=139>吉林大学博士学位论文I0 = 3.51×1016W / cm2 =1a.u., which cannot reach up in the previous lasermachine, so the previous result from the perturbation theory is accordto the one from the experiment. But when intensity of the laser fieldreaches up to 1013Wcm?2 , some experimental phenomena cannot beexplained by the perturbation theory, that is to say, the traditionalperturbation theory in the quantum mechanics will be invalidated forthe interaction with the laser and atom. In the past decade, variousnonperturbative methods have been developed and adopted, i.e.,Floquet theory method, R-matrix method, etc, but these methods cannotbe applied to the super-short and super-intense laser field. The methodssolving numerically time-dependent Schr?dinger equation (TDSE) havebeen applied to describe the interaction between the super-short andsuper-intense laser and atom, that is, TDSE is directly dicretized usingfinite differece, discrete variable representation, finite elements, Bsplines or a basis set expansion approach. In the basis set expansionapproach, the basis function set may be chosen as the eigenstate offree-field, Volkov state and so on. TDSE implies all the physical messages about the atom, the laserfield and the interaction with the laser and atom, so solving numericallyTDSE is one of the popular and the reasonable methods for the researchabout the interaction with the laser and atom in the present theoreticalresearch. In the interaction with the laser and atom, the electronicinfluence in the direction along the polarization of the laser field isgreater than by other directions, so the one-dimensional model atom ischosen in the research about the interaction between the laser and atomand makes the problem simpler. There is symplectic structure in the Hamilton system. Hamiltoncanonical equation maintains symplectic structure after symplectictransformation. The solutions of the Hamilton canonical equation canbe generated from symplectic group. Based on this, in the early 1980’s,Ruth and Feng Kang presented the symplectic algorithm of theHamilton system, which maintains the symplectic structure of thesystem. After that, many people have investigated on the symplecticstructure. Feng Kang and his research group presented the methodsgenerating the symplectic schemes, i.e., generating function metho更多还原