摘要
近几年来，由于超短超强激光技术的飞速发展，尤其是飞秒激光技术的发展，激光电场的峰值场强已经达到甚至超过基态氢原子内部的库仑场强。利用这样的强激光与原子相互作用，产生了许多新的强场物理现象，如阈上电离、隧穿电离、高次谐波发射、原子的动力学稳定等。面对这些崭新的强场物理现象，传统的微扰理论已经无能为力，因此需要建立和发展非微扰理论来研究和分析这些现象。
运用非微扰理论描述原子在强激光场中的动力学行为，最终都可以归结为求解相应的含时薛定谔方程。目前人们对这个方程的求解通常采用纯数值积分方法和Floquet方法，除此以外，原子本征态展开方法由于其自身的物理透明性和计算结果的可靠性也逐渐被人们采用。然而，原子在强激光场作用下发生电离，电离电子的连续态布居在低能区的分布往往比高能区分布复杂得多。因此采用原子本征态展开方法计算，若想获得一个收敛的结果，需要把能量步长取得很小以适应电离电子在小能量区的复杂分布，同时该方法本身的特点是在时间演化的每一步都包含了大量的关于能量的积分运算，所以利用该方法来计算是十分耗时的。为了解决这个耗时问题，我们采用了从能量E到q=(2E)~(1/(2E)的表象变换，这样大幅度地增加了小能量区的连续态密度，从而在保证计算准确性的同时，极大地节省了计算资源。关于改进方法的可靠性则通过两类计算结果的比较得到了严格的验证：(一)利用改进的本征
吉林大学博士学位论文
态展开方法计算得到的长度形式和加速度形式的谐波发射谱的
比较:(二)分别用改进本征态展开方法和Crank一Nicholson数泣
积分方法计算得到的加速度形式谐波谱的比较。此外，为了验证
我们改进的方法并从多角度研究强场物理现象，我们独立地编制
了用Crank一Nieholson方法直接数值积分求解含时Sehr6dinger方
程的程序。
在本论文，利用这两种非微扰的理论处理方法，我们系统地
研究了一维模型原子在强场中的动力学稳定和高次谐波发射的
问题。
原子的动力学稳定性(或称电离抑制)是指当峰值场强足够
大(一般大于几个原子单位)且光学频率足够高(一般大于原子
的最大束缚能)的激光脉冲辐照原子后，电子不仅仍有一定的儿
率滞留在原子束缚态上而没被完全电离，而且该几率竟然随着峰
值场强的进一步增强而增加的反直觉现象。这个现象自从Gersten
以及Gavrila等人在研究激光场作用下的氢原子时提出后，又被许多实
验和理论所证实。我们注意到，当前人们对动力学稳定性(DS)
的解释主要基于高频Floquet理论给出，而与此相反的是，相关的计
算却集中在各种波包方法。那么，能不能从波包本身出发对动力学稳定性
做出合理的解释呢?为了解决这个问题，我们首先分别用原子本征态展开
方法和直接数值积分方法独立地计算了在高频超强场下一个模型原子(修
正的P一T势)的电离。由两种方法计算结果的高度一致性，在本文所做近
似下实证了DS的物理实在性(迄今，这一争论并没有停息)。然后，提
出并证明直接用波包动力学的观点来解释DS将更有助于澄清这一现象背
后的物理机制。通过细致观察电离波包在坐标空间和能量空间中随时间演
化的动力学过程，发现电离波包在坐标空间的分布大体可以分成两部分:
漂移波包(在坐标空间远离束缚态的布居区，它是激光结束时电离产额的
全部)和核区附近波包(这部分波包能够同核区进行有效的交换)，而在
电离抑制区(在激光脉冲结束时，原子的电离几率随峰值场强增加而减小
吉林大学博士学位论文
的一段场强区域)的演化过程中，可以清晰地观察到一个‘死期’的存
在，且‘死期’随着激光峰值场强的增强在整个激光脉冲持续时间内所占
的比例越来越大，在这个时期内基本没有新的漂移波包产生，即‘死期’
对原子的最终电离是没有贡献的。同电离波包在坐标空间的分布相对应，
其在能量空间的分布也大体分成两部分，其中一部分分布较宽(我们称之
为宽台布居)，对应于坐标空间上核区附近的电离波包，另一部分分布较
窄(我们称之为窄峰布居，它在半个光学周期内分成左移分支和右移分
支)，对应于坐标空间上远离核区的漂移波包。通过进一步观察电离波包
在能量空间的动力学演化过程发现:决定最终电离产额多少的唯一因素是
电离能量波包中窄峰布居的面积，而该面积的大小取决于窄峰中左移分支
在每半个光学周期内同基态交换获得的‘净’的电子布居的总和(窄峰的
右移分支在这半个光学周期内面积基本不发生改变)。为此，针对电离能
量波包中的窄峰左移分支，我们重点考察了它的面积在不同峰值场强的激
光脉冲各个时段(本文选择在脉冲的峰值附近和下降沿)的任意半个光学
周期内的消长规律，并依据决定电离产额的三个因素，即基态和奇宇称连
续态的祸合强度、在该时段内激光场的强度以及在该时段内各能态(尤其
是基态)电子的布居特征，阐明了产生该消长规律的原因。
最后，通过对电离能量波包的动力学演化过程的深入分析，给出了导
致原子DS的原因:在电离抑制区，随着峰值场强的逐渐增加，在激光脉
冲峰值附近的时刻(光学场为零，总电离为1的时刻)，电离的能量波包
中的宽台布
As a result of the rapid development of ultra-short and ultra-intense laser technology, the peak electric field strength of lasers has reached or exceeded the coulomb field strength seen by the electron in the ground state of atomic hydrogen. The application of such intense laser fields to the atoms leaded to the discovery of a number of novel strong-field phenomena such as above-threshold ionization (ATI), tunneling ionization (Tl), high-order harmonic generation (HHG), dynamic stabilization (DS) of atoms, etc. Because of the failure of the traditional perturbative theories in this field region, it is necessary to establish and develop non-perturbative approaches for the treatment of these phenomena.
Non-perturbative theoretical investigations of atomic systems interacting with intense laser fields generally require the time-dependent solution of the corresponding Schro'dinger equation. The Floquet theory and pure numerical integral method are accepted as the most generally used approaches of solving the time-dependent Schrodinger equation. In addition, the field-free eigenstate expansion approach (FFEEA), which naturally gives the time-dependent population on each eigenstate, provides a powerful tool to gain more insights into the essence of the physical processes. However, for the reasons given
blow, the approach is of low computational efficiency. When the electrons are ionized under the action of the strong laser fields, their population on continuum states in low energy domain is much more complex than that in high energy domain. Accordingly, very small energy step-length is indispensable to guarantee computational convergence. On the other hand, the approach will have to involve the integrals of large numbers of matrix elements in every step of the evolution, which is really time-consuming.
To overcome these shortcomings, we improved the field-free eigenstate expansion approach by performing a representation transform from energy E Xoq = 2E . It is shown that the improved method works well in promoting the efficiency of computation since it results in increased state density in low energy domain. The reliability of the improved method is examined by two comparisons of the high-order harmonic generation (HHG) spectra: one is that obtained in the length and acceleration forms, respectively; the other is that obtained by itself and the purely numerical integral approach, respectively, in the same acceleration form. (We programmed the Crank-Nicloson approach independently in order to investigate physical phenomena from different standpoints and testify the improved approach.)
With the improved field-free eigenstate expansion approach (IFFEEA) and the Crank-Nicholson approach we studied the DS of the one-dimensional (ID) model atoms and the HHG of the ID united-atoms (single-electron molecular ions with large inter-nuclear distances)driven by intense laser fields.
The DS of atoms is defined as the phenomenon that the ionization probability at the end of the laser pulse of fixed shape and duration does not approach unity as the peak intensity is
increased, but either start decreasing with the intensity(possibly in a oscillatory manner), or flattens out at a value smaller than unity. The phenomenon has been reinforced by many theoretical and experimental works since its first discovery by Gersten and Gavrila. Up to now, the physical interpretation of the DS mainly comes from the high frequency Floquet theory; however, the related calculations are obtained from the direct solutions of the time-dependent Schrodinger equations (TDSE). Why shouldn't one explain the phenomenon from the viewpoint of wave-packets obtained by TDSE? For this purpose, we calculated the DS of a ID model atom in the super-intense and high-frequency laser pulses with the two methods mentioned above, respectively. The excellent agreement of the two results corroborates the physical reality of the DS, about which the dispute is still underway heretofore. And then
引文
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