Forward and backward scattering should not be ignored in above-threshold ionization

Electron spectra for ionization of xenon by strong mid-infrared laser field calculated from the quantum-mechanical rescattering amplitude. Classical cutoffs of the electron drift energy for some characteristic orbits are represented by black lines.

Above-threshold ionization (ATI), that is, ionization of an atom or molecule by an intense laser field, leads to an intricate electron spectrum that corresponds to a very large number of electron-photon interactions. Alternatively, the so-called simple-man model of ATI attempts, very successfully, a semiclassical description: Ionization into the lowest continuum state followed by classical motion of the electron in the laser field, at most one elastic scattering off the binding potential, and final propagation in the laser field towards the detector.

In recent years, ATI by a mid-infrared laser field into electron states with very low energy has revealed various effects that are as eye-catching as they were unexpected. The model just described was not applied to low-energy ATI, because in this case the effect of the Coulomb potential was considered too dominant for the simple model to apply. Moreover, in the rescattering process, usually only backward scattering was considered, since this allows the electron reach to high energies not attainable otherwise. Forward scattering was ignored, because the electron does not require rescattering to end up in a low-energy state.

However, forward scattering off the Coulomb potential is very strong so that it may become the dominant process. W. Becker and D. B. Milošević, from the Max-Born-Institute, Germany, and the Faculty of Science, University of Sarajevo, Bosnia and Herzegovina, demonstrate that the various recently observed low-energy ATI effects for mid-infrared laser fields can be traced to forward and backward rescattering processes. It is reported in Chinese Optics Letters Vol.13, No.7, 2015.

The simple picture was extended to electrons emitted into arbitrary direction with respect to the laser field yielding an intriguing velocity map. The corresponding quantum-mechanical so-called strong-field approximation has the classical model embedded and produces velocity maps that can be compared with experimental data.

In the words of the authors, Wilhelm Becker and Dejan B. Milošević, "It is truly amazing that the simple classical model allowing for at most one act of rescattering describes the rich low-energy electron kinematics as well as it does."

The features of low-energy ATI described in this work are universal, that is independent on the specific atom or molecule. Comparing measured velocity maps with this theory may help to identify atom- and molecule-specific materializations of the laser-matter interaction.

中红外强激光阈上电离过程中的前后向散射

图片说明：通过量子力学二次散射振幅计算的中红外强激光场电离氙原子产生的电子能谱。黑线表示电子在一些典型轨道的偏移能量经典截止区。

用强激光场电离原子或分子的阈上电离（ATI）过程中，大量的电子-光子相互作用会产生复杂的电子能谱。“单人模型”对ATI的半经典描述认为，电子被电离到最低的连续态，然后在激光场中做经典运动，至多再加一次束缚势的弹性散射，最终在激光场中朝着探测器方向传播。

近年来，利用中红外激光场ATI产生低能电子态，揭示了多种未知而有趣的效应。但是，在研究低能量ATI时使用“单人模型”中会夸大库仑势的影响；此外，在二次散射过程中，通常只考虑背向散射，因为这样可以得到其他方式得不到的高能电子。由于电子不需要二次散射就可以位于低能态，因此前向散射常被忽略。

然而，中红外激光的ATI过程中，库仑势的前向散射非常强，并起主导作用。来自德国Max-Born-Institute的W. Becker教授和来自波斯尼亚和黑塞哥维那University of Sarajevo理学院的D. B. Milošević博士近期观察到中红外激光场低能ATI效应中的前向和后向二次散射过程。相关实验结果发表在Chinese Optics Letters 2015年第7期上。

在激光场的作用下电子会获得各种速度，上面结论可以扩展到任意方向运动的电子。量子力学的强场近似也包括了经典模型，可以得到与实验数据类似的结果。

作者Wilhelm Becker和Dejan B. Milošević说道：“用简单的经典模型（至多适用于一个二次散射过程）描述低能电子运动的丰富行为，这确实很奇妙。”

这项研究中描述的低能ATI特征是普遍适用的，与原子或分子种类无关。比较理论预测值与测量结果可以帮助区分激光物质相互作用过程的原子和分子的特性。