Identifying two different configurations of the <inline-formula><tex-math id="Z-20200330064922-1">\begin{document}$ \rm H_3^{2+} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20200013_Z-20200330064922-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20200013_Z-20200330064922-1.png"/></alternatives></inline-formula> by the direct above-threshold ionization spectrum in two-color laser field
Authors: Zhou Xu-Cong , Shi Shang , Li Fei , Meng Qing-Tian , Wang Bing-Bing ,   School of Physics and Electronics, Shandong Normal University, Jinan 250358, China,   Laboratory of Optical Physics, Beijing National Laboratory for Condensed MatterPhysics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China,   University of Chinese Academy of Sciences, Beijing 100049, China
Published: December 2020

Since imaging the geometrical structure of molecules can help to understand the microscopic world intuitively, and thereby to promote the development of physics, chemistry, material science and biological science, it has long been an important subject for scientists to probe the molecular internal structure. Generally, however, because of the relative complexity of the molecular internal structure, it is difficult to obtain the relevant information by ordinary experimental means. With the development of laser technology, especially the advent of intense ultrafast laser field, ultrafast laser pulse provides an unprecedented detection tool to investigate the related ultrafast dynamics. In recent years, strong field high-order nonlinear ultrafast processes, such as above-threshold ionization(ATI), high-order above-threshold ionization(HATI), high harmonic generation(HHG), and non-sequential double ionization (NSDI), were produced by using femtosecond ultrafast laser to excite molecules. Since the molecules excited in these processes emit the photon and electron signals pertinent to their internal structures, it is natural that one can obtain the imaging of molecular structure by extracting the signals. Recently, we have demonstrated that the structural information of SF<sub>6</sub> molecules can be obtained by the interference fringes on the ATI spectrum using the infrared and ultraviolet bichromatic laser fields[<i>arXiv</i>, 1912.08499 (2019)]. In this paper, we use frequency-domian method, which is based on non-perturbed quantum electrodynamics, to investigate the direct above-threshold ionization (ATI) process of triatomic molecular ion <inline-formula><tex-math id="Z-20200330065026-1">\begin{document}$ \rm H_3^{2+} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20200013_Z-20200330065026-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20200013_Z-20200330065026-1.png"/></alternatives></inline-formula> with two different geometrical structures by monochromatic and bichromatic laser fields, and given the detailed analysis of the spectra for each case. Compared with the monochromatic laser field, it is found that the ATI spectrum by the bichromatic laser field is more sensitive to the geometrical configuration of molecular ion, thereby it can be applied to identify the different geometrical structure of molecules. In the case of bichromatic laser fields, the direct ATI spectrum show different interference fringes with different molecular configurations. We give the beginning and cutoff curves of each platform by employing the saddle-point approximation. Furthermore, we derive the destructive curves formulas for different molecular configurations in angle-resolved direct ATI energy spectra and momentum spectra, respectively, which carries the information about themolecular structure. In addition, it is found that the shape of the spectra can be modified by changing the molecular internuclear distance or varying the laser intensity. Thereby, it can be inferred that the ATI spectrum induced by bichromatic laser field has the ability to identify different configurations of the same molecules, which is instructive to image geometrical structure of complex molecules.