The interaction of atoms, molecules, and laser fields can generate many interesting nonlinear phenomena in the research on strong field physics. Among them, non-sequential double ionization (NSDI) has become a research hotspot. In the past, people mainly studied phenomena related to NSDI in the monochromatic laser field. With the continuous development of laser technology, a combined electric field has been applied to the study of NSDI for atoms and molecules. The electric field is composed of two circularly polarized (CP) laser fields with fixed frequency and is also called two-color CP laser field. At present, the counter-rotating two-color circularly polarized (CRTC) laser field is widely applied in research on enhancing the NSDI yield due to its special electric field structure. In recent years, studies have shown that the CRTC laser field is beneficial to increase the NSDI yield for O₂. However, for triatomic molecules with more nuclei, whether the CRTC laser field can still increase the NSDI yield is an unexplored question. The dynamics of linear triatomic molecules (CO₂) in the linearly polarized (LP) laser field and CP laser field have been studied, but there are few studies on the CO₂ dynamics in CRTC laser fields. Therefore, we compare and analyze the NSDI yield for CO₂ driven by intense laser fields, and further complement the research on the electron dynamics process in NSDI of linear triatomic molecules.

The method we adopt is based on the classical ensemble method for solving the time-dependent Newton equation. This method has been widely employed in the study of strong laser fields and atomic-molecular interactions. The NSDI electron dynamics of atomic molecules are simulated through the classical ensemble method in the following three steps. First, a stable initial ensemble is obtained. Second, the laser field components are added to the time-dependent Newton equation, and the initial ensemble is substituted to obtain the final coordinates and momentum distribution of the electrons. Third, the data with double ionization is screened. The initial ensemble is mainly obtained by the following ways. At first, the spatial positions of two electrons are given by the Gaussian random matrix, the total potential energy of two electrons is calculated, and the coordinates of the potential energy less than the total energy are filtered. Then the total kinetic energy is obtained by subtracting the total potential energy from the total energy, and the total kinetic energy is randomly assigned to the electrons to obtain their momentum and coordinates. Finally, the coordinates and momentum of two electrons are substituted into the time-dependent Newton equation without the laser field for a period of time, and then a stable initial system synthesis is obtained. The LP laser field we leverage has a wavelength of 1200 nm, the CP laser field has a wavelength of 1200 nm, and the CRTC laser field is a combination of two circularly polarized laser beams with wavelengths of 1200 nm and 600 nm.

First, we calculate the NSDI yield for CO₂ in LP, CP, and CRTC laser fields for various laser field intensities (Fig. 1). The results show that the yield of CO₂ molecules under the CRTC laser field is higher than that under the LP laser field when the laser field is higher. However, the opposite results are obtained when the laser field intensity is lower. Since the knee structure doesn't occur in the yield curve under the action of the CP laser field, it is not discussed in our paper. Then, we calculate the electron return energy diagram based on the main time distribution of the recollision (Fig. 3). The return energy diagram can help us derive the reason for the intersection of the CO₂ yield curves. Second, we investigate the factors affecting the CO₂ NSDI under the action of intense laser fields. By comparing the single ionization rate and double ionization rate of CO₂ in the LP laser field and CRTC laser field (Fig. 4), we can conclude that the main factors affecting the CO₂ NSDI are the laser intensity and laser field type. Third, we explore the electron dynamics process for CO₂NSDI in the areas with lower laser intensity and higher laser intensity respectively. The results show that under lower laser intensity, the NSDI yield driven by the LP laser field is higher than that driven by the CRTC laser field because of the lower suppression barrier (Fig. 5). However, when the laser intensity is higher, the suppression barrier will be distorted and then the main factor affecting the NSDI yield is the structure of the laser field in this case. As the CRTC has a three-lobed structure (Fig. 7) which helps to increase the number of electrons undergoing recollision, the NSDI yield in the CRTC laser field is higher than that in the LP laser field.

Our paper investigates the NSDI yield for linear triatomic molecular (CO₂) driven by LP, CP, and CRTC laser fields. The results indicate that the NSDI yield in the CRTC laser field is lower than that in the LP laser field under lower laser intensity. This is because the interaction between the laser field and the molecular coulomb potential forms a suppression barrier, and the suppression potential in the CRTC laser field is higher than that in the LP laser field. As a result, the ionization of the second electron in the CRTC laser field is limited. However, when the laser intensity is higher, the yield in the CRTC laser field is higher than that in the LP laser field. This is because with the increasing laser intensity, the molecular coulomb potential is distorted, and then the molecular structure almost no longer exerts an effect on the ionization rate, which is largely influenced by the laser field structure. The CRTC laser field is characterized by a special three-lobed structure, and it can help to increase the number of returning electrons and the electron recollision possibility. Therefore, the CO₂ yield is higher under the action of the CRTC laser field. We further complement the study of the NSDI electron dynamics process of linear triatomic molecules driven by intense laser fields, and our results also provide references to improve the NSDI yield of molecules in experiments.