## 3 Results and Discussion  
When the laser pulse interacts with the dielectric material, the atoms or molecules in the dielectric material absorb one or several photons and ionize, which is called photoionization. For ultrafast laser pulses, the effect of avalanche ionization and electron recombination and attachment process on electron density is small and can be ignored. After absorbing multiple photons, bound electrons in atoms or molecules will transition from a bound state to a continuous state, called multi-photon ionization [20]. When the laser field is strong enough and its frequency is low, it can be regarded as a quasi-electrostatic field. This quasi-electrostatic field is superimposed on the Coulomb potential of the matching electron to form a potential barrier. The bound electron has a certain probability of passing through this potential barrier and becoming a free electron. This process is called tunneling ionization [21,22]. According to different ionization mechanisms, photoionization can be  
Figure 2: Experimental setup of femtosecond laser damage to optical thin films (M is the 800 nm mirror; HWP is the half-wave plate; Glan is the Glan-laser polarizer; Q is the quarter-wave plate; L is focusing lens). divided into multi-photon ionization and tunnel ionization [23; 24]. Tunneling ionization of atoms or molecules is the same effect as multi-photon ionization in a sense. Compared with multi-photon ionization, tunneling ionization occurs at higher light intensity. Therefore, the polarization dependence of femtosecond laser largely depends on nonlinear ionization processes, such as multi-photon ionization, tunneling ionization, and avalanche ionization [25]. Firstly, the LIDT of the Ta\({}_{2}\)O\({}_{5}\)/SiO\({}_{2}\) multilayer film under linearly polarized and circularly polarized femtosecond lasers was measured at 1-on-1. Figure 3 shows the evolution of damage probability with femtosecond laser fluence under linearly polarized and circularly polarized femtosecond laser radiation at 1-on-1. In the experiment, the microscopic method was used to identify the film damage. The working mode was to place the tested sample under a microscope and observe whether there were damaged spots on the film surface. If there were damage spots on the film, the film was considered to be damaged. According to the international standard ISO/1125454 in the optical film damage standard, the film was placed in the laser optical path, and the laser irradiated the film. Next, the irradiated film was placed under a microscope with a magnification of 200 times, observed whether the film had apparent damage, and recorded the number of damage spots at the same time. By dividing the number of damage points by the number of laser shots, the damage probability was obtained. According to Figure 3, the damage threshold of linearly polarized and circularly polarized femtosecond pulsed lasers is 1.68 and 1.70 J/cm\({}^{2}\), respectively. As the laser energy increases, the damage probability of the linearly polarized femtosecond laser is significantly higher than that of the circularly polarized femtosecond laser, which is attributed to the fact that the multi-photon ionization cross-section of the linearly polarized femtosecond laser is considerably higher than that of circularly polarized femtosecond laser [25]. [PERSON] et al. [25] suggested that six-photon ionization was considered to be the primary ionization mechanism in fused quartz and sapphire, and the dependence of ionization rate on laser polarization was obviously different; that is, the ionization rate of linear polarization was dominant in high-order multi-photon ionization. It can be seen that the difference of photon ionization process under different polarization was the main reason leading to the difference of damage process [26].