## 3 Results and Discussion  
The effects of the pulse number on ablation shapes and subwavelength ripples on the titanium surface are experimentally investigated in this study. Figure 2 shows SEM images of ablation shapes and subwavelength ripples on titanium obtained at different femtosecond pulses. In these experiments, the selected number of pulses (N) is 10, 50, and 100. The repetition rate and incident laser fluence are 100 Hz and0.20 J/cm\({}^{2}\), respectively. The orange circular regions in Figure 2a,c,e represent regions with surface periodic structures, and the diameter of a region with ripple structures is represented by D. The diameters of rippled regions are approximately 14.0, 18.1, and 18.6 \(\upmu\)m after 10, 50, and 100 shots, respectively. These diameters increased by 29.3% and 32.9% for 50 and 100 shots, respectively, compared with that for 10 shots. The change in the rippled region from 10 shots to 50 shots is considerably larger than that from 50 to 100 shots, which is attributed to incubation. The periods of ripples formed on the titanium surface are affected by the pulse number. The morphologies of rippled structures are shown in Figure 2b,d,f after 10, 50, and 100 shots, respectively. The period of ripple structures is represented by \(\lambda\). The periods of ripples with an orientation perpendicular to laser polarization are approximately 620, 550, and 480 nm for 10, 50, and 100 shots, respectively. The interference between the surface plasmon field and laser field are crucial in forming subwavelength ripples, based on the study in [11]. At the interface between a metal with permittivity \(\varepsilon_{\text{M}}\) and air with permittivity \(\varepsilon_{\text{A}}\), if the value of the real component of the complex dielectric function is less than \(-1\), surface plasmons can be resonantly excited by the coupling between the surface electrons of the dielectric and the incident field, which is characterized by surface electromagnetic waves (also named the surface plasmon field). For metals, the excitation conditions of surface plasma field are always satisfied after the incident femtosecond laser irradiation. Because of the interference between the absorbed laser field and surface plasmon field, coupling field intensity is enhanced in some areas and reduced in other areas. The absorbed laser beam profile is reshaped by the presence of surface plasmons, which displays periodic patterns. Then energy with spatially periodic patterns leads to the periodic patterns of the free electron temperature distribution and lattice temperature distribution. Under the interactions of laser and materials, sub-wavelength ripples are formed in some areas. During the formation of subwavelength ripples, the absorbed energies are gradually absorbed. The cumulative absorbed energy is attributed to differences of subwavelength ripples and ablation areas on titanium obtained at different femtosecond pulses. Figure 1: Schematic diagram of experimental setup. To investigate the evolution of ablation craters and subwavelength ripples with the increasing pulse number, the corresponding experiments are performed. Figure 3 presents dimensions and periods of multiple-shot ablated regions with subwavelength ripples as a function of the pulse number. Figure 3 shows that the ablated areas with ripple structures increase with the increasing number of pulses. The diameters of ablated areas significantly change from 14.0 \(\upmu\)m to 18.1 \(\upmu\)m during the first 50 pulses, which further indicates the incubation behavior of the femtosecond pulse laser ablation of metals. When the pulse number increased from 60 to 100, the diameters of ablated areas are the same, varying from 18.4 \(\upmu\)m to 18.6 \(\upmu\)m.  
Figure 2: SEM images of ablation shapes and subwavelength ripples on titanium obtained at different femtosecond pulses: (**a**,**b**) N = 10, (**c**,**d**) N = 50, and (**e**,**f**) N = 100. The pulse number has considerable effects on the periods of subwavelength ripples (Figure 3).