## 3 Results and Discussion
### Influence of Numerical Aperture on Movement of Absorption Point  
As mentioned above, different focusing situations were obtained by using objective lenses of different numerical apertures. It was also understood that absorption point moved repeatedly in laser irradiation direction and molten area was created around the focusing point [19]. Therefore, it can be considered that numerical aperture would have an influence on movement of absorption point, and  
Figure 9: Measurement method and results of diameter of laser spot focused in glass. this was experimentally investigated by the formation phenomena of molten area and the absorption rate with different numerical apertures in this section. The absorption of laser energy is based on multi-photon ionization and avalanche ionization of nonlinear phenomenon, when an ultrashort pulsed laser beam is tightly focused inside the glass. The focusing point is considered as the starting point for laser absorption, which is defined as the absorption point. In this study, high-speed video camera was used to observe the absorption point movement without illumination light. Only plasma light was observed during this observation, which was easy to recognize the absorption point, as shown in Figure 10. The laser irradiation condition of pulse repetition rate 1.0 MHz, scanning velocity 20 mm/s and pulse energy 2.4 \(\upmu\)J was employed in this experiment. In order to estimate the amount of effective laser pulses that reached the glass per spot volume, the number of overlapped laser pulses \(N\) was calculated using Equation (3). \[N=\frac{D_{\text{in}}R_{\text{P}}}{v} \tag{3}\]  
where \(D_{\text{in}}\) is the spot diameter in glass, \(R_{\text{P}}\) is the pulse repetition rate and \(v\) is the scanning velocity [29]. Here, pulse repetition rate and scanning velocity are \(R_{\text{P}}\) = 1.0 MHz and \(v\) = 20 mm/s, respectively. According to the results shown in Figure 9c, spot diameter \(D_{\text{in}}\) is estimated as 10 \(\upmu\)m. Therefore, the calculation result of \(N\) is 500, showing that 500 overlapped laser pulses reached the glass per spot volume in this experiment. In the captured images of Figure 10, the absorption point of laser beam moved in upper direction with increasing time from the starting point. It should be noticed that there were two white spots at t = 0 \(\upmu\)s. This phenomenon indicates the transition of absorption point, which was dropped down from the upper side. Then, the location of absorption point was measured in these captured images by calculating the feed rate of specimen. The location of lowest point of absorption movement was set to 0 \(\upmu\)m, and the direction to the laser source was considered as positive value. These measurement results were arranged as the relationship between location of absorption point \(L_{\text{a}}\) and time for various numerical apertures, which indicated the influence of numerical aperture on formation phenomena of molten area, as shown in Figure 11. Figure 11a shows the measurement results at the start region of laser irradiation. N.A. of 0.45 showed a constant maximum location of absorption point from the start. On the other hand, maximum location of absorption point movement during one cycle increased with time at beginning in the case of N.A. of 0.65 and 0.85. Then, the location of absorption point of these two numerical apertures took a constant maximum value, and each cycle of absorption point movement was almost constant after 400 \(\upmu\)s and 300 \(\upmu\)s, respectively. This state was referred to as the steady region. After recounting the time, the relationship between \(H_{\text{a}}\) and time of the steady region is shown in Figure 11b. It can be seen that location of absorption point was varied by numerical apertures. Lower N.A., which showed a constant maximum location of absorption point from start of irradiation, obtained a larger location of absorption point and longer cycle of absorption point movement in the steady region, compared with higher N.A.