## 3 Results and Discussion
For a spherical bubble in free liquid, the first collapse shock wave has a similar or even larger amplitude than the breakdown shock wave [27; 43]. However, in this case, the strength of the first collapse shock wave was notably diminished compared to the strength of the breakdown shock wave, resembling the shock wave emitted at the collapse of the re-oscillating bubble with a considerably smaller size, as shown in Figure 2d. This can be attributed to the enhanced non-spherical  
Figure 2: Cavitation dynamics for the case \(d=10\) mm and \(h=27\) mm. (**a**) Photographic series with a frame interval of 4 \(\upmu\)s. The length scale was 5 mm, with the laser pulse incident from the left; temporal evolution of the laser bubble radius and its comparison to the Rayleigh–Plesset simulation (**b**) and the total area of secondary bubble clouds on the upstream side of the laser bubble (**c**), determined from images series; (**d**) far-filed acoustic signal. Shock waves emitted at secondary bubble collapse were detected (blue arrows). collapse, resulting from the asymmetrical interactions between the laser bubble and the secondary bubble clouds, as well as the direct influence of vibrational rarefaction waves. Figure 3 depicts the evolution of \(T_{\text{osc1}}/T_{\text{Ray}}\) with \(R_{\text{max}}\). Here, \(T_{\text{Ray}}\) and \(R_{\text{Ray}}\) denote the first oscillation time and maximum size of the laser bubble in free liquid, respectively. Their linear relationship can be described by the Rayleigh formula \(R_{\text{Ray}}=\frac{T_{\text{Ray}}}{1.83}\sqrt{\frac{p_{\infty}-p_{\
u}}{\rho}}\)[44]. The parameters are \(p_{\
u}\) the saturated vapor pressure, \(p_{\infty}\) the static pressure, and \(\rho\) the liquid density. In this work, \(p_{\
u}=2330\) Pa, \(p_{\infty}=100\) kPa, and \(\rho=998\) kg/m\({}^{3}\). \(T_{\text{Ray}}\) was calculated from \(R_{\text{max}}\). The maximum radius of the laser bubble was reduced remarkably by the confined effect, leading to an underestimation of \(T_{\text{Ray}}\). It was observed that the ratio \(T_{\text{osc1}}/T_{\text{Ray}}\) slightly decreased with increasing bubble size at first, and reached a minimum at \(R_{\text{max}}\approx 380\) um, which corresponds to \(T_{\text{osc1}}\) of 65 \(\upmu\)s. This is because, these laser bubbles collapsed before tensile vibrational pressure and only suffered from the confined effect-induced compressive pressure. On further increasing \(R_{\text{max}}\) and \(T_{\text{osc1}}\), the laser bubble suffers from the strong tensile pressure of the vibrational rarefaction wave, leading to a rapid increase in the ratio \(T_{\text{osc1}}/T_{\text{Ray}}\). It is worth noting that the growth rate of the ratio \(T_{\text{osc1}}/T_{\text{Ray}}\) reduced in the range between \(R_{\text{max}}\approx 550\) um and \(R_{\text{max}}\approx 650\) um, and increased again after that. This is associated with the bipolar property of the rarefaction wave. Laser bubble expansion and its induced liquid-mass oscillation along the free surface in the confined finite liquid produce pressure rises within the liquid, which deform the elastic walls and lead to wall vibrations [23; 25]. The alternating stretching and then the compression of the wall resulted in a series of extra vibrational rarefaction waves within the liquid, as shown in Figure 4. It was the initial tensile part of each rarefaction wave induced by outward stretching of the wall that led to the prolongation and re-oscillations of the laser bubble and to the periodic expansion of pre-nucleated secondary bubble clouds along the laser path. Subsequent tensile waves, triggered by liquid-mass oscillation-induced wall vibrations, drive the re-oscillations of the laser bubble and the subsequent initiation of secondary bubble clouds. The superposition of adjacent waves is negligible because the vibrational rarefaction wave decays fast [23].