## 3 Results and Discussion
### Ejection-Based Transfer Mechanism
Finally, the assumed ejection in normal direction of the donor substrate polyimide expansion over a distance \(z_{0}\) toward the acceptor substrate for two time points ((**c**); red and blue) and the qualitative shape function \(\left.B(r)\right|_{z_{0}}\) for different \(z_{0}\) is shown ((**d**); \(T=10\) ms, \(P=160\) mW, and \(\omega=42.5\) μm). the maximum polyimide surface was already analytically determined Equation (14), the expansion \(z(r,t)\) can be stated by Equation (16). Then, \(c(t)\) can be set to \(h_{P}(t)\) Equation (17), because a \(\approx\)3:1 radius to height ratio of the polyimide expansion was observed. With this approximation, 99.7% of the polyimide surface expansion is covered. The term \(\tan(\alpha)\) can be obtained through the derivative of Equations (17) and (18) and thus, the geometric mapping can be obtained by Equation (19). \[z(r,t)=h_{P}(t)e^{-\left(\frac{r}{\pi(t)}\right)^{2}} \tag{16}\] \[z(r,t)=h_{P}(t)e^{-\left(\frac{r}{h_{P}(t)}\right)^{2}}\] (17) \[\tan(\alpha(r,t))=-2\frac{r}{h_{P}(t)}e^{-\left(\frac{r}{h_{P}(t) }\right)^{2}}\] (18) \[\theta(r,t)\big{|}_{z_{0}}=r\Bigg{(}1-2\Bigg{(}z_{0}h_{P}(t)-e^{- \left(\frac{r}{h_{P}(t)}\right)^{2}}\Bigg{)}e^{-\left(\frac{r}{h_{P}(t)} \right)^{2}}\Bigg{)} \tag{19}\]  
As of now, the ejection was considered to be equal for every location. However, this would imply that the largest irradiance (location \(r=0\)) has the same ejection as the lowest (\(r\rightarrow\infty\)). Thus, the ejection is assumed to be related to the induced Gaussian irradiance, which results in Equation (20) after introducing the mapping \(\left(r,t\right)\mapsto\left.\theta(r,t)\right|_{z_{0}}\). Through this proportionality, the distribution of ejection over the lasing duration can be expressed by Equation (21). The distribution contains the qualitative shape function \(B(r)\big{|}_{z_{0}}\) Equation (22), which characterizes the observed main spot with its surrounding ring structure in two dimensions (Figure 3d). \[\rho(\theta(r,t)\big{|}_{z_{0}},t)\propto I(\theta(r,t)\big{|}_{z_{0}},t) \tag{20}\]  
\[R(r)\big{|}_{z_{0}}=\int_{0}^{T}\rho(\theta(r,t)\big{|}_{z_{0}},t)dt=\left. \gamma(r)\right|_{z_{0}}\int_{0}^{T}\frac{2P}{\pi\omega^{2}}e^{-2\left(\frac{ \theta(r,t)\big{|}_{z_{0}}}{\omega}\right)^{2}}dt. \tag{21}\]  
\[B(r)\big{|}_{z_{0}}=\int_{0}^{T}\frac{2P}{\pi\omega^{2}}e^{-2\left(\frac{ \theta(r,t)\big{|}_{z_{0}}}{\omega}\right)^{2}}dt \tag{22}\]  
As observed within the experiment, an increasing distance between the acceptor and donor substrates \(z_{0}\) reduces the width of the center peak (i.e., main spot) and shifts the two surrounding peaks (i.e., ring structure) to the outside (Figure 3d). Yet, the shape function does not capture the ejection ratios between the main spots and ring structures. Moreover, the location of the ring structures (for the different acceptor-donor substrate distances) are falsely predicted. For completeness, it was identified that the function \(R(r)\big{|}_{z_{0}}\) follows an exponential form (Figure S4 and Equation (23)). \[\theta(r,t)\big{|}_{z_{0}}=r+\left.\Delta r(r,t)\right|_{z_{0}}=r+(z_{0}-z(r,t ))\tan(\alpha(r,t))\quad\text{with }z_{0}\geq z(r,t) \tag{15}\]0