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If enough energy is deposited, the local increase of temperature can also vaporize a part of the surface of the medium \cite{scruby1990laser}. Ejection of particles leads to a displacement inside the medium which can create shear waves: this constitutes the \textit{ablative regime}.
Solving equation \ref{eq:eqChaleurApprox} with same experimental parameters as before but a laser energy of 200 mJ, we find a maximum increase of temperature of 60 K, which is close to the vaporization point of our medium, about 373K (water vaporization temperature). Besides the uncertainty of some values, it has been demonstrated that the presence of small particles like the graphite particles in our medium acts as nucleation sites for vaporization, which facilitate the vaporization of the medium at lower temperature \cite{Alimpiev_1995}: the laser energy can in reality be sufficient to
get a "vaporization" regime. vaporize the medium. Vaporization of particles leads by reaction to displacements inside the medium, which can create shear waves: this constitutes the \textit{ablative regime}.
This phenomenon can be modeled as To describe this vaporization, we take a
homogeneous and isotropic medium. The stress $\sigma_{zz}$
in is, similarly to the
medium, as previous section, the sum of the P-wave modulus and a term given by the second law of motion \cite{scruby1990laser}:
\begin{equation}
\sigma_{zz} = (\lambda + 2 \mu) \frac{\partial u_z}{\partial z} - \frac{1}{\rho}\frac{I^2}{(L+C(T_V-T_0))^2}
\label{eq:stressAbla}
\end{equation} where $L$ is the latent heat required to vaporize the solid, $T_0$ and $T_V$ the initial and vaporization temperatures.
Similarly to the thermoelastic regime, this The stress leads to a displacement $u_z$:
\begin{equation}
u_z = \frac{\zeta}{\rho (\lambda + 2 \mu)}\frac{I^2}{(L+C(T_V-T_0))^2}
\label{eq:deplAbla}
...
\end{equation}
Estimating $\zeta$ equal to 50 $\mu$m (average depth of absorption), $\lambda$ = 2 GPa (first Lamé's coefficient of water), $L$ = 2.2 MJ.kg$^{-1}$ (vaporization latent heat of water), $T_V-T_0$ = 373-293 = 80 K (water vaporization temperature minus laboratory temperature), $C$ = 4180 J.kg$^{-1}$.K$^{-1}$, $\rho$ = 1000 kg.m$^{-3}$, $E$ = 200 mJ, $S$ = 20 mm$^2$ and $\tau$ = 10 ns, we obtain a displacement $u_z$ approximately equal to 3.9 $\mu$m. This is in the order of magnitude of the experimental measured displacement (2 $\mu$m).
This displacement along Z can create shear waves. We modeled the ablation
regime as a point force directed along Z direction with a depth of 50 $\mu$m and increasing linearly from -2.5 to 0 mm and decreasing symmetrically from 0 to 2.5 mm, to simulate an approximate Gaussian shape. Propagation as a shear wave was calculated using Green operators $G_{zz}$ \cite{aki1980quantitative}:
\begin{equation}
G_{zz}(r,\theta,z) G_{zz}(r,\theta,z,t) = \frac{\cos^2 \theta}{4\pi \rho c_p^2 r}
\delta_P f(t-\frac{r}{c_p}) + \frac{\sin^2 \theta}{4\pi \rho c_s^2 r}
\delta_S f(t-\frac{r}{c_s}) + \frac{3\cos^2 \theta-1}{4\pi \rho r^3} \int_{r/c_p}^{r/c_s}{\tau
\delta_{NF}} f_{NF}}
\label{eq:Gzz}
\end{equation}
where $\theta$ is the angle between the applied force and the considered point (r,$\theta$,z), $\rho$ the medium density, $c_p$ and $c_s$ the compression and shear wave speed respectively,
$\delta_S$ and $\delta_P$ Dirac distribution indicating the position of the compression and shear waves along space and time, $\tau$ the time and
$\delta_{NF}$ $f_{NF}$ representing near-field effects. The three terms correspond respectively to the far-field compression wave, the far-field shear wave and the near-field component.
Displacement can again be computed by convoluting the 4-D matrix $H_z(x,y,z,t)$ of the applied force with $G_{zz}$. The medium density $\rho$ was taken equal to 1000 kg.m$^{-3}$, the compression wave speed to 1500 m.s$^{-1}$ and the shear wave speed to 5.5 m.s$^{-1}$.
