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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 leads to a maximum temperature of about 360 K. While slightly below to the vaporization point of our medium,
about supposed close to 373K (water vaporization
temperature). Besides temperature), it can be be sufficient to vaporize the
uncertainty of some values, medium; Moreover, 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 vaporize the medium. \cite{Alimpiev_1995}. Vaporization of particles leads by reaction to displacements inside the medium, which can create shear waves: this constitutes the \textit{ablative regime}.
To describe this vaporization, we
take a suppose the medium as homogeneous and
isotropic medium. isotropic. The stress $\sigma_{zz}$ is, similarly to the 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}
...
u_z = \frac{\zeta}{\rho \lambda}\frac{I^2}{(L+C(T_V-T_0))^2}
\label{eq:deplAblaApprox}
\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 (2.5 $\mu$m).
To calculate the propagation of the displacement along space and time, 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. Propagation as a shear wave was calculated using Green operators $G_{zz}$ \cite{aki1980quantitative}:
\begin{equation}
G_{zz}(r,\theta,z,t) = \frac{\cos^2 \theta}{4\pi \rho c_p^2 r} f(t-\frac{r}{c_p}) + \frac{\sin^2 \theta}{4\pi \rho c_s^2 r} 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 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, $\tau$ the time and $f_{NF}$ 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. with same notations as in equation \ref{eq:Gyz}.
Displacement can again be computed by convoluting the
applied force 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$^{-1}$.
Results Using same values for the physical quantities as previously, results are
shown on illustrated in Figure \ref{figGreen}-(B) which represents displacement maps between each frame along Z axis 1.0, 1.5, 2.0, 2.5 and 3.0 ms after force application. The displacement maps present many similarities with the experimental results of the Figure \ref{Figure2}: initial displacement is
positive only directed inside the medium and
only two half cycles are propagating.
Ablation regime has also confirmed visually: at high power, a disk of paler color of the same size as the beam diameter appears at the impact location of the laser on the phantom, which is coherent to a vaporization of a fraction of the material.
This was not observed in the low-energy experiments.
