deletions | additions       diff --git a/Absorption_of_the_laser_beam__.tex b/Absorption_of_the_laser_beam__.tex  index 57dbdd2..bd9f18f 100644  --- a/Absorption_of_the_laser_beam__.tex  +++ b/Absorption_of_the_laser_beam__.tex 
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Substituting low-energy experimental parameters ($E$ = 10 mJ, $S$ = 20 mm$^{2}$) leads to a maximum increase in temperature of 3 K, which produces a local dilatation of the medium. The induced displacements can then generate shear waves, which constitutes the \textit{thermoelastic regime}.  To estimate the initial displacement amplitude in this regime, we assumed the medium was as  homogeneous and isotropic. As the depth of absorption (about 40 $\mu$m) is 100 times smaller than the beam diameter (5 mm), we discarded any boundary effects. The stress, $\sigma_{zz}$, is the sum of the axial strain component and the thermal expansion component \cite{scruby1990laser}: \begin{equation}  \sigma_{zz} = (\lambda + 2 \mu) \frac{\partial u_z}{\partial z} - 3(\lambda + \frac{2}{3}\mu) \alpha \frac{ E}{\rho C S \zeta}  \label{eq:stressThermo} 
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u_z = \frac{3 \alpha E}{\rho C S}  \label{eq:deplThermoApprox}  \end{equation}  Substituting the same experimental parameters used previously along with $\alpha$ = 70.10$^{-6}$ K$^{-1}$ (water linear thermal dilatation coefficient), we obtain a displacement $u_z$ of 0.025 $\mu$m. This value is very close to the measured experimental displacement (about 0.02 $\mu$m). Note that both thetheoretical and  experimental and theoretical  central displacements are directed towards the outside of the medium (see white circle arrow in the Figure \ref{figElastoPVA}-(A)). Figures \ref{figElastoPVA}-(A) and \ref{figGreen}-(A)).  To calculate the propagation of the displacements as shear waves, we must first consider the transverse dilatation, which leads to stronger displacements than those occurring along the Z axis. We thus modeled the thermoelastic regime in 2D as two opposite forces directed along the Y axis with a depth of 40 $\mu$m and with an amplitude decreasing linearly respectively from 2.5 to 0 mm and from -2.5 to 0 mm \cite{Davies_1993}. The magnitude of the force along space and time is stored in a matrix, $H_y^{thermo}(y,z,t)$. Displacements along the Z axis are then equal to the convolution between $H_y^{thermo} (y,z,t)$ and $G_{yz}$ \cite{aki1980quantitative}:  \begin{equation}