deletions | additions       diff --git a/When_a_laser_beam_of__1.tex b/When_a_laser_beam_of__1.tex  index b414d4c..e496609 100644  --- a/When_a_laser_beam_of__1.tex  +++ b/When_a_laser_beam_of__1.tex 
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I=I_0 \exp(- \gamma z)  \end{equation}  where $I_0$ is the incident intensity distribution at the surface and $\gamma$ is the absorption coefficient of the medium. In non-metallic solids, the absorption coefficient $\gamma$ is relatively small, so that the radiation is able to penetrate into the bulk of the material - contrary to metals where the radiation is absorbed within a few nanometres. The absorption of the laser beam by the medium gives then rise to an absorbed optical energy $q$ equal to $\gamma I$.  Assuming that all the optical energy is converted to heat, a local increase of temperature appears. Temperature In absence of convection, temperature  distribution can be computed using heat equation \cite{Li_2014}: \begin{equation}  \frac{k}{c_k} \frac{\partial^2 T}{\partial^2 t}+ \rho C  \frac{\partial T}{\partial t} = k \frac{k}{\rho C}  \nabla ^2 T + q \frac{q}{\rho C}  \end{equation}  where $T$ is the temperature distribution,$c_k$ the thermal wave speed (usually taken as equal to the compression wave speed),  $\rho$ the density,$\kappa$ the thermal diffusivity and  $C$ the heat capacity. capacity and $\kappa$ the thermal diffusivity.  This parameter needs to be compared to the thermal diffusion path, given by $\sqrt(4 \kappa t)$. $\kappa$ is approximately equal to 10${^6}$ m$^2$.s$^{-1}$ for water, the main component of biological tissues; for a 10 ns laser pulse, the thermal diffusion path is then equal to 0.01 to 0.1 $\mu$m. $\gamma^{-1}$ of water is equal to 0.1 m, which is a million times higher; even for melanin and haemoglobin, highly absorbing at 532 nm, $\gamma^{-1}$ is respectively equal to 10 and 100 $\mu$m, far higher than the thermal diffusion path. The thermal conductivity effects are consequently negligible, and increase of temperature lies in laser absorption zone. The local increase of temperature can lead to two main effects creating elastic waves: (1) Thermoelastic expansion and (2) Ablation of medium. In metals, transition from first to second regime occurs approximately about 10$^7$ W.cm$^{-2}$. This is equal to the energy of the laser we used, so the predominant regime in our experiment cannot be determined yet. 
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