deletions | additions       diff --git a/Physical model.tex b/Physical model.tex  index cc0cab8..2ee801f 100644  --- a/Physical model.tex  +++ b/Physical model.tex 
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Let's describe these phenomena in a physical point of view.Z is defined as the laser beam axis and origin of coordinates (0,0,0) as the laser impact location on the medium.  The optical intensity $I_0$ of the laser beam is defined as $I_0=\frac{1}{S}\frac{d E}{dt}$, where $E$ is the beam energy and $S$ the beam surface. When emitted on a medium surface, the laser beam is absorbed with an exponential decay along medium depth $z$:  \begin{equation}  I(z)=(1-R) I_0 \exp(- \gamma z)  \label{eq:expontentialDecay}  \end{equation}  where $R$ is the reflection coefficient of the material (supposed negligible on a black mat material as the one used here) and $\gamma$ the absorption coefficient of the medium. This absorption coefficient $\gamma$ can be estimated through the skin depth $\delta$ with the relation $\gamma=2/\delta=2(\pi \sigma \mu_r \mu_0 \nu)^{\frac{1}{2}}$, where $\sigma$ is the electrical conductivity of the medium, $\mu_r \mu_0$ its permeability, $\nu$ the frequency of the radiation and factor 2 is due the relation of $\delta$ with magnitude of the electrical field while $\gamma$ is related to the magnitude of the optical energy, equal to the square of the electrical field magnitude. Substituting $\sigma \approx$ 0.1 S.m$^{-1}$, $\mu_r \mu_0$ = 4 $\pi \times 10^{-7}$ H.m$^{-1}$ and $\nu$ = 3 10$^8$ / 532 10$^{-9}$ = 5.6 10$^{14}$ Hz, we find that $\gamma^{-1} \approx$ 35 $\mu m$: it means that about 63\% of the radiation energy is absorbed in the first 35 micrometers of the sample. We have validated experimentally this value by measuring the fraction of light which go through different thicknesses of the medium (0, 30, 50 and 100 $\mu$m) with a laser beam power energy  measurement device (QE50LP-S-MB-D0 energy detector, Gentec, Qu\'ebec, QC, Canada). We found respective transmitted powers of 100\%, 42\%, 28\% and 11\%: an exponential fit indicated that $\gamma^{-1} \approx$ 40 $\mu m$ in our sample, which is in accordance with the value found previously.