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Pol Grasland-Mongrain edited Physical model.tex
over 8 years ago
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Let's describe these phenomena in a physical point of view.
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, in absence of reflection, the laser beam is absorbed with an exponential decay along medium depth $z$: $I(z)=I_0 \exp(- \gamma z)$, where $\gamma$ is the absorption coefficient of the
medium. medium.% This 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 measured experimentally
this value $\gamma$ 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 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, sample.%, which is in accordance with the value found previously.