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Pol Grasland-Mongrain edited Physical model.tex
over 8 years ago
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\gamma=\frac{2}{\delta}=2(\pi \sigma \mu_r \mu_0 \nu)^{\frac{1}{2}}
\label{eq:skinDepth}
\end{equation}
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 (respectively 0, 30, 50 and 100 $\mu$m) with a laser beam power 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 $\gamma^{-1} \approx$
50 40 $\mu m$ in our sample, which is in accordance with the theoretical value found previously.