deletions | additions       diff --git a/Dependance with beam power.tex b/Dependance with beam power.tex  index a20a316..1c93657 100644  --- a/Dependance with beam power.tex  +++ b/Dependance with beam power.tex 
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%Shear wave amplitude has been shown to be linearly dependent on laser beam power in thermoelastic and ablative regime. However, at higher amplitude (about 10$^9$ W.cm$^{-2}$ in metals \cite{scruby1990laser}), a plasma occurs and lead to a non-linear amplitude of the displacement with laser energy.  The dependence of the generated shear wave amplitude with laser energy was finally investigated quantitatively by increasing the laser beam energy from 10 to 200 mJ. To increase the signal-to-noise ratio, amplitude have been averaged over four experiments for each energy level. Successive energy levels were randomly chosen to avoid any time-related bias and impact location was changed after each laser emission to avoid any potential local degradation of the medium. Shear wave amplitude was measured as the mean square amplitude at t = 1 ms of the displacement between 0 and 10 mm of the medium surface, an arbitrary location where shear waves had high amplitudes. Resulting measurements are illustrated in Figure \ref{figDepEnergy}. Two linear dependences dependencies  are observed: one from 10 to 40 mJ, with a slope of 1.05 (R$^2$ = 0.87), and one from 30 mJ to 200 mJ, with a slope of 2.18 (R$^2$ = 0.97). This is in accordance with the theory which presents a linear dependence of the displacement with energy at low energy, i.e. in the thermoelastic regime as described in equation \ref{eq:deplThermoApprox}, and a quadratic dependence at high energy, i.e. in the ablative regime as described in equation \ref{eq:deplAblaApprox}.