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Characterization of the laser induced damage threshold of mirrors in ...

Characterization of the laser induced damage threshold of mirrors in ...

Dependence on

Dependence on the positioning relative to the foci Due to the previously discussed astigmatism of the laser it is hard to find a perfectly rotational symmetric focus position, as the foci of the two main axes of the beam are at different positions in space. In order to apply equation 3.1 we need to extend Aσ. Let’s assume that the two beam main axes are Gaussian in space and both can be seen as main axis of an elliptic focus. The focus of the beam is then described by the Gaussian beam waist function x − x0 w = w0 · 1 + where w0 ist the beam waist diameter, x0 the focus position and zr the Raleigh length. We can get all these values by a fit of the Gaussian beam waist function to the data shown in figure 3.6. An example fit is shown in figure 3.11. zr 2 (3.3) Figure 3.11: Example fit of the Gaussian beam waist function on experimental data. Counts refer to the output of every pixel of the CCD or the beam profiling camera. Anyhow we need to transfer the FWHM diameter measured by the beam profiling camera into the required 1 e 2 values first, before we can apply them to equation 3.3. Its trivial to show that for a Gaussian beam σ = The area of an elliptical focus is Including equations 3.3 and 3.4 we get 1 2ln(2) · dF W HM = 0.849 · dF W HM (3.4) Aσ(x) = π · wAxis1(x) · wAxis2(x) (3.5) 28

Aσ(x) = π 2ln(2) · dAx1 · 1 + Angular dependence x − x0Ax1 zrAx1 2 x − x0Ax2 · dAx2 · 1 + zrAx2 2 (3.6) The setup and the damage detection principle allows us to change the angle of incidence (AOI) of the laser light on the sample. In order to implement the dependence of the AOI in equation 3.1 we introduce the effective area Aeff. The illuminated area on the sample changes by Aeff = Aσ(x) · 1 cos(θ) We had some problems operating the setup under zero degree AOI, due to the fact that back reflections from our setup in the multi pass amplifier strongly influenced the general laser output. After an incident, where a back reflection from the damage (3.7) threshold setup caused damage on the amplifier crystal the implementation of a Faraday isolator was evaluated but the provided protection would have been insufficient, so these plans were discarded. In order to avoid complications with the laser, all measurements nominally at zero degrees were done under approximately 1.5 degrees AOI. The final expression Putting together equations 3.1, 3.2, 3.6 and 3.7 we get ˆJ a + b · UP = 2 · · frep 2ln(2) · cos(θ) · ... π x − x0Ax1 ... dAx1 · 1 + ( zrAx1 ) 2 · dAx2 · x − x0Ax2 1 + ( ) 2 zrAx2 This equation is used to calculate the peak fluence on the sample from the output voltage from the power detection diode and to evaluate the statistical error from this measurement. 3.2.6 Error evaluation We calculated the statistical error by applying the Gaussian error propagation to equation 3.8 ∆ ˆ Jstatistical = N i=0 29 d ˆ J dF Pi · ∆F Pi 2 −1 (3.8) (3.9)

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