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

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

σ = e 2 · τc c · ɛ0

σ = e 2 · τc c · ɛ0 · n0 · m · 1 1 + ω 2 · τ 2 c e is the electron charge, τc the collision time, m the effective electron mass and ω the (2.11) laser frequency. The collision time is determined by the electron-phonon scattering rate. Arnold et al. pointed out theoretically that electron momentum relaxation rates in SiO2 are electron energy dependent varying by 2 orders of magnitude. The corresponding value of τ is approximately 0.1 fs to 10 fs.[60] The collision time in SiO2 was measured to be about 1.7 fs at a CB electron density near 5 · 10 −19 cm −3 after excitation with a 130 fs, 800 nm pulse.[61] It should be obvious that while the contribution to the CB density from the MPI is decreasing, the contribution of the avalanche is increasing proportional to λ 2 . 2.3.4 Incubation effects Similar to the thin film data from Mero et al.[6] presented in figure 2.8 there have been other investigations on this topic. Ashkenasi et al.[27] studied the dependence of the damage threshold of fused silica and YLF 10 on the number of incident pulses. While Mero et al. used rate equations to explain the decreasing damage threshold with increasing pulse number, Ashkenasi et al. used a simple phenomenological model assuming an exponential decay from the single pulse damage threshold FT h(1) to a constant lower damage threshold FT h∞. FT h(N) = FT h(∞) + [FT h(1) − FT h(∞)] · e −k·(N−1) (2.12) FT h(1) - FT h(∞) and the decay constant k depend on the material, the temperature and whether sample is in vacuum or in air. 2.3.5 Impact of the beam diameter on the damage threshold Martin et al studied the dependence of the damage threshold on the beam diameter for fs-pulses.[62, 9] The behavior of Schott BG 18 ion doped glass can be seen in figure 2.11. DeShazer et al. has developed in 1973 a model that is able to describe this, by assuming Poisson distributed defects and a lower damage threshold of a defect site.[63] It can be shown, that the probability of hitting a defect site with a Gaussian laser beam is given by equation 2.13, where w0 is the beam radius and d0 is the mean defect distance. π2 − 32 P (w0) = 1 − e ·( w0 ) d0 2 10 yttrium lithium fluoride in crystalline configuration 16 (2.13)

Figure 2.11: Dependence of the laser ablation threshold on the beam radius measured with 1000 pulses of 30 fs at 1 kHz. Fit according to the presented model. [9] Introducing two ablation thresholds Fdefect and Fintrinsic one can determine the beam size dependent ablation threshold as: Fth(ω0) = P (ω0) · Fdefect + [1 − P (ω0)] · Fintrinsic 2.3.6 Dependence on the band gap (2.14) A dependence of the damage threshold on the band gap has been measured.[5, 33] The data from Mero et al. is shown in figure 2.12. It is by far the most interesting dependence for manufacturing considerations of dielectric mirrors, as this knowledge can be easily used in the design process. Abromavicius et al. for instance increased the damage threshold of their optics by almost a factor of two just by adjusting the layer structure in such a way, that the highest occurring electric fields are located in the high band gap material.[64] This dependence can be readily explained by the rate equation model presented earlier. Qualitatively both the avalanche ionization rate displayed in equation 2.5 and the photo ionization rate as displayed in equation 2.4 are dependent on the bandgap. 2.4 About literature values of damage threshold The extensive dependencies on various parameters make it hard to use literature values for damage threshold. What is often neglected is the problem of incomparable samples, for instance there are various suppliers for fused silica substrates with large differences in surface quality and purity. Furthermore, the already presented dependencies are only the very elementary ones, there are further influences like cracks and pores, emerging 17

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