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Saturation of ablation channels micro-machined in fused silica with many femtosecond laser pulses

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Abstract

We investigate the effect of saturation in the propagation of ablation channels performed in fused silica with many incident femtosecond pulses and laser fluence slightly above the ultrafast ablation threshold. A 110 fs Ti:Sapphire laser system is used in the experiments and the results are compared with theoretical predictions performed with a numerical model developed by the authors. Diffraction of the incoming pulses at the entrance of the channel as well as reflections at the walls of the channel play a crucial role in the progress of the crater as it is shown by means of the numerical results. The effect of the pulse duration in the shape of the ablation channel is also investigated.

©2006 Optical Society of America

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Supplementary Material (5)

Media 1: GIF (99 KB)     
Media 2: GIF (119 KB)     
Media 3: GIF (566 KB)     
Media 4: GIF (556 KB)     
Media 5: GIF (603 KB)     

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Figures (5)

Fig. 1.
Fig. 1. Ablation depth of the channels (in μm) in terms of the number of incident laser pulses. a) Experimental results for 110 fs pulses and F 0 = 7 J/cm2. The FWHM beam size was 10.4 μm (red dots) and 8.2 μm (blue dots). b) Numerical results for 50 fs pulses and F 0 = 5.2 J/cm2 (2Fth ). The same beam sizes were employed as in the experiments.
Fig. 2.
Fig. 2. Digital pictures of the saturated ablation channels for beam sizes a) 8.2 μm and b) 10.4 μm. Laser parameters are the same as in Fig. 1 a). The movies at the bottom (c) [98.9 KB] [Media 1] and d) [118.6 KB] [Media 2]) are numerical simulations for the evolution of the ablation channel. Each frame corresponds to an additional incident pulse. The parameters in the simulations are the same as in Fig. 1 b).
Fig. 3.
Fig. 3. Numerical simulations for the propagation of the a) [566 KB] 1st [Media 3], b) [556 KB] 15th [Media 4] and c) [603 KB] 40th [Media 5] incident laser pulse. The movies show different time steps of the propagation. Panels on the left represent the squared magnitude of the electric field (in logarithmic scale). Panels on the right represent the free-electron density. The logarithmic color scale is given in m -3. The pulse duration in the simulations was 50 fs, the fluence F 0 = 2Fth (50fs) = 5.2 J/cm2 and the beam size 8.2 μm.
Fig. 4.
Fig. 4. Diffraction pattern generated by an aperture equal to the entrance diameter of the saturated channel of the previous figure (≃ 11 μm) and 50 fs pulses. The pattern has been computed by numerical integration of the scalar wave-equation with no further approximation. The gray scale is linear with the energy density.
Fig. 5.
Fig. 5. Ablation depth of the channels performed with 40 fs pulses (blue dots) and with 20 fs pulses (red dots) in terms of the number of incident laser pulses. The beam size in both cases is the same and the fluence F 0(40fs) = 2Fth (40fs) = 4.80 J/cm2 and F 0(20fs) = 2Fth (20fs) = 3.62 J/cm2. In dashed line it is also shown the entrance diameter of the ablation hole. The computed saturated ablation channels appear at the bottom for the 40 fs (left) and 20 fs (right) pulses.

Equations (5)

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[ 2 z 2 + 2 ρ 2 + 1 ρ ρ 1 c 2 2 t 2 ] E z ρ t = 1 ε 0 c 2 2 P z ρ t t 2 ,
2 P z ρ t t 2 = Ω 0 2 P z ρ t γ P z ρ t t n B e 2 m P z ρ t .
n F t = W imp n F + W SFI W rec n F .
E ( z = 0 , ρ , t ) = E 0 exp ( 2 ln 2 t 2 τ 2 ) exp ( ρ 2 ρ 0 2 ) sin ( ωt ) ,
W ( z , ρ ) = 0 E z ρ t E z ρ t dt .
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