The purpose of this study is to estimate ablated crater depth with sufficient numerical accuracy when multi-shot channels of ultra-short pulsed laser are executed for micro drilling processes on thin glass plates. In this analytical model, the plasma model, in which the free electron density and the complex dielectric function of the Lorentz model are evaluated, is applied to estimate the ablated regions and the regions damaged by laser ablation when glass is considered to be a dielectric material. The absorption coefficient and the threshold fluence are important parameters in the evaluation of the ablated crater depth and ablation rate. The parameters obtained in this numerical analysis are in agreement with the experimental results and are computed quantitatively to several laser irradiation conditions. The experimental results and analysis results are examined for multi-shot channels. In an experiment involving laser ablation using multi-shot laser beams, ablation rates for the initial shot are lower than subsequent ablation rates. The effectiveness of the modified absorption coefficient and modified threshold fluence for initial shots is confirmed for the reduction of ablation rate.

1. [1]  J. R. Vazquez de Aldana, C. Mendez, L. Roso, and P. Moreno, “Propagation of ablation channels with multiple femtosecond laser pulses in dielectrics: numerical simulations and experiments,” J. of Phys. D: Applied Physics, Vol.38, pp. 2764-2768, 2005.
2. [2]  M. Sun, U. Eppelt, S. Russ, C. Hartmann, C. Siebert, J. Zhu, and W. Schulz, “Numerical analysis of ablation and damage in glass with multiple picosecond laser pulses,” Optics Express, Vol.21, No.7, pp. 7858-7868, 2013.
3. [3]  L. Jiang and H. L. Tsai, “A plasma model combination with improved two-temperature equation for ultrafast ablation of dielectrics,” J. of Applied Physics, Vol.104, pp. 093101-1-8, 2008.
4. [4]  L. Jiang and H. L. Tsai, “Energy transport and material removal in wide bandgap materials by a femtosecond laser pulse,” I. J. Heat and Mass Transfer, Vol.48, pp. 487-499, 2005.
5. [5]  L. Jiang and H. L. Tsai, “Improved Two-emperature Model and Its Application in Ultrashort Laser Heating of Metal Films,” J. Heat Transfer, Vol.127, pp. 1167-1173, 2005.
6. [6]  A. Ben-Yakar and R. L. Byer, “Femtosecond laser ablation properties of borosilicate glass,” J. of Applied Physics, Vol.96, No.9, pp. 5316-5323, 2004.
7. [7]  A. Ben-Yakar, A. Harkin, J. Ashmore, R. L. Byer, and H. A. Stone, “Thermal and fluid processes of a thin melt zone during femtosecond laser ablation of glass: the formation of rims by single laser pulses,” J. of Phys. D: Applied Physics, Vol.40, pp. 1447-1459, 2007.
8. [8]  P. K. Kennedy, “A First-Order Model for Computation of Laser-Induced Breakdown Thresholds in Ocular and Aqueous Media: Part I-Theory,” IEEE J. of Quantum Electronics, Vol.31, No.12, pp. 2241-2249, 1995.
9. [9]  C. H. Fan, J. Sun and J. P. Longtin, “I Breakdown threshold and localized electron density in water induced by ultrashort laser pulses,” J. Applied Physics, Vol.91, No.4, pp. 2530-2536, 2002.
10. [10]  V. S. Popov, “Tunnel and multiphoton ionization of atoms and iones in a strong laser field (Keldysh theory),” Physics Uspekhi, Vol.47, No.9, pp. 855-885, 2004.
11. [11]  L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Soviet Physics JETP, Vol.20, No.5, pp. 1307-1314, 1965.
12. [12]  A. Kaiser, B. Rethfeld, M. Vicanek, and G. Simon, “Microscopic processes in dielectrics under iradiation by subpicosecond laser pulses,” Physical review B, Vol.61, No.17, pp. 437-450, 2000.
13. [13]  B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Petty, “Nanosecond-to-femtosecond laser-induced breakdown in dielectrics,” Physical review B, Vol.53, No.4, pp. 1749-1761, 1996.
14. [14]  M. Lenzner, J. Kruger, S. Sartania, Z. Cheng, C. Spielmann, G. Mourou, W. Kautec, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Physical review letters, Vol.80, No.18, pp. 4076-4079, 1998.