Geodesic
Boundary conditions in the modeling of the material modification by laser pulses
Matematičeskoe modelirovanie, Tome 35 (2023) no. 4, pp. 65-87.

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To modify transparent materials by femtosecond laser pulses sharply focused pulses are required. To model the modification process, it is necessary to compute the distribution of the electric field of the pulse in the vicinity of the order or less 100 microns from the focus. An often-used paraxial formulas in the case of sharp focus are not applicable. In the case, when a parabolic mirror is used as a focusing element, the desired field distribution can be obtained using Stratton-Chu integral (SCI). In the presented paper the generalization of SCI on the short in time pulses, the simplification of SCI in the limit of the mirror's focus length much larger 100 microns, and concrete formulas of SCI for the pulses of different polarizations are given. The main achievement of the paper is development of extremely effective numerical methods of SCI computation. The last one is a difficult problem. Using this method unexpected and intriguing properties of the field created by sharp focusing top-hat laser pulse are demonstrated.
Keywords: Stratton-Chu integral, integration of fast oscillating function, laser-matter interaction, parabolic mirror, femtosecond laser pulse, top-hat pulse.
Mots-clés : large aperture 
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V. P. Zhukov; M. P. Fedoruk. Boundary conditions in the modeling of the material modification by laser pulses. Matematičeskoe modelirovanie, Tome 35 (2023) no. 4, pp. 65-87. http://geodesic.mathdoc.fr/item/MM_2023_35_4_a3/

[1] D. Tan, K. N. Sharafudeen, Y. Yue, J. Qiu, “Femtosecond laser induced phenomena in transparent solid materials: Fundamentals and applications”, Progress in Materials Science, 76 (2016), 154–228

[2] H. Misawa, S. Juodkazis, 3D Laser Microfabrication: Principles and Applications, Wiley-VCH Verlag GmbH, Weinheim, 2006

[3] R. R. Gattass, E. Mazur, “Femtosecond laser micromachining in transparent materials”, Nature Photonics, 2 (2008), 219–225

[4] S. M. Yalisove, K. Sugioka, C. P. Grigoropoulos, “Advances and opportunities of ultrafast laser synthesis and processing”, MRS Bulletin, 41:12 (2016), 955–959

[5] N. Linz, S. Freidank, X. X. Liang, A. Vogel, “Wavelength dependence of femtosecond laser-induced breakdown in water and implications for laser surgery”, Phys. Rev. B, 94 (2016), 024113

[6] A. Couairon, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses”, Physical Review B, 71 (2005), 125435, 11 pp.

[7] M. Burakov, N. M. Bulgakova, R. Stoian, A. Mermillod-Blondin, E. Audouard, A. Rosenfeld, A. Husakou, I. V. Hertel, “Spatial distribution of refractive index variation induced in bulk fused silica by single ultrashort and short laser pulses”, J. Of Applied Physics, 101 (2007), 043506, 7 pp.

[8] A. V. Dostovalov, A. A. Wolf, V. K. Mezentsev, A. G. Okhrimchuk, S. A. Babin, “Quantitative characterization of energy absorption in femtosecond laser micro-modification of fused silica”, Optics Express, 23:25 (2015), 32541–32547

[9] K. I. Popov, C. McElcheran, K. Briggs, S. Mack, L. Ramunno, “Morphology of femtosecond laser modification of bulk dielectrics”, Optics Express, 19:1 (2011), 271–282

[10] C. L. Arnold, A. Heisterman, W. Ertmer, H. Lubatschowski, “Computational model for nonlinear plasma formation in high NA micromachining of transparent materials and biological cells”, Optical Express, 15:16 (2007), 10303–10317

[11] V. P. Zhukov, M. P. Fedoruk, “Numerically Implemented Impact of a Femtosecond Laser Pulse on Glass in the Approximation of Nonlinear Maxwell Equations”, Mathematical Models and Computer Simulations, 12:1 (2020), 77–89

[12] V. P. Zhukov, A. M. Rubenchik, M. P. Fedoruk, N. M. Bulgakova, “Interaction of doughnut-shaped laser pulses with glasses”, JOSA B, 34:2 (2017), 463–471

[13] V. P. Zhukov, N. M. Bulgakova, M. P. Fedoruk, “Nonlinear Maxwell's and Schrodinger equations for describing the volumetric interaction of femtosecond laser pulses with transparent solid dielectrics: effect of the boundary conditions”, J. of Optical Technology, 84:7 (2017), 439–446

[14] A. Becker, N. Akozbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas”, Appl. Phys. B, 73 (2001), 287–290

[15] Q. Sun, F. Liang, R. Vallee, S. L. Chin, “Nanograting formation on the surface of silica glass by scanning focused femtosecond laser pulses”, Opt. Lett, 33 (2008), 2713–2715

[16] J. A. Stratton, L. J. Chu, “Diffraction theory of electromagnetic waves”, Physical Review, 56 (1939), 99–107

[17] K. I. Popov, V. Yu. Bychenkov, W. Rozmus, R. D. Sydora, “Electron vacuum acceleration by tightly focused laser pulse”, Phys. of Plasmas, 15 (2008), 013108, 9 pp.