УДК: 537.87 535.8

Nonlinear Maxwell’s and Schrödinger equations for describing the volumetric interaction of femtosecond laser pulses with transparent solid dielectrics: effect of the boundary conditions

Zhukov, V.P., Bulgakova, N.M., Fedoruk, M.P.

Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Жуков В.П., Булгакова Н.М., Федорук М.П. Нелинейные уравнения Максвелла и Шрёдингера для описания объемного взаимодействия фемтосекундных лазерных импульсов с прозрачными твердыми диэлектриками. Влияние граничных условий // Оптический журнал. 2017. Т. 84. № 7. С. 13–21.

Zhukov V.P., Bulgakova N.M., Fedoruk M.P. Nonlinear Maxwell’s and Schrödinger equations for describing the volumetric interaction of femtosecond laser pulses with transparent solid dielectrics: effect of the boundary conditions [in Russian] // Opticheskii Zhurnal. 2017. V. 84. № 7. P. 13–21.

For citation (Journal of Optical Technology):

V. P. Zhukov, N. M. Bulgakova, and M. P. Fedoruk, "Nonlinear Maxwell’s and Schrödinger equations for describing the volumetric interaction of femtosecond laser pulses with transparent solid dielectrics: effect of the boundary conditions," Journal of Optical Technology. 84(7), 439-446 (2017). https://doi.org/10.1364/JOT.84.000439

Abstract:

This paper compares models based on nonlinear Maxwell’s and Schrödinger equations developed for modeling typical experiments involving the three-dimensional modification of glasses (using fused quartz as an example) under the action of femtosecond laser pulses. It is shown that the results can be appreciably different when the Maxwell’s and Schrödinger equations are used. A substantial role in this case is played not only by the equations themselves, but also by the form of the boundary condition that describes the focused laser pulse at the input to the region of calculation.

Keywords:

femtosecond laser pulse, three-dimensional modification, nonlinear Maxwell equations, fused quartz, nonlinear Schrödinger equation, boundary conditions

Acknowledgements:

This work was carried out with the financial support of Program No. I.33P of fundamental research of the Presidium of the RAS for strategic directions of the development of science.

OCIS codes: 140.3390, 140.3440, 320.7110, 320.7130

References:

1. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
2. R. Taylor, C. Hnatovsky, and E. Simova, “Applications of femtosecond laser induced planar nanocracks inside fused silica glass,” Laser Photon. Rev. 2, 26–46 (2008).
3. A. Vogel and V. Venugopalan, “Mechanisms of pulsed laser ablation of biological tissues,” Chem. Rev. 103, 577–644 (2003).
4. K. Sugioka, Y. Hanada, and K. Midorikawa, “Three-dimensional femtosecond laser micromachining of photosensitive glass for biomicrochips,” Laser Photon. Rev. 4, 386–400 (2010).
5. S. Richter, M. Heinrich, S. Döring, A. Tünnermann, and S. Nolte, “Formation of femtosecond laser-induced nanogratings at high repetition rates,” Appl. Phys. A 104, 503–507 (2011).
6. N. M. Bulgakova, V. P. Zhukov, S. V. Sonina, and Yu. P. Meshcheryakov, “Modification of transparent materials with ultrashort laser pulses: what is energetically and mechanically meaningful?” Appl. Phys. 118(23), 233108 (2015).
7. N. M. Bulgakova, V. P. Zhukov, I. Mirza, Yu. P. Meshcheryakov, J. Tomáštík, V. Michálek, O. Haderka, L. Fekete, A. M. Rubenchik, M. P. Fedoruk, and T. Mocek, “Ultrashort-pulse laser processing of transparent materials: insight from numerical and semi-analytical models,” Proc. SPIE 9735, 97350N (2016).
8. N. M. Bulgakova, V. P. Zhukov, Yu. P. Meshcheryakov, L. Gemini, J. Brajer, D. Rostohar, and T. Mocek, “Pulsed laser modification of transparent dielectrics: what can be foreseen and predicted in numerical experiments?” J. Opt. Soc. Am. B 31(11), C8–C14 (2014).
9. N. M. Bulgakova, V. P. Zhukov, and Yu. P. Meshcheryakov, “Theoretical treatments of ultrashort pulse laser processing of transparent materials: towards understanding the volume nanograting formation and “quill” writing effect,” Appl. Phys. B 113(3), 437–449 (2013).
10. A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysurowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71, 125435 (2005).
11. I. M. Burakov, N. M. Bulgakova, R. Stoian, A. Mermillod-Blondin, and E. Audouard, “Spatial distribution of refractive index variations induced in bulk fused silica by single ultrashort and short laser pulses,” Appl. Phys. 101, 043506 (2007).
12. A. Mermillod-Blondin, I. M. Burakov, Y. P. Meshcheryakov, N. M. Bulgakova, E. Audouard, A. Rosenfeld, A. Husakou, I. V. Hertel, and R. Stoian, “Flipping the sign of refractive index changes in ultra-fast and temporally shaped laser-irradiated borosilicate crown optical glass at high repetition rates,” Phys. Rev. B 77, 104205 (2008).
13. K. I. Popov, C. McElcheran, K. Briggs, S. Mack, and L. Ramunno, “Morphology of femtosecond laser modification of bulk dielectrics,” Opt. Express 19, 271–282 (2010).
14. H. Schmitz and V. Mezentsev, “Full-vectorial modeling of femtosecond pulses for laser inscription of photonic structures,” J. Opt. Soc. Am. B 29, 1208–1217 (2012).
15. C. L. Arnold, A. Heisterman, W. Ertmer, and H. Lubatschowski, “Computational model for nonlinear plasma formation in high NA micromachining of transparent materials and biological cells,” Opt. Express 15(16), 10303–10317 (2007).
16. V. P. Zhukov, N. M. Bulgakova, and M. P. Fedoruk, “Numerical modeling of the propagation of a femtosecond laser pulse in nonlinear media,” Vych. Tekhnol. 17(4), 14–28 (2012).

17. N. M. Bulgakova and V. P. Zhukov, “Continuum models of ultrashort laser–matter interaction in application to wide-bandgap dielectrics,” in Lasers in Materials Science, M. Castillejo, P. M. Ossi, and L. Zhigilei, eds. (Springer, Switzerland, 2014), pp. 101–124.
18. P. G. Petropoulos, “Reflectionless sponge layers for the numerical solution of Maxwell’s equations in cylindrical and spherical coordinates,” Appl. Numer. Math. 33, 517–524 (2000).
19. K. I. Popov, V. Y. Bychenkov, W. Rozmus, D. Sydora, and S. S. Bulanov, “Vacuum electron acceleration by tightly focused laser pulses with nanoscale targets,” Phys. Plasmas 16, 053106 (2009).
20. E. S. Efimenko, A. V. Kim, and M. Quiroga-Teixeiro, “Ionization-induced dynamics of laser-matter interaction in a focused laser pulse: a comparative analysis,” Phys. Plasmas 18, 032107 (2011).