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Diffraction-Beam Optics of Filamentation: I–Formalism of Diffraction Beams and Light Tubes

Abstract

The concept of nonstationary diffraction-beam optics of high-power femtosecond laser pulses is presented. According to the concept, the power of a beam propagates along specific light structures—diffraction- beam tubes. These tubes do not intersect and do not exchange energy, but changes in their shape and cross sections during propagation show the effect of physical processes that occur with radiation in the medium. The nonstationary theory is supplemented with evolutionary equations for time-averaged diffraction rays and effective squared radii of diffraction tubes.

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References

  1. 1.

    Self-focusing: Past and Present. Fundamentals and Prospects, Ed. By R.W. Boyd, S.G. Lukishova, and Y.R. Shen (Springer, Berlin, 2009).

    Google Scholar 

  2. 2.

    S. Tzortzakis, B. Prade, M. Franco, and A. Mysyrowicz, “Time-evolution of the plasma channel at the trail of a self-guided IR femtosecond laser pulse in air,” Opt. Commun. 181, 123–127 (2000).

    ADS  Article  Google Scholar 

  3. 3.

    A. A. Ilyin, S. S. Golik, and K. A. Shmirko, “Absorption and emission characteristics of femtosecond laser plasma filaments in the air,” Spectrochim. Acta 112, 16–22 (2015).

    Article  Google Scholar 

  4. 4.

    A. Couairon and A. Myzyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441 (2–4), 47–189 (2007).

    ADS  Article  Google Scholar 

  5. 5.

    S. V. Chekalin and V. P. Kandidov, “From self-focusing light beams to femtosecond laser pulse filamentation,” Phys.-Uspekhi 56 (2), 123–140 (2013).

    ADS  Article  Google Scholar 

  6. 6.

    V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media (or supercontinuum generation),” Appl. Phys. B 77 (2-3), 149–166 (2003).

    Google Scholar 

  7. 7.

    L. Woste, C. Wedekind, H. Wille, P. Rairoux, B. Stein, S. Nikolov, Ch. Werner, S. Niedermeier, H. Schillinger, and R. Sauerbrey, “Femtosecond atmospheric lamp,” Laser Optoelektron. 29, 51–53 (1997).

    Google Scholar 

  8. 8.

    M. Rodriguez, R. Bourayou, G. Mejean, J. Kasparian, J. Salmon, E. Yu, A. Scholz, B. Stecklum, J. Eisloffel, U. Laux, A. P. Hatzes, R. Sauerbrey, L. Woste, and J.-P. Wolf, “Kilometer-range non-linear propagation of femtosecond laser pulses,” Phys. Rev., E 69, 036607 (2004).

    ADS  Article  Google Scholar 

  9. 9.

    R. Ackermann, G. Mechain, G. Mejean, R. Bourayou, M. Rodriguez, K. Stelmaszczyk, J. Kasparian, J. Salmon, E. Yu, S. Tzortzakis, Y.-B. Andre, J.-F.Bourrillon, L. Tamin, J. -P. Cascelli, C. Campo, C. Davoise, A. Mysyrowicz, R. Sauerbrey, L. Woste, and J.-P. Wolf, “Influence of negative leader propagation on the triggering and guiding of high voltage discharges by laser filaments,” Appl. Phys. B 82, 561–566 (2006).

    ADS  Article  Google Scholar 

  10. 10.

    M. Durand, A. Houard, B. Prade, A. Mysyrowicz, A. Durecu, B. Moreau, D. Fleury, O. Vasseur, H. Borchert, K. Diener, R. Schmitt, F. Theberge, M. Chateauneuf, J.-F. Daigle, and J. Dubois, “Kilometer range filamentation,” Opt. Express 21, 26836–26845 (2013).

    ADS  Article  Google Scholar 

  11. 11.

    A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20 (1), 73–75 (1995).

    ADS  Article  Google Scholar 

  12. 12.

    E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21 (1), 62–64 (1996).

    ADS  Article  Google Scholar 

  13. 13.

    V. N. Lugovoi and A. M. Prokhorov, “A possible explanation of the small-scale self-focusing filaments,” JETP Lett. 7, 117–119 (1968).

    ADS  Google Scholar 

  14. 14.

    A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22 (5), 304–306 (1997).

    ADS  Article  Google Scholar 

  15. 15.

    R. Y. Ciao, E. Garmiere, and C. H. Towens, “Self-trapping of optical beams,” Phys. Rev. Lett. 13, 479–482 (1964).

    ADS  Article  Google Scholar 

  16. 16.

    M. Mlejnek, E. M. Wright, and J. V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382–384 (1998).

    ADS  Article  Google Scholar 

  17. 17.

    A. Lotti, A. Couairon, D. Faccio, and P. Di Trapani, “Energy-flux characterization of conical and spacetime coupled wave packets,” Phys. Rev., A 81, 023810 (2010).

    ADS  Article  Google Scholar 

  18. 18.

    T. D. Grow, A. A. Ishaaya, L. T. Vuong, A. L. Gaeta, N. Gavish, and G. Fibich, “Collapse dynamics of super-gaussian beams,” Opt. Express. 14, 5468–5475 (2006).

    ADS  Article  Google Scholar 

  19. 19.

    T.-T. Xi, X. Lu, and J. Zhang, “Spatiotemporal moving focus of long femtosecond-laser filaments in air,” Phys. Rev., E 78, 055401 (2008).

    ADS  Article  Google Scholar 

  20. 20.

    A. A. Zemlyanov, A. D. Bulygin, and Yu. E. Geints, “Diffraction optics of a light filament generated during self-focusing of a femtosecond laser pulse in air,” Atmos. Ocean. Opt. 25 (2), 97–105 (2012).

    Article  Google Scholar 

  21. 21.

    A. A. Zemlyanov, A. D. Bulygin, and Yu. E. Geints, “Energy light structures during femtosecond laser radiation filamentation in air. To the 50th anniversary of the first paper about light self-focusing,” Atmos. Ocean. Opt. 27 (6), 463–475 (2014).

    Article  Google Scholar 

  22. 22.

    J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52 (2), 116–130 (1962).

    ADS  MathSciNet  Article  Google Scholar 

  23. 23.

    V. I. Talanov, “Self-focusing of wave beams in nonlinear media,” JETP Lett. 2 (5), 138–140 (1965).

    ADS  Google Scholar 

  24. 24.

    S. G. Rautian, Quasi-beam tubes, Opt. Spektrosk. 87 (3), 494–496 (1999).

    Google Scholar 

  25. 25.

    A. A. Gershun, Selected Papers on Photometry and Lighting Engineering (Fizmatgiz, Moscow, 1958) [in Russian].

    Google Scholar 

  26. 26.

    Yu. E. Geints and A. A. Zemlyanov, “Ring-Gaussian laser pulse filamentation in a self-induced diffraction waveguide,” J. Opt. 19, 105502 (2017).

    ADS  Article  Google Scholar 

  27. 27.

    A. A. Zemlyanov, A. D. Bulygin, Yu. E. Geints, and O. V. Minina, “Dynamics of light structures during filamentationof femtosecond laser pulses in air,” Atmos. Ocean. Opt. 29 (5), 395–404 (2016).

    Article  Google Scholar 

  28. 28.

    A. E. Siegman, Defining and Measuring Laser Beam Quality, Solid State Lasers: New Developments and Applications (Plenum Press, New York, 1994).

    Google Scholar 

  29. 29.

    Yu. E. Geints and A. A. Zemlyanov, “On the focusing limit of high-power femtosecond laser pulse propagation in air,” Eur. Phys. J. D 55, 745–754 (2009).

    ADS  Article  Google Scholar 

  30. 30.

    Optical waves and laser beams in the irregular atmosphere, Ed. By N. Blaunstein, N. Kopeika (CRC Press, New York, 2018).

    Google Scholar 

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Correspondence to Yu. E. Geints.

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Original Russian Text © Yu.E. Geints, A.A. Zemlyanov, O.V. Minina, 2018, published in Optika Atmosfery i Okeana.

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Geints, Y.E., Zemlyanov, A.A. & Minina, O.V. Diffraction-Beam Optics of Filamentation: I–Formalism of Diffraction Beams and Light Tubes. Atmos Ocean Opt 31, 611–618 (2018). https://doi.org/10.1134/S1024856018060088

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Keywords

  • femtosecond laser pulses
  • self-focusing
  • filamentation
  • diffraction ray
  • diffraction-beam tube