Vol. 34, issue 09, article # 1

Geints Yu. E., Zemlyanov A. A. Numerical simulations of filamentation of synthesized femtosecond coronal laser beams in air. // Optika Atmosfery i Okeana. 2021. V. 34. No. 09. P. 665–675. DOI: 10.15372/AOO20210901 [in Russian].
Copy the reference to clipboard


Theoretical aspects of nonlinear propagation in air under filamentation of high-power ultrashort laser radiation with coronalike transverse intensity distribution are theoretically considered. A coronal intensity profile is assumed to be formed by incoherent superposition of several emitting sub-apertures arranged into a ring. Using the numerical solution to the time-averaged nonlinear Schrödinger equation, the transformations along an optical path of the intensity profile of the synthesized beams by varying the number and power of the partial emitters composing them are investigated. We show that the synthesized beams of coronal profile have a number of advantages from the point of view of control over the filamentation region. Particularly, by changing the number and geometric size of the individual subapertures it is possible to significantly delay the beginning of filamentation of the whole beam and increase the distance of its existence in comparison with beams of traditional unimodal profile (Gaussian, plateau-shaped).


self-focusing, filamentation, ultra-short laser radiation, synthesized beams


  1. Self-focusing: Past and Present. Fundamentals and Prospects / R.W. Boyd, S.G. Lukishova, Y.R. Shen (eds.). Berlin: Springer, 2009. 605 р.
  2. Couairon A., Myzyrowicz A. Femtosecond filamentation in transparent media // Phys. Rep. 2007. V. 441. P. 47–189.
  3. Bergé L., Skupin S., Nuter R., Kasparian J., Wolf J.-P. Ultrashort filaments of light in weakly-ionized, optically-transparent media // Rep. Prog. Phys. 2007. V. 70. P. 1633.
  4. Chekalin S.V., Kandidov V.P. From self-focusing light beams to femtosecond laser pulse filamentation // Phys.-Usp. 2013. V. 56. P. 123–140.
  5. Kasparian J., Rodriguez M., Mejean G., Yu J., Salmon E., Wille H., Bourayou R., Frey S., Andre Y.-B., Mysyrowicz A., Sauerbrey R., Wolf J.-P., Wöste L. White-light filaments for atmospheric analysis // Science. 2003. V. 301. P. 61.
  6. Mechain G., Amico C.D., Andre Y.-B., Tzortzakis S., Franco M., Prade B., Mysyrowicz A., Couairon A., Salmon E., Sauerbrey R. Range of plasma filaments created in air by a multi-terawatt femtosecond laser // Opt. Commun. 2005. V. 247. P. 171.
  7. Gejnts Yu.E., Zemlyanov A.A. Chislennoe modelirovanie samofokusirovki i filamentatsii trubchatyh lazernyh puchkov v vozduhe // Optika atmosf. i okeana. 2013. V. 26, N 8. P. 647–653.
  8. Grow T.D., Ishaaya A.A., Vuong L.T., Gaeta A.L., Gavish N., Fibich G. Collapse dynamics of super-Gaussian beams // Opt. Express. 2006. V. 14. P. 5468.
  9. Roskey D.E., Kolesik M., Moloney J.V., Wright E.M. The role of linear power partitioning in beam filamentation // Appl. Phys. B. 2007. V. 86. P. 249–258.
  10. Kompanets V.O., Chekalin S.V., Kosareva O.G., Grigor’evskii A.V., Kandidov V.P. Conical emission of a femtosecond laser pulse focused by an axicon into a K 108 glass // Quant. Eleсtron. 2006. V. 36, N 9. P. 821–824.
  11. Mills M., Christodoulides D., Kolesik M. Dressed optical filaments // Opt. Lett. 2013. V. 38. P. 25–27.
  12. Mills M., Heinrich M., Kolesik M., Christodoulides D. Extending optical filaments using auxiliary dress beams // J. Phys. B. 2015. V. 48. P. 094014.
  13. Gejnts Yu.E., Zemlyanov A.A. Zakonomernosti femtosekundnoj filamentatsii pri superpozitsii gaussova i kol'tsevogo lazernyh puchkov // Kvant. elektron. 2017. V. 47, N 8. P. 722–729.
  14. Kandidov V.P., Akozbek N., Kosareva O.G., Nyakk A.V., Luo Q., Hosseini S.A., Chin S.L. Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse // Appl. Phys. B. 2005.V. 80, N 3. P. 267–275.
  15. Ionin A.A., Iroshnikov N.G., Kosareva O.G., Larichev A.V., Mokrousova D.V., Panov N.A., Seleznev L.V., Sinitsyn D.V., Sunchugasheva E.S. Filamentation of femtosecond laser pulses governed by variable wavefront distortions via a deformable mirror // J. Opt. Soc. Am. B. 2013. V. 30, N 8. Р. 2257–2261.
  16. Daigle J.-F., Kamali Y., Châteauneuf M., Tremblay G., Théberge F., Dubois J., Roy G., Chin S.L. Remote sensing with intense filaments enhanced by adaptive optics // Appl. Phys. B. 2009. V. 97, N 3. Р. 701–713.
  17. Apeksimov D.V., Geints Yu.E., Zemlynov A.A., Kabanov A.M., Oshlakov V.K., Petrov A.V., Matvienko G.G. Controlling TW-laser pulse long-range filamentation in air by a deformable mirror // Appl. Opt. 2018. V. 57, N 34. Р. 9760–9769.
  18. Chu C., Shipilo D.E., Lu D., Zhang Z., Chuchupal S.V., Panov N.A., Kosareva O.G., Liu W. Femtosecond filament emergence between p-shifted beamlets in air // Opt. Express. 2020. V. 28. P. 1002–1013.
  19. Sprangle P., Peñano J., Hafizi B., Ting A. Incoherent combining of high-power fiber lasers for long-range directed energy applications // J. Dir. Energy. 2007. V. 2. P. 273–284.
  20. Sprangle P., Ting A., Peñano J., Fischer R., Hafizi B. Incoherent combining and atmospheric propagation of high-power fiber lasers for directed-energy applications // IEEE J. Quantum Electron. 2009. V. 45. P. 1–2.
  21. Weyrauch T., Vorontsov M.A., Carhart G.W., Beresnev L.A., Rostov A.P., Polnau E.E., Liu J.J. Experimental demonstration of coherent beam combining over a 7 km propagation path // Opt. Lett. 2011. V. 36. P. 4455–4457.
  22. Fairchild S.R., Walasik W., Kepler D., Baudelet M., Litchinitser N.M., Richardson M. Free-space nonlinear beam combining for high intensity projection // Sci. Rep. 2017. V. 7. P. 10147.
  23. Lapointe J., Kashyap R. A simple technique to overcome self-focusing, filamentation, supercontinuum generation, aberrations, depth dependence and waveguide interface roughness using fs laser processing // Sci. Rep. 2017. V. 7. P. 499.
  24. Kolesik M., Moloney J.V. Nonlinear optical pulse propagation simulation: From Maxwell’s to unidirectional equations // Phys. Rev. E. 2004. V. 70. P. 036604–08.
  25. Bergé L., Skupin S., Lederer F., Méjean G., Yu J., Kasparian J., Salmon E., Wolf J.-P., Rodriguez M., Woste L., Bourayou R., Sauerbrey R. Multiple filamentation of terawatt laser pulses in air // Phys. Rev. Lett. 2004. V. 92. P. 225002.
  26. Bergé L., Schmidt M.R., Rasmussen J.J., Christiansen P.L., Rasmussen K.O. Amalgamation of interacting light beamlets in Kerr-type media // J. Opt. Soc. Am. B. 1997. V. 14. P. 2550.
  27. Siegman A.E. Lasers. Mill Valley, CA: Oxford University Press, 1986. 568 p.
  28. Geints Yu.E., Zemlyanov A.A. Ring-Gaussian laser pulse filamentation in a self-induced diffraction waveguide // J. Optics. 2017. V. 19. P. 105502.
  29. Talanov V.I. Self-focusing of wave beams in nonlinear media // JETP Lett. 1965. V. 2, N 5. Р. 138–141.
  30. Zemlyanov A.A., Bulygin A.D., Gejnts Yu.E. Difraktsionnaya optika svetovogo filamenta, obrazovannogo pri samofokusirovke femtosekundnogo lazernogo impul'sa v vozduhe // Optika atmosf. i okeana. 2011. V. 24, N 10. P. 839–847; Zemlyanov A.A., Bulygin A.D., Geints Yu.E. Diffraction optics of a light filament generated during self-focusing of a femtosecond laser pulse in air // Atmos. Ocean. Opt. 2012. V. 25, N 2. Р. 97–105.
  31. Geints Yu.E., Zemlyanov A.A. Diffraction-ray optics of laser-pulse filamentation // Phys. Rev. A. 2018. V. 98. Р. 023846.
  32. Gejnts Yu.E., Zemlyanov A.A., Minina O.V. Modelirovanie samofokusirovki femtosekundnyh lazernyh impul'sov v vozduhe metodom difraktsionno-luchevyh trubok // Optika atmosf. i okeana. 2019. V. 32, N 2. P. 120–130; Geints Yu.E., Zemlyanov A.A., Minina O.V. Simulation of self-focusing of femtosecond laser pulses in air by the method of diffraction-beam tubes // Atmos. Ocean. Opt. 2019. V. 32, N 4. Р. 420–429.
  33. Born M., Vol'f E. Osnovy optiki. M.: Nauka, 1973. 720 p.
  34. Rautian S.G. Kvaziluchevye trubki // Opt. i spektroskop. 1999. V. 87, N 3. P. 494–496.
  35. Agrawal G.P., Ghatak A.K., Mehta C.L. Propagation of a partially coherent beam through Selfoc fibers // Opt. Commun. 1974. V. 12, N 3. P. 333–337.
  36. Geints Yu.E., Zemlyanov A.A. On the focusing limit of high-power femtosecond laser pulse propagation in air // Eur. Phys. J. D. 2009. V. 55. P. 745–754.
  37. Geints Yu.E., Zemlyanov A.A. Dynamics of CO2 laser pulse filamentation in air influenced by spectrally selective molecular absorption // Appl. Opt. 2014. V. 53, N 25. P. 5641–5648.
  38. Perelomov A.M., Popov V.S., Terent'ev M.V. Ionizatsiya atomov v peremennom elektricheskom pole // ZhTEF. 1966. V. 50. P. 1393–1397.
  39. Geints Y.E., Zemlyanov A.A. Near- and mid-IR ultrashort laser pulse filamentation in a molecular atmosphere: a comparative analysis // Appl. Opt. 2017. V. 56. P. 1397–1403.
  40. Informatsionno-vychislitel'nyj tsentr Novosibirskogo gosudarstvennogo universiteta [Elektronnyj resurs]. URL: http://nusc.nsu.ru/wiki/doku.php/doc/index (data obrashcheniya: 12.07.2021).