Abstract
The beam self-cleaning phenomenon is theoretically predicted by the two-dimensional nonlinear Schrödinger equation, which describes self-focusing, and is observed in the case of femtosecond laser filamentation in the collimated regime of propagation. However, the impact of external focusing on the self-cleaning has not been investigated so far. In this paper we systematically study this impact in a wide range of focusing conditions. We show that the energy range, in which self-cleaning can be observed, shrinks monotonically with the numerical aperture growth at some point vanishing at all.
Similar content being viewed by others
Data Availability
Due to confidentiality agreements between authors, data and/or its analysis during the current study is available from the corresponding author [D. V. Pushkarev via email: d-push@yandex.ru] on reasonable request to bona fide researchers.
References
Braun, A., Korn, G., Liu, X., Du, D., Squier, J., Mourou, G.: Self-channeling of high-peak-power femtosecond laser pulses in air. Opt. Lett. 20(1), 73–75 (1995)
Chin, S.L., Petit, S., Liu, W., Iwasaki, A., Nadeau, M.-C., Kandidov, V.P., Kosareva, O.G., Andrianov, K.Y.: Interference of transverse rings in multifilamentation of powerful femtosecond laser pulses in air. Opt. Commun. 210(3–6), 329–341 (2002)
Ciao, R.Y., Garmire, E., Townes, C.H.: Self-trapping of optical beams. Phys. Rev. Lett. 13(15), 479–482 (1991)
Couairon, A., Mysyrowicz, A.: Femtosecond filamentation in transparent media. Phys. Rep. 441, 47–189 (2007)
Couairon, A., Biejert, J., Hauri, C.P., Kornelis, W., Helbing, F.W., Keller, U., Mysyrowicz, A.: Self-compression of ultra-short laser pulses down to one optical cycle by filamentation. J. Mod. Opt. 53(1–2), 75–85 (2006)
Geints, Y.E., Mokrousova, D.V., Pushkarev, D.V., Rizaev, G.E., Seleznev, L.V., Geints, I.Y., Ionin, A.A., Zemlyanov, A.A.: Energy limit for linear-to-nonlinear femtosecond laser pulse focusing in air. Opt. Laser Technol. 143, 107377 (2021)
Ionin, A.A., Kudryashov, S.I., Makarov, S.V., Seleznev, L.V., Sinitsyn, D.V.: Multiple filamentation of intense femtosecond laser pulses in air. JETP Lett. 90(6), 423–427 (2009)
ISO Standard No. 11146-1: Lasers and laser-related equipment—test methods for laser beam widths, divergence angles and beam propagation ratios—part 1: stigmatic and simple astigmatic beams (2021). https://www.iso.org/standard/77769.html
Kandidov, V.P., Shlenov, S.A., Kosareva, O.G.: Filamentation of high-power femtosecond laser radiation. Quantum Electron. 39(3), 205–228 (2009)
Kosareva, O.G., Panov, N.A., Uryupina, D.S., Kurilova, M.V., Mazhorova, A.V., Savel’ev, A.B., Volkov, R.V., Kandidov, V.P., Chin, S.L.: Optimization of a femtosecond pulse self-compression region along a filament in air. Appl. Phys. B 91(1), 35–43 (2008)
Kurilova, M.V., Uryupina, D.S., Mazhorova, A.V., Gorgutsa, S.R., Volkov, R.V., Kosareva, O.G., Savel’ev, A.B.: Investigation of the transformation of the spectrum of femtosecond laser radiation on filamentation in gas medium. Opt. Spectrosc. 107(3), 429–434 (2009)
Landman, M.J., Papanicolaou, G.C., Sulem, C., Wang, X.P.: Stability of isotropic singularities for the nonlinear Schrödinger equation. Physica D 47(3), 393–415 (1991)
Liu, W., Chin, S.L.: Understanding the beam self-cleaning behavior of ultrashort laser pulse filamentation. Sci. China Ser. E Technol. Sci. 50(4), 413–421 (2007a)
Liu, W., Chin, S.L.: Abnormal wavelength dependence of the self-cleaning phenomenon during femtosecond-laser-pulse filamentation. Phys. Rev. A 76, 013826 (2007b)
Liu, W., Gravel, J.-F., Théberge, F., Becker, A., Chin, S.L.: Background reservoir: its crucial role for long-distance propagation of femtosecond laser pulses in air. Appl. Phys. B 80(7), 857–860 (2005)
Milchberg, H.M., Chen, Y.-H., Cheng, Y.-H., Jhajj, N., Palastro, J.P., Rosenthal, E.W., Varma, S., Wahlstrand, J.K., Zahedpour, S.: The extreme nonlinear optics of gases and femtosecond optical filamentation. Phys. Plasmas 21, 100901 (2014)
Milián, C., Jukna, V., Couairon, A., Houard, A., Forestier, B., Carbonnel, J., Liu, Y., Prade, B., Mysyrowicz, A.: Laser beam self-symmetrization in air in the multifilamentation regime. J. Phys. B At. Mol. Opt. Phys. 48(9), 094013 (2015)
Moll, K.D., Gaeta, A.L., Fibich, G.: Self-similar optical wave collapse: observation of the Townes profile. Phys. Rev. Lett. 90, 203902 (2003)
Prade, B., Franco, M., Mysyrowicz, A., Couairon, A., Buersing, H., Eberle, B., Krenz, M., Seiffer, D., Vasseur, O.: Spatial mode cleaning by femtosecond filamentation in air. Opt. Lett. 31(17), 2601–2603 (2006)
Qi, P., Qian, W., Guo, L., Xu, J., Zhang, N., Wang, Y., Zhang, Z., Lin, L., Sun, C., Zhu, L., Liu, W.: Sensing with femtosecond laser filamentation. Sensors 22(18), 7076 (2022)
Rainio, O.: Different coefficients for studying dependence. Sankhya B 84(2), 895–914 (2022)
Reyes, D., Baudelet, M., Richardson, M., Rostami Fairchild, S.: Transition from linear-to nonlinear-focusing regime of laser filament plasma dynamics. J. Appl. Phys. 124(5), 053103 (2018)
Théberge, F., Aközbek, N., Liu, W., Becker, A., Chin, S.L.: Tunable ultrashort laser pulses generated through filamentation in gases. Phys. Rev. Lett. 97(2), 023904 (2006a)
Théberge, F., Liu, W., Simard, P.T., Becker, A., Chin, S.L.: Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing. Phys. Rev. E 74(3), 036406 (2006b)
Théberge, F., Châteauneuf, M., Ross, V., Mathieu, P., Dubois, J.: Ultrabroadband conical emission generated from the ultraviolet up to the far-infrared during the optical filamentation in air. Opt. Lett. 33(21), 2515–2517 (2008)
Uryupina, D., Kurilova, M., Mazhorova, A., Panov, N., Volkov, R., Gorgutsa, S., Kosareva, O., Savel’ev, A., Chin, S.L.: Few-cycle optical pulse production from collimated femtosecond laser beam filamentation. J. Opt. Soc. Am. B 27(4), 667–674 (2010)
Zvorykin, V.D., Ionin, A.A., Levchenko, A.O., Mesyats, G.A., Seleznev, L.V., Sinitsyn, D.V., Smetanin, I.V., Sunchugasheva, E.A., Ustinovskii, N.N., Shutov, A.V.: Production of extended plasma channels in atmospheric air by amplitude-modulated UV radiation of GARPUN-MTW Ti: sapphire—KrF laser. Part 2. Accumulation of plasma electrons and electric discharge control. Quantum Electron. 43(4), 339–346 (2013)
Zvorykin, V.D., Ionin, A.A., Levchenko, A.O., Seleznev, L.V., Sinitsyn, D.V., Smetanin, I.V., Ustinovskii, N.N., Shutov, A.V.: Extended plasma channels created by UV laser in air and their application to control electric discharges. Plasma Phys. Rep. 41, 112–146 (2015)
Zwillinger, D., Kokoska, S.: CRC Standard Probability and Statistics Tables and Formulae. CRC Press, London (2000)
Funding
The work is supported by Russian Science Foundation (Grant 21-12-00109).
Author information
Authors and Affiliations
Contributions
All authors participated in experiments and data processing. D. V. P., G. E. R. and L. V. S. have written the main manuscript. All authors contributed to the revision.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest or competing interests.
Consent for publication
Not applicable.
Ethics approval and consent to participate
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Pushkarev, D.V., Rizaev, G.E., Mokrousova, D.V. et al. Focused beam self-cleaning during laser filamentation. Opt Quant Electron 55, 577 (2023). https://doi.org/10.1007/s11082-023-04861-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-023-04861-2