Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states

L. Bergé, C. Gouédard, Jens Schjødt-Eriksen, H. Ward

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    The filamentation of optical beams in focusing Kerr media is investigated. First, the creation of filamentary structures is shown to strongly depend on the radial distribution of the incident beam in the diffraction plane. With a cubic nonlinearity, broadening an input beam from Gaussian to super-Gaussian (SG) shapes relaxes the self-focusing (SF) attractor and triggers the formation of independent filaments. Analytical criteria for the mutual coalescence of filaments in the context of collapsing and saturating nonlinearities are proposed. Second, the influence of the polarization state on the filamentation instability is investigated. Rigorous conditions for the SF of beams with different polarizations are derived, which prove that the power threshold for collapse noticeably increases for circularly-polarized beams. The growth rate for modulational instability decreases accordingly and the minimal separation distance for coalescence becomes larger, which slows down the production of uncorrelated filaments. Implications of these results in atmospheric propagation are finally discussed. (C) 2002 Elsevier Science B.V. All fights reserved.
    Original languageEnglish
    JournalPhysica D: Nonlinear Phenomena
    Volume176
    Issue number3-4
    Pages (from-to)181-211
    ISSN0167-2789
    DOIs
    Publication statusPublished - 2003

    Cite this

    Bergé, L. ; Gouédard, C. ; Schjødt-Eriksen, Jens ; Ward, H. / Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states. In: Physica D: Nonlinear Phenomena. 2003 ; Vol. 176, No. 3-4. pp. 181-211.
    @article{a945ca5c35c94775acdff49d00d337bd,
    title = "Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states",
    abstract = "The filamentation of optical beams in focusing Kerr media is investigated. First, the creation of filamentary structures is shown to strongly depend on the radial distribution of the incident beam in the diffraction plane. With a cubic nonlinearity, broadening an input beam from Gaussian to super-Gaussian (SG) shapes relaxes the self-focusing (SF) attractor and triggers the formation of independent filaments. Analytical criteria for the mutual coalescence of filaments in the context of collapsing and saturating nonlinearities are proposed. Second, the influence of the polarization state on the filamentation instability is investigated. Rigorous conditions for the SF of beams with different polarizations are derived, which prove that the power threshold for collapse noticeably increases for circularly-polarized beams. The growth rate for modulational instability decreases accordingly and the minimal separation distance for coalescence becomes larger, which slows down the production of uncorrelated filaments. Implications of these results in atmospheric propagation are finally discussed. (C) 2002 Elsevier Science B.V. All fights reserved.",
    author = "L. Berg{\'e} and C. Gou{\'e}dard and Jens Schj{\o}dt-Eriksen and H. Ward",
    year = "2003",
    doi = "10.1016/S0167-2789(02)00740-6",
    language = "English",
    volume = "176",
    pages = "181--211",
    journal = "Physica D: Nonlinear Phenomena",
    issn = "0167-2789",
    publisher = "Elsevier",
    number = "3-4",

    }

    Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states. / Bergé, L.; Gouédard, C.; Schjødt-Eriksen, Jens; Ward, H.

    In: Physica D: Nonlinear Phenomena, Vol. 176, No. 3-4, 2003, p. 181-211.

    Research output: Contribution to journalJournal articleResearchpeer-review

    TY - JOUR

    T1 - Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states

    AU - Bergé, L.

    AU - Gouédard, C.

    AU - Schjødt-Eriksen, Jens

    AU - Ward, H.

    PY - 2003

    Y1 - 2003

    N2 - The filamentation of optical beams in focusing Kerr media is investigated. First, the creation of filamentary structures is shown to strongly depend on the radial distribution of the incident beam in the diffraction plane. With a cubic nonlinearity, broadening an input beam from Gaussian to super-Gaussian (SG) shapes relaxes the self-focusing (SF) attractor and triggers the formation of independent filaments. Analytical criteria for the mutual coalescence of filaments in the context of collapsing and saturating nonlinearities are proposed. Second, the influence of the polarization state on the filamentation instability is investigated. Rigorous conditions for the SF of beams with different polarizations are derived, which prove that the power threshold for collapse noticeably increases for circularly-polarized beams. The growth rate for modulational instability decreases accordingly and the minimal separation distance for coalescence becomes larger, which slows down the production of uncorrelated filaments. Implications of these results in atmospheric propagation are finally discussed. (C) 2002 Elsevier Science B.V. All fights reserved.

    AB - The filamentation of optical beams in focusing Kerr media is investigated. First, the creation of filamentary structures is shown to strongly depend on the radial distribution of the incident beam in the diffraction plane. With a cubic nonlinearity, broadening an input beam from Gaussian to super-Gaussian (SG) shapes relaxes the self-focusing (SF) attractor and triggers the formation of independent filaments. Analytical criteria for the mutual coalescence of filaments in the context of collapsing and saturating nonlinearities are proposed. Second, the influence of the polarization state on the filamentation instability is investigated. Rigorous conditions for the SF of beams with different polarizations are derived, which prove that the power threshold for collapse noticeably increases for circularly-polarized beams. The growth rate for modulational instability decreases accordingly and the minimal separation distance for coalescence becomes larger, which slows down the production of uncorrelated filaments. Implications of these results in atmospheric propagation are finally discussed. (C) 2002 Elsevier Science B.V. All fights reserved.

    U2 - 10.1016/S0167-2789(02)00740-6

    DO - 10.1016/S0167-2789(02)00740-6

    M3 - Journal article

    VL - 176

    SP - 181

    EP - 211

    JO - Physica D: Nonlinear Phenomena

    JF - Physica D: Nonlinear Phenomena

    SN - 0167-2789

    IS - 3-4

    ER -