Vectorial and random effects in self-focusing and in multiple filamentation

Gadi Fibich*, Boaz Ilan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

90 Scopus citations


The standard explanation for multiple filamentation of laser beams is that breakup of cylindrical symmetry is initiated by noise in the input beam. In this study we propose an alternative deterministic explanation based on vectorial effects. We derive a scalar equation from the vector Helmholtz equation that describes self-focusing in the presence of vectorial and nonparaxial effects. Numerical simulations of the scalar equation show that when the input beam is sufficiently powerful, vectorial effects lead to multiple filamentation. We compare multiple filamentation due to vectorial effects with the one due to noise, and suggest how to decide which of the two leads to multiple filamentation in experiments. We also show that vectorial effects and nonparaxiality have the same effect on self-focusing of a single filament, leading to the arrest of catastrophic collapse, followed by focusing-defocusing oscillations. The magnitude of vectorial effects is, however, significantly larger than that of nonparaxiality.

Original languageEnglish
Pages (from-to)112-146
Number of pages35
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
StatePublished - 1 Sep 2001


FundersFunder number
United States-Israel Binational Science Foundation


    • Beam breakup
    • Blowup
    • Collapse
    • Modulation theory
    • Noise
    • Nonlinear Schrödinger equation


    Dive into the research topics of 'Vectorial and random effects in self-focusing and in multiple filamentation'. Together they form a unique fingerprint.

    Cite this