Atmospheric propagation of gradient-shaped and spinning femtosecond light pulses

Theory of singular vortex solutions of the nonlinear Schrödinger equation

“…Azimuthal modulation instability of vortices was also analyzed in [29,5]. The number of filaments predicted in these studies is different from our prediction, yet was in agreement with the numerical simulations conducted in these studies.…”

“…Lemma 7. Let G m (r ) be a solution of (29). Then G m (r ) = r m g m (r ), where g 0 = g m (0) = 0 and g m (r ) is the analytic solution of…”

“…To do that, we modify the method which was developed by Soto-Crespo and co-workers in [9,10] for azimuthal modulation instability of stationary vortex-free ring solutions. This method was later applied to stationary vortex solutions [29,5]. To the best of our knowledge, this (or any other) method has not been used to analyze the azimuthal modulation stability of collapsing rings or vortices.…”

“…The noise caused the vortex to break into filaments before it could start to collapse and approach the ψ G profile. Therefore, the analysis in [29,5] predicts the number of filaments for essentially stationary vortices. In contrast, we study a different regime where the initial noise is small enough to allow the vortex solution to collapse with ψ G profile and only then breakup.…”

Multifilamentation of powerful optical pulses in silica

“…At the wavelength λ 0 = 355 nm, a "long" supergaussian pulse with t p = 500 fs (FWHM 1 ps), small waist w 0 = 200 µm, 100 critical powers, and suffering 5% random noise both in spatial and temporal amplitudes, develops regular modulations on its steepest boarders, before the most intense filaments reach the ionization threshold [29,30]. Figure 3(a) displays the evolution of the maximum pulse intensity and electron density.…”