Nonlinear plasma-assisted collapse of ring-Airy wave packets

We numerically demonstrate that femtosecond ring-Airy wave packets are able to overcome the reference intensity clamping of $4\times {10}^{13}$ W/${\mathrm{cm}}^2$ for filaments generated with Gaussian beams at low numerical apertures and form an intense sharp intensity peak on axis. Numerical simulations, with unidirectional propagation models for the pulse envelope and the carrier resolved electric field, reveal that the driving mechanism for this unexpected intensity increase is due to the self-generated plasma. The plasma formation, in conjunction with the circular geometry of the beam, force the wave packet into a multistage collapse process which takes place faster than the saturating mechanisms can compensate. We report here a nonstandard mechanism that increases the intensity of a collapsing wave packet, due to the joint contributions of the cubic phase of the Airy beam and the formation of a partially reflecting plasma.

Figure 1

Iso-intensity of the NLRAB in $xyt$ coordinates carrying $24P_{cr}$. The ring-Airy has a radius of $r_0=921\mu \mathrm{m}$ (main ring), $w_0=61.4\mu \mathrm{m}$, apodization factor $\alpha =0.05$, and a duration of $t_p=200$ fs at $1/e^2$ radius. $\text{Isovalue}=5\times {10}^{11}$ W/${\mathrm{cm}}^2$. Propagation is from left to right.

Figure 2

(a) Peak intensity at the focal spot as a function of total input power for the NLRAB (black squares), and Gaussian beam (blue triangles). (b) Peak intensity versus propagation distances close to the focus for various input powers.

Figure 3

Spatiotemporal dynamics of the NLRAB close to the focus at $z=22, 22.11, 22.168$, and $22.18$ cm (columns 1 to 4). First row, $r-t$ intensity; second row, $r-t$ plasma density; and third row, $r-t$ overall refractive index modulation $\mathrm{\Delta }n$. Propagation is from right to left. See corresponding movie in the Supplemental Material online [43].

Figure 4

Radial fluence vs propagation distance at the focal spot of the NLRAB. Propagation is from right to left.

Figure 5

$r-t$ intensity distribution at the focal spot ($z=22.18\mathrm{cm}$) for various physical effects switched off at the second stage ($z=22.11\mathrm{cm}$). (a) All effects taken into account, (b) Kerr effect switched off, (c) MPI switched off, (d) both MPI and Kerr switched off. Propagation is from right to left.

Figure 6

Electric-field reshaping of an $800-\mathrm{nm}$ pulse propagating in air at $z=22.2\mathrm{cm}$ (red continuous line) versus initial unperturbed field (black dashed line) using the UPPE model.