Regularizing Aperiodic Cycles of Resonant Radiation in Filament Light Bullets

We demonstrate an up to now unrecognized and very effective mechanism which prevents filament collapse and allows persistent self-guiding propagation retaining a large portion of the optical energy on axis over unexpected long distances. The key ingredient is the possibility of continuously leaking energy into the normal dispersion regime via the emission of resonant radiation. The frequency of the radiation is determined by the dispersion dynamically modified by photogenerated plasma, thus allowing us to excite new frequencies in spectral ranges which are otherwise difficult to access.

Figure 1

(a) Peak electron density (orange curve) and peak intensity (blue curve) along optical axis $z$ for a filament seeded by a $20\mu \mathrm{J}$, 1900 nm pulse, simulated using the numerical model with the full dispersion profile. (b) Corresponding aperiodic evolution of the on-axis temporal intensity profile. (c) Filament fluence versus radial longitudinal filament coordinates and (d) spectral evolution along $z$ at $r=0$. Panels (e)–(h) depict the equivalent information for the same pulse, simulated using dispersion including only the ${\beta }_2$ term.

Figure 2

Pulse dynamics for a lower peak power for different wavelengths and dispersion profiles. (a) On-axis temporal intensity profile for a $5.6\mu \mathrm{J}$ pulse at 1800 nm, the model with full dispersion. (b) Train of light bullets at $z=7\mathrm{mm}$. (c),(d) The same as (a),(b) but with reduced parabolic dispersion. (e),(f) The same as (a),(b) but for a $7\mu \mathrm{J}$ pulse at 2000 nm.

Figure 3

(a) Spectrogram of the on-axis temporal intensity profile at $z=3\mathrm{cm}$ (for more details, see Supplemental Material [54]). White dashed lines: Fit according to Eq. (2) of branches I–VI. (b) Inverse group velocity for an increasing electron density. (c) ZDW frequency vs the free electron density.

Figure 4

(a) Frequency of RR according to Eq. (3) vs the electron density, for $\mathrm{\Delta }k=0$ and $k_{\perp }=0$. (b) Fourier-Hankel transform of $\mathcal{E}(r,t)$ at $z=19.2\text{mm}$. Black dashed lines: MI gain curves for $\rho =0$ and $\mathrm{\Delta }k=20$ and $150{\mathrm{cm}}^{-1}$. Red dashed line: hyperbolic component of the curve for electron density $8.3\times 10^{18}{\mathrm{cm}}^{-3}$ and $\mathrm{\Delta }k=20{\mathrm{cm}}^{-1}$.