PHz-wide Supercontinua of Nondispersing Subcycle Pulses Generated by Extreme Modulational Instability

Modulational instability (MI) of 500 fs, $5\mu \mathrm{J}$ pulses, propagating in gas-filled hollow-core kagome photonic crystal fiber, is studied numerically and experimentally. By tuning the pressure and launched energy, we control the duration of the pulses emerging as a consequence of MI and hence are able to study two regimes: the classical MI case leading to few-cycle solitons of the nonlinear Schrödinger equation; and an extreme case leading to the formation of nondispersing subcycle pulses (0.5 to 2 fs) with peak intensities of order ${10}^{14}\mathrm{W}{\mathrm{cm}}^{-2}$. Insight into the two regimes is obtained using a novel statistical analysis of the soliton parameters. Numerical simulations and experimental measurements show that, when a train of these pulses is generated, strong ionization of the gas occurs. This extreme MI is used to experimentally generate a high energy ($>1\mu \mathrm{J}$) and spectrally broad supercontinuum extending from the deep ultraviolet (320 nm) to the infrared (1300 nm).

Figure 1

Group velocity dispersion of a $9\mu \mathrm{m}$ core radius kagome-PCF filled with 3 and 10 bar Xe.

Figure 2

MI dynamics of a 500 fs pulse at 800 nm with $5\mu \mathrm{J}$ energy, launched through a $9\mu \mathrm{m}$ core radius kagome-PCF filled with 10 bar Xe. (a) Temporal intensity and (b) spectral intensity (log scale). (c) Corresponding free electron density. (d) Temporal profile after 6 cm; the red line is the squared envelope and the blue line the squared electric field; inset shows a subcycle pulse structure. (e) Spectrograms at different positions individually normalized. The dashed lines represent the zero dispersion wavelength and $A$ and $N$ indicate anomalous and normal dispersion regions.

Figure 3

Distribution of MI induced pulses as a function of peak power and FWHM duration in different MI regimes in a $9\mu \mathrm{m}$ radius Xe-filled kagome PCF. Top row: 2 ps, $2.5\mu \mathrm{J}$ pump pulse at 3 bar pressure; the expected MI induced soliton duration is 7.6 fs (few-cycle pulse); (a) initial stage of MI; (b) distribution after propagation over $\sim 4L_D$. Bottom row: 0.5 ps, $5\mu \mathrm{J}$ pulse at 10 bar pressure; expected MI induced pulse duration is 1 fs (subcycle pulses); (c) initial stages of extreme MI; (d) converged distribution after propagation over $\sim 20L_D$. The solid lines represent the expected behavior for fundamental NLSE solitons. The histograms are normalized to the peak value within each row. Red dashed lines indicate the expected distribution peaks based on Eq. (2).

Figure 4

(a) Energy dependent experimental spectra for 500 fs pump pulses at 800 nm at the output of a 20 cm long $9\mu \mathrm{m}$ radius kagome-PCF filled with 10 bar Xe; (b) corresponding numerical results. (c) Comparison between simulated (blue line) and experimental (black line) spectra at $5\mu \mathrm{J}$ pump energy. (d) Output energy scaling with pump energy: experiment (red dots); simulation including fiber loss (i, blue dashed line); and simulations including fiber and photoionization-induced losses (ii, green line).