PHz-Wide Spectral Interference Through Coherent Plasma-Induced Fission of Higher-Order Solitons

We identify a novel regime of soliton-plasma interactions in which high-intensity ultrashort pulses of intermediate soliton order undergo coherent plasma-induced fission. Experimental results obtained in gas-filled hollow-core photonic crystal fiber are supported by rigorous numerical simulations. In the anomalous dispersion regime, the cumulative blueshift of higher-order input solitons with ionizing intensities results in pulse splitting before the ultimate self-compression point, leading to the generation of robust pulse pairs with PHz bandwidths. The novel dynamics closes the gap between plasma-induced adiabatic soliton compression and modulational instability.

Figure 1

(a) Experimental output spectra, measured over an integration time of 5 ms ($>750$ laser shots). Using a conventional Si CCD spectrometer, only the spectral range from 0.27 to 1.54 PHz (1.12 to $0.2\mu \mathrm{m}$) could be measured. Dispersion is anomalous on the low-frequency side of the ZDP (I). A DW is emitted at a phase-matched frequency in the UV (II). Ionization of the filling gas leads to emission of a blueshifted soliton (III), which generates a second DW at lower frequencies (IV). At high input energies, distinct interference fringes are visible across the entire spectrum (V). (b) Output energy and transmission of the fiber (including incoupling losses). (c) Temporal separation of the pulses in a pulse pair corresponding to the spectrum in (a), retrieved via Fourier transform for frequencies above 0.39 PHz. When distinct interference fringes occur in the output spectra [region V in (a)], they have a spectral spacing of $\sim 50\mathrm{THz}$, which corresponds to a temporal separation of $\sim 20\mathrm{fs}$.

Figure 2

Pulse measurement at the output of the fiber via noncollinear second harmonic generation FROG in a $10\text{−}\mu \mathrm{m}$-thick beta-barium-borate crystal. The dispersion in the measurement path was numerically corrected after retrieval of the pulses. Despite the thin crystal, only part of the multioctave-spanning spectra could be measured, but the conclusions drawn from these measurements are representative of a wider spectral range, given that they agree with the independent measurements shown in Fig. 1. (a) Temporal pulse shape before the onset of pulse splitting, with a FWHM duration of 4.6 fs, limited by the bandwidth of the FROG device. (b),(c) Temporal pulse shape in the input energy regime where pulse splitting occurs, Fourier filtered above 0.39 PHz to suppress the residual pump pulse, which did not compress strongly. (d),(e) Measured and retrieved FROG traces corresponding to (c). The FROG trace was retrieved on a $2048\times 2048$ grid, with an error of $G=0.95\%$.

Figure 3

Simulated pulse dynamics for moderate ($5\mu \mathrm{J}$) and high ($13\mu \mathrm{J}$) input energy. The input pulse was measured via FROG. (a),(b) Evolution of the temporal pulse shape with propagation distance. At moderate input energy, the input pulse undergoes clean self-compression (I), whereas at high input energy, it splits into two subpulses (II), which then individually undergo self-compression. (c),(d) Evolution of the ionization rate $\partial \rho (z,t)/\partial t$. It closely follows the temporal pulse shape, but significant values only occur when the pulse is sufficiently intense ($>300\mathrm{MW}$ of power).

Figure 4

Time-frequency analysis (spectrogram) of the $13\mu \mathrm{J}$ pulse shown in Fig. 3, at $z=1.5\mathrm{cm}$ and $z=2.7\mathrm{cm}$ along the fiber, calculated using a 5-fs-long Gaussian gate pulse. (a) The pulse experiences asymmetric spectral broadening towards high frequencies due to ionization at its leading edge. (b) Upon further propagation, the pulse breaks up and two subpulses emerge.