Generation of bright isolated attosecond soft X-ray pulses driven by multicycle midinfrared lasers

Abstract

High harmonic generation driven by femtosecond lasers makes it possible to capture the fastest dynamics in molecules and materials. However, to date the shortest subfemtosecond (attosecond, 10(-18) s) pulses have been produced only in the extreme UV region of the spectrum below 100 eV, which limits the range of materials and molecular systems that can be explored. Here we experimentally demonstrate a remarkable convergence of physics: when midinfrared lasers are used to drive high harmonic generation, the conditions for optimal bright, soft X-ray generation naturally coincide with the generation of isolated attosecond pulses. The temporal window over which phase matching occurs shrinks rapidly with increasing driving laser wavelength, to the extent that bright isolated attosecond pulses are the norm for 2-µm driving lasers. Harnessing this realization, we experimentally demonstrate the generation of isolated soft X-ray attosecond pulses at photon energies up to 180 eV for the first time, to our knowledge, with a transform limit of 35 attoseconds (as), and a predicted linear chirp of 300 as. Most surprisingly, advanced theory shows that in contrast with as pulse generation in the extreme UV, long-duration, 10-cycle, driving laser pulses are required to generate isolated soft X-ray bursts efficiently, to mitigate group velocity walk-off between the laser and the X-ray fields that otherwise limit the conversion efficiency. Our work demonstrates a clear and straightforward approach for robustly generating bright isolated attosecond pulses of electromagnetic radiation throughout the soft X-ray region of the spectrum.

Keywords: coherent; nonlinear optics; ultrafast.

Fig. 1.

Schematic of the setup for attosecond high-resolution Fourier transform spectroscopy. The number of discrete bursts in an attosecond pulse train driven by 0.8-, 1.3-, and 2.0-μm lasers is directly measured using soft X-ray interferometry, by delaying one part of the HHG pulse with respect to itself with ultrahigh precision of 1.5 as.

Fig. 2.

Comparison of the experimental HHG autocorrelation data (normalized) from Ar driven by ∼10 cycle laser pulses at wavelengths of (A) 0.8 μm, (B) 1.3 μm, and (C) 2 μm for high and low laser intensity conditions (red and blue lines). (Left) Field autocorrelation of the HHG field and enlarged view near time 0 with the coherence time of the central pulse envelope. The temporal phase-matching window is highlighted in yellow. Note that the bandwidth-limited pulse duration is half of this coherence time. (Right) HHG spectra obtained from the FFT of the field autocorrelation traces (filled-area plots), showing excellent agreement with the experimental spectra (black dotted lines). The low-intensity spectra are enhanced to see their fine structure. The predicted phase-matching cutoffs are also shown (green dashed lines).

Fig. 3.

Calculated phase mismatch Δk (blue line), L_coh (red line and yellow highlight), and instantaneous HHG cutoff photon energy (green) for HHG in Ar driven by 10-cycle laser pulses: (A) 0.8 μm, 2.42 × 10¹⁴ W/cm²; (B) 1.3 μm, 1.87 × 10¹⁴ W/cm²; and (C) 2.0 μm, 1.5 × 10¹⁴ W/cm². The temporal window during which phase matching occurs is highlighted in yellow.

Fig. 4.

Numerical calculations showing the dependence of the phase-matching window on the number of driving laser cycles of a 2-µm laser, and the gas pressure. The laser field is shown both at the entrance (red) and exit (blue) of a 2-mm gas cell at pressures of (A and D) 5 torr, (B and E) 100 torr, and (C and F) 600 torr for 1.5 cycles and 8 cycles FWHM at phase-matching intensities of 1.3 × 10¹⁴ W/cm² and 1.2 × 10¹⁴ W/cm², respectively, from the central part of a driving laser field with a Bessel profile of radius 60 µm. The time window during which phase matching is possible is highlighted in yellow. The temporal profile of the HHG emission from the eight-cycle laser field is shown for (G) 5 torr and (H) 600 torr. (Right) Time–frequency analysis together with the HHG spectrum and temporal emission, which evolves from an as pulse train (G) to an isolated 300-as chirped pulse (H). Note that for a 1.5-cycle driving laser, at the high pressures required for bright HHG emission, phase matching is not possible due to group velocity walk-off.