Attosecond pulse shaping

High-order harmonic generation is routinely used to produce coherent XUV and soft x-ray radiation. However, our ability to shape the spectral and temporal profiles of this radiation is highly limited. Attoscience [1] requires ever-broader spectra and higher photon energies with the attosecond chirp compensated, which has so far been achieved below 100 eV using metal films. Imaging [2] would benefit from a tunable narrowband source.Here, we propose an in-situ method for the production of attosecond pulses with arbitrary spectral and temporal profiles, including removal of the attosecond chirp. It employs quasi-phase matching [3] with a modulation of the dipole excitation that is spatially addressable along the propagation axis. This result is effectively a filter applied to the single-atom response. The filter transfer function is the spatial Fourier transform of the modulation. Attosecond chirp compensation is achieved by a spatially chirped modulation. We focus on implementations based on a counterpropagating pulse, in which existing femtosecond pulse shapers may be used. The method is applicable over the entire spectrum and in principle can be applied up to multi-keV photon energies. It raises the possibility of multiphoton spectroscopies and coherent control of atomic-scale electron motion. We present analytic results for chirp compensation and arbitrary filter synthesis, and offer detailed simulations of experimentally realistic scenarios, including the generation of transform-limited single and double pulses of 20 as duration in the water window. Figure 1 depicts the setup and results of one simulation. A few-cycle, 6 × 1014 W/cm2, 2 μm pulse (red, Fig. 1(a)) is launched into an argon-filled cylindrical waveguide of diameter 100 μm and length 3mm. The duration, carrier-envelope phase and intensity of the pulse is such that its single-atom response produces, via ionization gating [4], an isolated attosecond pulse with bandwidth 220-440 e- . An 800 nm counterpropagating field is applied (green, Fig. 1(b)), with its profile tailored to both compensate the chirp of the single atom response and to produce a double pulse with tunable delay; here we demonstrate delays of 24 as (1) and 48 as (2). The output (violet, Fig. 1(c)) passes through a 100 nm Cu filter to reject the fundamental, after which it consists of two 20 as transform-limited pulses with the specified delay.