Attosecond pulses measured from the attosecond lighthouse

The attosecond lighthouse is a method of using ultrafast wavefront rotation with high-harmonic generation to create a series of coherent, spatially separated attosecond pulses. Previously, temporal measurements by photoelectron streaking characterized isolated attosecond pulses created by manipulating the single-atom response1–4. The attosecond lighthouse, in contrast, generates a series of pulses that spatially separate and become isolated by propagation. Here, we show that ultrafast wavefront rotation maintains the single-atom response (in terms of temporal character) of an isolated attosecond pulse over two octaves of bandwidth. Moreover, we exploit the unique property of the attosecond lighthouse—the generation of several isolated pulses—to measure the three most intense pulses. These pulses each have a unique spectrum and spectral phase. When an intense ultrashort laser pulse (peak intensity ∼10–10 W cm) is incident on a gas, coherent radiation spanning up to the extreme ultraviolet (XUV) or soft X-ray regimes can be created5. The radiation is emitted in a train of short, subcycle (of the driving field), attosecond (1 as = 10 s) bursts6–10. If the driving field wavefront rotates at the focus on the timescale of an optical cycle, then each pulse is directed uniquely. It is predicted that this effect leads to a series of spatially separated, isolated attosecond pulses11. The pulses are such that the attosecond pulse train nature is still maintained in the nonlinear medium, and each sequential pulse is spatially separated in the far field, allowing for the study of both intraand inter-pulse dynamics12. Previously, the spatial separation of attosecond pulses has been demonstrated with spatially resolved spectra12,13. However, the formation of the isolated pulse at the far field has never been reported. We show that with an aperture in the far field, it is possible to isolate a single pulse in the series. We refocus the pulse to measure its temporal character. We also show that although the pulse selection process occurs in the far field, the single-atom response to the driving field in the generating medium determines the pulse characteristics. Finally, we present the photoelectron streaking measurements of three isolated pulses generated on subsequent half cycles, where the temporal character of the pulse is dependent on its time of creation within the driving field envelope. In Fig. 1, we illustrate the generating medium response and the resulting pulse propagation to a strong driving field undergoing ultrafast wavefront rotation. The parameters used here match those of the experiment given in the Methods. We show the magnitude squared of the complex dipole response near the focus, calculated in the strong field approximation (SFA), as a function of time and the vertical displacement within the driving field. The rotating driving field generates a pulse train, where each pulse has a unique, rotated wavefront. The wavefront determines the direction of each pulse. The simulated pulses propagate with an angular divergence coordinate system, maintaining the temporal dependence of the pulse train and of each pulse. In the far field, the pulses are now separated, and each pulse has a unique spectrum and spectral phase. The spatially resolved spectrum is projected on the right, and the bottom projection is the short-time Fourier transform showing that each pulse has a unique temporal character. Experimentally, we use an aperture in the far field to isolate a single pulse of interest, and refocus it to measure its temporal profile. Spectral phase control is necessary in the generation of sub-100 attosecond pulses, and will be crucial in reaching an atomic unit of time (24 as). Thus far, the spectral phase has been controlled by the anomalous group dispersion of filters14,15, pressure tuning of the generating medium16,17 and careful dispersion management in the XUV18,19. However, the spectral phase is also dependent on the driving field pulse envelope20. Judiciously selecting the attosecond pulse from the train may allow for improved pulse compression. We select the most intense pulse, generated at the peak of the driving field, to measure the spectrum and spectral phase across the broadest energy range possible, and pass this pulse through a 200 -nm-thick beryllium filter. The generated spectrum spans the entire transmission bandwidth of nearly 90 eV. This bandwidth enables us to measure the spectral phase of an isolated attosecond pulse with photon energy spanning from just above the ionization potential (Ip) of neon through the plateau to the cutoff, a spectral breadth covering two octaves. We reconstruct the isolated attosecond pulse in Fig. 2 using the principal component generalized projection algorithm (PCGPA)21,22, the details of which are provided in the Supplementary Information. In Fig. 2a, we show the measured spectrogram, which is taken over five optical cycles (one period Tcycle ≈ 2.53 fs) of the streaking field. The reconstructed spectrogram after 1 × 10 iterations is shown in Fig. 2b. The streaking-field free reference spectrum (orange) in Fig. 2c is compared with the reconstructed spectrum (blue). The most prominent difference is an amplitude modulation of the reconstructed spectrum due to the satellite pulses. The origin of the decreased modulation is due to the comparable spot sizes of the streaking field and the attosecond pulses, causing a spatially dependent streaking intensity23. The beryllium filter transmission bandwidth is shown in black for reference. The reconstructed pulse, shown in Fig. 2d has a full-width at half-maximum (FWHM) pulse duration of 310 as. The strong quadratic phase (green) implies a linear chirp responsible for the pulse duration being longer than its transform limit of 48 as. The inset is the logarithm of the intensity of the Fourier transform of the reference pulse (orange) showing the satellite pulse intensity 10 down from the main pulse, while the reconstructed pulse (blue) calculates the satellite pulse intensity to be 10 of the main pulse. Because we are taking the spatial average at the focus, we cannot detect any potential spatial chirp caused by the driving field wavefront rotation. The strong quadratic phase is consistent with the high-harmonic generation process. In Fig. 3a, we calculate the single-atom dipole