Direct reconstruction of isolated XUV or soft x-ray attosecond pulses from high-harmonic generation streaking spectra

Characterization of an isolated attosecond pulse (IAP) in the extreme ultraviolet (XUV) or soft x-ray (SXR) region is essential for its applications. Here we propose to retrieve an IAP in the time domain directly through the modulation of high-harmonic generation (HHG) spectra in the presence of a time-delayed intense few-cycle infrared or mid-infrared laser. The retrieval algorithm is derived based on the strong-field approximation and an extended quantitative rescattering model. We show that both isolated XUV pulses with a narrow spectral bandwidth and isolated SXR pulses with a broad bandwidth can be well characterized through the HHG streaking spectra. Such an all-optical method for characterizing the IAP differs from the commonly used approach based on the streaked photoelectron spectra that would require electron spectrometers. We check the robustness of the retrieval method by changing the dressing laser or by adjusting the steps of time delay. We also show that the XUV pulse can be accurately retrieved by treating the HHG streaking spectra calculated from solving the time-dependent Schrodinger equation for single atoms as the 'experimental' data.