Extreme-ultraviolet pulses of attosecond duration carrying orbital angular momentum (OAM) can be produced by spectrally filtering vortex high harmonics generated in a gas medium. Here we reveal that fractional high harmonics (FHHs) with non-integer OAM generated by a short duration Laguerre-Gaussian laser beam are origins for the change of helical attosecond pulse train (APT) with azimuthal angle. We show that these harmonics have gap and minimum structures in the annular intensity profile and discontinue phase distribution along azimuthal angle. And each FHH can be expressed as a superposition of OAM modes with integer topological charges. Features of FHH can be identified by coherently combining selected OAM modes. We also uncover that these features are formed after FHH is propagated in gas medium and in vacuum. We finally demonstrate that the generation of FHHs and the dependence of helical APTs on azimuthal angle are changed by varying the macroscopic condition.

Ultrafast extreme ultraviolet (XUV) transient absorption spectroscopy measures the time- and frequency-dependent light losses after light–matter interactions. In the linear region, the matter response to an XUV light field is usually determined by the complex refractive index n ˜ . The absorption signal is directly related to the imaginary part of n ˜ , namely, the absorption index. The real part of n ˜ refers to the real refractive index, which describes the chromatic dispersion of an optical material. However, the real refractive index information is usually not available in conventional absorption experiments. Here, we investigate the refractive index line shape in ultrafast XUV transient absorption spectroscopy by using a scheme that the XUV pulse traverses the target gas jet off-center. The jet has a density gradient in the direction perpendicular to the gas injection direction, which induces deflection on the XUV radiation. Our experimental and theoretical results show that the shape of the frequency-dependent XUV deflection spectra reproduces the refractive index line profile. A typical dispersive refractive index line shape is measured for a single-peak absorption; an additional shoulder structure appears for a doublet absorption. Moreover, the refractive index line shape is controlled by introducing a later-arrived near-infrared pulse to modify the phase of the XUV free induction decay, resulting in different XUV deflection spectra. The results promote our understanding of matter-induced absorption and deflection in ultrafast XUV spectroscopy.

Attosecond transient absorption (ATA) has been developed as an all-optical technique for probing the electron dynamics in the matter. Here we present a scheme that can modify the laser-induced state and the corresponding ATA spectrum via excitation by a pair of XUV attosecond pulses and probe by a time-delayed mid-infrared (MIR) laser. Different from the scheme of the electronic excitation by a single XUV attosecond pulse, the application of a pair of XUV pulses provides with extra degrees of freedom, such as the time delay and the intensity ratio between two XUV pulses, which make it possible to adjust the pump process, resulting in the modification of ATA spectrum. We show that by varying the time delay between the two XUV pulses, the population of the dark state and the ATA spectrum of laser-induced state have periodic modulations. We also demonstrate that the peak of the ATA spectrum of laser-induced state appears at a fixed time delay between the XUV pair and the MIR laser when the intensity ratio is large, and it changes with the time delay when the intensity ratio is small, which can be related to either one of two peaks in the population of the dark state.

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 Schr¨odinger equation for single atoms as the “experimental” data.