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We present the application of a previously proposed multiple-Gaussian approach to characterize ultrashort vacuum (VUV) and deep ultraviolet (DUV) pulses via auto- and cross-correlation methods. The knowledge of the temporal variation of amplitude and phase of such pulses is important for spectroscopic and dynamical imaging techniques. The method, which is an extension of the single Gaussian autocorrelation technique, is based on the expansion of the pulse in a series of Gaussian functions at different frequencies and the use of analytic solutions for two-photon ionization of atoms by Gaussian pulses. Using this approach we compare the characterization of a pulse via the auto- and the cross-correlation techniques and find that an accurate characterization even in the case of more complex pulse forms can be achieved. Furthermore, the comparison of the application of unchirped and chirped Gaussian pulses reveals some specific advantages in the use of pulses with a linear chirp. Finally, we quantify our conclusions from the qualitative comparisons by defining errors and using results from information theory. 

We have performed macroscopic calculations for the thin medium or low gas density regime and a central gas jet using microscopic numerical solutions of the time-dependent Schrödinger equation. In the case of a spatial phase distribution for broadband Gaussian pulses with a negative Porras factor, our theoretical results show an interference pattern in the angular distribution of below- and near-threshold harmonics, which is not present for the monochromatic Gouy phase distribution. The interference pattern is due to off-center contributions that are in-phase with those at the central points in the focus. The location of the maxima in the interference pattern can be estimated using the well-known double-slit formula with an effective slit separation. 

Characterization of ultrashort vacuum and deep ultraviolet pulses is important in view of applications of those pulses for spectroscopic and dynamical imaging of atoms, molecules, and materials. We present an extension of the autocorrelation technique, applied for measurement of the pulse duration via a single Gaussian function. Analytic solutions for two-photon ionization of atoms by Gaussian pulses are used along with an expansion of the pulse to be characterized using multiple Gaussians at multi-color central frequencies. This approach allows one to use two-photon autocorrelation signals to characterize isolated ultrashort pulses and pulse trains, i.e., the time-dependent amplitude and phase variation of the electric field. The potential of the method is demonstrated using vacuum and deep ultraviolet pulses and pulse trains obtained from numerical simulations of macroscopic high harmonic spectra. 

Abstract Progress in ultrafast science allows for probing quantum superposition states with ultrashort laser pulses in the new regime where several linear and nonlinear ionization pathways compete. Interferences of pathways can be observed in the photoelectron angular distribution and in the past they have been analyzed for atoms and molecules in a single quantum state via anisotropy and asymmetry parameters. Those conventional parameters, however, do not provide comprehensive tools for probing superposition states in the emerging research area of bright and ultrashort light sources, such as free-electron lasers and high-order harmonic generation. We propose a new set of generalized asymmetry parameters which are sensitive to interference effects in the photoionization and the interplay of competing pathways as the laser pulse duration is shortened and the laser intensity is increased. The relevance of the parameters is demonstrated using results of state-of-the-art numerical solutions of the time-dependent Schrödinger equation for ionization of helium atom and neon atom.