Benchmarking accurate spectral phase retrieval of single attosecond pulses

Abstract

A single extreme-ultraviolet (XUV) attosecond pulse or pulse train in the time domain is fully characterized if its spectral amplitude and phase are both determined. The spectral amplitude can be easily obtained from photoionization of simple atoms where accurate photoionization cross sections have been measured from, e.g., synchrotron radiations. To determine the spectral phase, at present the standard method is to carry out XUV photoionization in the presence of a dressing infrared (IR) laser. In this work, we examine the accuracy of current phase retrieval methods (PROOF and iPROOF) where the dressing IR is relatively weak such that photoelectron spectra can be accurately calculated by second-order perturbation theory. We suggest a modified method named swPROOF (scattering wave phase retrieval by omega oscillation filtering) which utilizes accurate one-photon and two-photon dipole transition matrix elements and removes the approximations made in PROOF and iPROOF. We show that the swPROOF method can in general retrieve accurate spectral phase compared to other simpler models that have been suggested. We benchmark the accuracy of these phase retrieval methods through simulating the spectrogram by solving the time-dependent Schrödinger equation numerically using several known single attosecond pulses with a fixed spectral amplitude but different spectral phases.