Using GRENOUILLE to measure spatio-temporal distortions in ultrafast laser beams

Abstract

The couplings between the spatial coordinates and time and/or frequency are very common in ultrashort laser pulses. We previously showed that, the ultrashort pulse intensity and phase measurement devices, single-shot FROG and GRENOUILLE also measure some of the very common spatio-temporal distortions. Specifically, GRENOUILLE yields a sheared trace in frequency if the input pulse has spatial chirp. It also yields a trace shifted in delay, if the input pulse has pulse-front tilt. The shear and shift can also be used to measure the distortions. While this approach holds valid for relatively simple pulse, as the pulse gets more complicated, so does the effect of the spatio-temporal distortions. Therefore, we develop methods to extract the spatio-temporal distortions from GRENOUILLE traces, even for fairly complex pulses and distortions. First, we have developed a general model of GRENOUILLE for arbitrary spatio-temporal input beams. We then develop two algorithms to be run on distorted GRENOUILLE traces. The first perturbative algorithm is approximate, but is adequate for most cases where the spatio-temporal distortions are relatively small. The advantage of this perturbative approach is that it requires little modification to the existing FROG program, which is fast, reliable and robust. The second rigorous algorithm is numerically more complicated but is capable of accurately measuring the pulse intensity and phase and the spatio-temporal distortion parameters in more general cases. We tested this algorithm with several pulses that have various complexities and showed that this new algorithm retrieves the intensity and phase and the spatio-temporal distortions very accurately.