Regularized differential evolution for a blind phase retrieval problem in ultrashort laser pulse characterization

Obtaining the temporal shape of an ultrashort laser pulse using the method of dispersion scan entails solving a nonlinear inverse problem, a challenging prospect on its own, yet still aggravated when the pulse shape being measured is temporally varying from pulse to pulse. For this purpose, we use a Differential Evolution (DE) algorithm enhanced by three different regularization methods. The DE algorithm in its standard form is insufficient for reconstructing the pulse in the case of unstable pulse trains. By modifying it to retrieve two independent functions and with the help of regularization, we were able to show that it is possible to simultaneously infer the average length and the coherence length of the pulses. The latter is the shortest pulse the laser source can produce. We also discuss the three different approaches for regularization used in this paper, and from the numerical results we present, we can conclude that a spline-based regularization method is far superior compared to the two other methods under investigation.