Multi-mode root preserving ptychographic phase retrieval algorithm for dispersion scan

We present a phase retrieval algorithm for dispersion scan (d-scan), inspired by ptychography, which is capable of characterizing multiple mutually-incoherent ultrafast pulses (or modes) in a pulse train simultaneously from a single d-scan trace. In addition, a form of Newton's method is employed as a solution to the square root problem commonly encountered in second harmonic pulse measurement techniques. Simulated and experimental phase retrievals of both single-mode and multi-mode d-scan traces are shown to demonstrate the accuracy and robustness of the root preserving ptychographic algorithm (RPPA).