Reliable determination of pulse-shape instability in trains of ultrashort laser pulses using frequency-resolved optical gating.

We describe a reliable approach for determining the presence of pulse-shape instability in a train of ultrashort laser pulses. While frequency-resolved optical gating (FROG) has been shown to successfully perform this task by displaying a discrepancy between the measured and retrieved traces for unstable trains, it fails if its pulse-retrieval algorithm stagnates because algorithm stagnation and pulse-shape instability can be indistinguishable. So, a non-stagnating algorithm-even in the presence of instability-is required. The recently introduced Retrieved-Amplitude N-grid Algorithmic (RANA) approach has achieved extremely reliable (100%) pulse-retrieval in FROG for trains of stable pulse shapes, even in the presence of noise, and so is a promising candidate for an algorithm that can definitively distinguish stable and unstable pulse-shape trains. But it has not yet been considered for trains of pulses with pulse-shape instability. So, here, we investigate its performance for unstable trains of pulses with random pulse shapes. We consider trains of complex pulses measured by second-harmonic-generation FROG using the RANA approach and compare its performance to the well-known generalized-projections (GP) algorithm without the RANA enhancements. We show that the standard GP algorithm frequently fails to converge for such unstable pulse trains, yielding highly variable trace discrepancies. As a result, it is an unreliable indicator of instability. Using the RANA approach, on the other hand, we find zero stagnations, even for highly unstable pulse trains, and we conclude that FROG, coupled with the RANA approach, provides a highly reliable indicator of pulse-shape instability. It also provides a typical pulse length, spectral width, and time-bandwidth product, even in cases of instability.