Reliable Characterization of Unstable Pulse Trains in Third-Order Versions of Frequency-Resolved Optical Gating

We show that the RANA approach, which reliably retrieves pulses in stable trains, reliably retrieves pulses in third-order FROG even in the presence of unstable pulse shapes. Importantly, it reliably indicates the presence of instability.

One of the remaining critical unsolved problems in the field of ultrashort-laser-pulse measurement—one that has remained problematic since the 1960s—is the reliable detection of instability of pulse shapes in a pulse train. Many pulse-measurement techniques, such as autocorrelation, suffer from coherent-artifact [1], [2] issues and, unless the instability is extreme, fail to indicate it, and, worse, yield an erroneously short pulse. On the other hand, Frequency-Resolved Optical Gating (FROG) [3] can detect instability by a discrepancy between the measured and retrieved FROG traces [1], [2]. But such a discrepancy is potentially also due to algorithm stagnation, and the two causes cannot be distinguished. Unfortunately, most FROG algorithms are prone to stagnation, even for simple pulses. Recently, however, we developed a new FROG algorithmic approach, called the Retrieved-Amplitude N-grid Algorithmic (RANA) approach [4], [5], which achieves 100% convergence in the absence of instability (even in the presence of noise in the measured trace and for extremely complex pulses). However, it must also be tested for convergence in the presence of pulse-shape instability. This task is complicated by the fact that, because instability necessarily prevents agreement between measured and retrieved traces, even the concept of "convergence" must be redefined. Last year, we reported results that showed that the RANA approach performed perfectly for the second-harmonic-generation (SHG) version of FROG, eliminating the possibility of stagnation causing trace discrepancies [6]. This year, we do the same for third-order versions of FROG, including Polarization-Gating (PG) and Transient-Grating (TG) FROG. This is important because these methods are common, as they are required when SHG is not possible, such, for UV and ultrabroadband pulses.