Frequency-resolved optical gating (FROG) is a popular technique for characterizing ultrashort laser pulses. This technique comprises two steps. First, a spectrogram, named FROG trace, is constructed for a pulse by measuring process. Second, an efficient algorithm is employed to retrieve the pulse information from its FROG trace. By expressing an arbitrary FROG trace using matrix multiplication, we confirm that the data on all the complex spectral components constituting the relative pulse are, in principle, encoded in the value of each point of the trace. Considering this fact and the characteristics of the measuring devices, flexibly shaped FROG traces are built by simultaneously applying low-pass filtering and up-sampling along the frequency axis and down-sampling along the delay axis to the conventional square ones. Furthermore, these practical traces can be used for the effective reconstruction of ultrashort laser pulses via the ptychography algorithm. Utilizing this specially designed trace will significantly reduce the difficulty and time-consumption in the first step of the FROG process.

The fast reconstruction of an ultrashort laser pulse can be realized from flexibly shaped cross-phase-modulated frequency-resolved optical gating (FROG) traces via ptychography algorithm, which are composed of only three time-shift steps.