Reconstruction of an Ultrashort Laser Pulse from Flexibly Shaped FROG Trace via Ptychography Algorithm

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.