Simulations of frequency-resolved optical gating for measuring very complex pulses

Frequency-resolved optical gating (FROG) and its variations are the only techniques available for measuring complex pulses without a well-characterized reference pulse. We study the performance of the FROG generalized-projections algorithm for retrieving the intensity and phase of very complex ultrashort laser pulses [with time-bandwidth products (TBPs) of up to 100] in the presence of noise. We compare the performance of three versions of FROG: second-harmonic-generation (SHG) FROG, polarization-gate (PG) FROG, and cross-correlation FROG (XFROG), the last of which requires a well-characterized reference pulse. We found that the XFROG algorithm converged in all cases on the first initial guess. The PG FROG algorithm converged for all moderately complex pulses, for 99% of the pulses we tried, and for more than 95% of even the most complex pulses (TBP~100). The SHG FROG algorithm converged for 95% of the pulses we tried and for over 80% of even the most complex pulses. We found no additional ambiguities in any of these techniques.