Ambiguity Removal of Two-Color SHG-FROG Traces by Time Seperation

The complete temporal characterization of two-color ultrashort pulses is important for many applications, especially the study of ultrafast events and generation of high-order harmonics in the soft x-ray and extreme ultraviolet regions. While Second-Harmonic Generation (SHG) Frequency-Resolved Optical‑Gating (FROG) has proven to be a powerful and reliable technique for precisely measuring even complex pulses, it (and all other known self-referenced techniques) suffer from an inherent relative-phase ambiguity for two-color pulses and so will not provide complete information about the pulse total electric field in some cases. In this work, we demonstrate that such ambiguities in SHG FROG measurements can be eliminated by separating the components (colors) of the two-color pulse in time. We find that the ability to remove this ambiguity in SHG-FROG strongly depends on the pulse separation, as well as the pulse durations. The dependence of the rms difference between the actual and ambiguous SHG-FROG traces on pulse separation exhibits an oscillatory behavior and is non-zero (that is, the ambiguity is removed) only for a certain range of separations. We demonstrate this behavior for multi-cycle and few-cycle pulses.