Frequency-resolved optical gating with the use of second-harmonic generation

We discuss the use of second-harmonic generation (SHG) as the nonlinearity in the technique of frequency-resolved optical gating (FROG) for measuring the full intensity and phase evolution of an arbitrary ultrashort pulse. FROG that uses a third-order nonlinearity in the polarization-gate geometry has proved extremely successful, and the algorithm required for extraction of the intensity and the phase from the experimental data is quite robust. However, for pulse intensities less than ~1 MW, third-order nonlinearities generate insufficient signal strength, and therefore SHG FROG appears necessary. We discuss the theoretical, algorithmic, and experimental considerations of SHG FROG in detail. SHG FROG has an ambiguity in the direction of time, and its traces are somewhat unintuitive. Also, previously published algorithms are generally ineffective at extracting the intensity and the phase of an arbitrary laser pulse from the SHG FROG trace. We present an improved pulse-retrieval algorithm, based on the method of generalized projections, that is far superior to the previously published algorithms, although it is still not so robust as the polarization-gate algorithm. We discuss experimental sources of error such as pump depletion and group-velocity mismatch. We also present several experimental examples of pulses measured with SHG FROG and show that the derived intensities and phases are in agreement with more conventional diagnostic techniques, and we demonstrate the high-dynamic-range capability of SHG FROG. We conclude that, despite the above drawbacks, SHG FROG should be useful in measuring low-energy pulses.