Second-harmonic generation frequency-resolved optical gating in the single-cycle regime

Abstract—The problem of measuring broad-band femtosecond pulses by the technique of second-harmonic generation frequency-resolved optical gating (SHG FROG) is addressed. We derive the full equation for the FROG signal, which is valid even for single-optical-cycle pulses. The effect of the phase mismatch in the second-harmonic crystal, the implications of the beam geometry, and the frequency-dependent variation of the nonlinearity are discussed in detail. Our numerical simulations show that, under carefully chosen experimental conditions and with a proper spectral correction of the data, the traditional FROG inversion routines work well even in the single-cycle regime. The developed description of the SHG FROG signal was applied to measure the white-light continuum pulses in the spectral region of 500–1100 nm. The obtained spectral phase of these pulses served as a target function for the pulse compressor design. The pulses produced by compression around 800 nm were also characterized by SHG FROG. The resulting pulse duration measures 4.5 fs which corresponds to 2.5 optical cycles. Index Terms—Frequency conversion, nonlinear optics, optical beam focusing, optical pulse compression, optical pulse measure-ments, ultrafast optics. I