Chirp And Self-phase Modulation In Induced-grating Autocorrelation Measurements Of Ultrashort Pulses

Abstract

nized oscillations in the wings. These variations in the trace are the same as those that occur to the envelope of the high-frequency fringes in ISHGA traces, which are generally used to indicate the presence of the above two phase distortions. Conveniently, however, no highfrequency fringes occur in IGA methods. Other advantages of IGA methods include automatic phase-matching, single-wavelength operation, and applicability to most wavelength ranges (using a thermal grating simply requires an absorbing medium). We also show that a wide range of four-wave-mixing autocorrelation and IGA arrangements (that is, three-beam induced grating? two-beam coupling? phase conjugation, etc.) all yield identical theoretical results, specifically, the same two-dimensional integral of a fourth-order electric-field coherence function, which does not reduce to an intensity autocorrelation. In addition, we have performed numerical integrations, obtaining IGA and ISHGA traces for a variety of theoretical pulse distortions, including linear chirp, SPM, wave breaking, and phase and/or amplitude jitter. The table on the next page shows some of these traces. Note the close connection between IGA and ISHGA traces. ultrashort pulses <1 psec to 120 psec long at 1.06 pm and 532 nm from pulse trains of a cw mode-locked Nd:YAG laser. While any slowly responding nonlinear medium is appropriate for such measurements, we have used KNbO,, BaTiO,, and GaAs:Cr photo-refractive crystals, yielding simultaneous IGA and (non-interferometric) second-harmonic autocorrelations? We obtained varying amounts of chirp and SPM by using different wavelengths, different beam attenuations before propagation through a fiber, and different spacings between the pair of diffraction gratings in a fiber-grating compressor (or not using the gratings at all). The table also shows some of our experimental traces, illustrating the chirp-induced narrowing and SPM-induced oscillations in the wings.