Femtosecond self-focusing dynamics measured by three-dimensional phase-retrieval cross correlation

We use a phase-retrieval cross-correlation technique to analyze the spatiotemporal field evolution of self-focused ultrashort pulses. The technique features a new phase-retrieval algorithm based on functional differentiation. Its sensitivity, rapid convergence, and temporal nonreciprocality enable reliable three-dimensional waveform reconstruction. At less than the critical power, the experiments verify conventional description of self-focusing and give a direct proof of the Kerr-lens mode-locking mechanism. In contrast, for pulses with peak power much more than the critical power, nearly uniform self-focusing and quasi-stable single-filament trapping to a universal beam diameter were observed. The trapping can be explained by the saturation of the nonlinear refractive-index change at Δn ∼ 7 × 10^-5. The saturation is verified by an independent cross-polarization modulation measurement.