Pulse breathing dynamics in a mode-locked laser measured via SHG autocorrelation

Pulse-to-pulse fluctuations in mode-locked lasers fundamentally limit applications from optical frequency combs to supercontinuum generation. While timing jitter has been extensively characterized, pulse amplitude and width fluctuations remain less accessible experimentally. We present a statistical autocorrelation method that demonstrates pulse breathing dynamics through Fano factor analysis of second-harmonic generation (SHG) autocorrelation. This reveals a characteristic W-shape in the enhanced Fano profile, a signature of pulse shape dynamics that is invisible to time-averaged fluctuations. Applying this method to two commercially available passively mode-locked oscillators operating at 1030 nm and 1045 nm, with different performance specifications, we measure pulse width fluctuations of 3.2(1) fs and 2.86(2) fs, respectively. The two independent instruments serve as a cross-validation of the technique across different laser platforms. This diagnostic capability opens the door to identifying and suppressing specific breathing mechanisms, paving the way for the design of ultra-stable oscillators required for precision frequency metrology.