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 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.