Spectral Correlations in Laser Instabilities beyond Stable Mode Locking

Mode-locked lasers only emit stationary ultrashort pulses in a narrow parameter space. Generally, they exhibit instabilities, outputting non-stationary yet localized structures. Soliton explosions and noise-like pulsing are two representative instabilities regularly encountered in mode-locked lasers. Enabled by emerging fast detection techniques, these laser instabilities can now be readily accessed. However, in-depth knowledge on these instabilities is extremely challenging as standard statistical tools such as correlation analysis is only sensitive to linear relationship between variables, overlooking the nonlinear parts. Here, we employ the mutual information to analyze soliton explosions and noise-like pulsing in mode-locked fiber lasers. We show that the mutual information is more sensitive compared to the standard correlation analysis. While the correlation between a signal and itself returns a value of 1 independent of the signal structure, mutual information has varying values depending on the structure. Both Pearson correlation and mutual information reveal that noise-like pulses thought-to-be stochastic radiation are generally correlated and some of them even has a high degree of correlation. Our work is conducive to understand complexities in laser systems.