Measuring single-shot modulation instability and supercontinuum spectra at megahertz rates^*

Single-shot spectra of modulation instability (MI) and long-pulse supercontinuum (SC) are acquired at megahertz repetition rates (using time-stretch dispersive Fourier transformation) and analysed over a broad wavelength range. We find varied statistical distributions—including heavy-tailed, bimodal, Gaussian-like, and hybrid forms—depending on the input parameters and selected output wavelength. These distributions are investigated with the aid of simulations, which show that that the redshifted energy and peak intensity of the individual events are well correlated for low soliton number. Similar experimental and simulated single-shot spectra are also found, suggesting that input noise conditions can be accurately identified. The library of spectra provides new insights into noise-driven MI and long-pulse SC generation at the single-shot level.