Beam instability of broadband stochastic laser fields

Unlike the deterministic theory of modulation instability (MI), which describes this process in terms of a well-defined gain spectrum and a well-resolved threshold, the statistical treatment of MIs, presented in this study, is concerned with a question as to how probable MI-driven beam-instability events are. We show that stochastic laser beams that nominally meet the deterministic beam-stability criterion can emerge as unstable on large pulse samples. With the laser peak power set well below the deterministic MI threshold, the count rate of MI-driven beam-instability events within a large sample of laser pulses is shown to be Poissonian-distributed, with its mean defined by the exponent of the extreme-event beam-instability statistics. We present a closed-form analytical solution for this beam-instability count rate, revealing the key tendencies in its behavior as a function of the signal-to-noise ratio and the bandwidth of its noise component. We demonstrate that the stochastic beam-instability dynamics of high-power laser field waveforms, including the laser pulses used for the ignition of inertial confinement fusion, can be scaled down in laser power and studied in laboratory-scale laser experiments.