Dynamics and statistics of noise-like pulses in modelocked lasers

Noise-like pulses and optical rogue waves are connected nonlinear phenomena which can occur in passively modelocked laser systems. Here we consider a range of model systems to explore the conditions under which noise-like pulses can be expected to occur, and further when the resulting statistics meet the optical rogue wave criteria. We show, via a series of careful simulations, that noise-like pulses and optical rogue waves can arise either separately or together, and that they may emerge from standard soliton-like solutions via different mechanisms. We also propose a quantitative definition of noise-like pulses, and explore the issues carefully in convergence testing numerical methods for such systems.