Complexity of modulation instability

In this Research Letter, using experimental data, we analyze the computational complexity of modulation instability of a light wave propagating in a single-mode optical fiber. We show that computational complexity is an excellent tool which provides an insight into the emergence from noise of modulation-instability-induced coherent structures in the linear stage, before they become fully developed in the temporal traces, and substantially anticipating other statistical methods. Furthermore, computational complexity captures qualitatively the statistical signature of the recurrences in the nonlinear stage of modulation instability too.