Spatial Akhmediev breathers and modulation instability growth-decay cycles in a quadratic optical medium

We investigate the spatial nonlinear localization of light on a quasi-plane-wave background with a harmonic perturbation induced by modulation instability in a quadratic nonlinear optical medium. In particular, we demonstrate experimentally the excitation of deterministic Akhmediev breathers and thus the growth-decay dynamics of modulation instability in a LiNbO3 slab waveguide. The results should stimulate new interest in modulation instability, extreme events, turbulence, recurrence, and supercontinuum generation in quadratic nonlinear optics.