Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime

We report and discuss analytical solutions of the vector nonlinear Schr¨odinger equation that
describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and
dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed
by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue wave formation.
The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in
explaining extreme waves in a variety of physical scenarios described by multi-component systems,
from oceanography to optics and plasma physics.