We construct and discuss a semi-rational, multi-parametric vector solution of coupled nonlinear Schrödinger equations (Manakov system). This family of solutions includes known vector Peregrine solutions, bright-dark-rogue solutions, and novel vector unusual freak waves. The vector freak (or rogue) waves could be of great interest in a variety of complex systems, from optics to Bose-Einstein condensates and finance.

We report and discuss analytical solutions of the vector nonlinear Schrödinger 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 multicomponent systems, from oceanography to optics and plasma physics.

The optical response of metallic nanostructures after intense excitation with femtosecond-laser pulses has recently attracted increasing attention: such response is dominated by ultrafast electron-phonon coupling and offers the possibility to achieve optical modulation with unprecedented terahertz bandwidth. In addition to noble metal nanoparticles, efforts have been made in recent years to synthesize heavily doped semiconductor nanocrystals so as to achieve a plasmonic behavior with spectrally tunable features. In this work, we studied the dynamics of the localized plasmon resonance exhibited by colloidal Cu(2-x)Se nanocrystals of 13 nm in diameter and with x around 0.15, upon excitation by ultrafast laser pulses via pump-probe experiments in the near-infrared, with ∼200 fs resolution time. The experimental results were interpreted according to the two-temperature model and revealed the existence of strong nonlinearities in the plasmonic absorption due to the much lower carrier density of Cu(2-x)Se compared to noble metals, which led to ultrafast control of the probe signal with modulation depth exceeding 40% in transmission.