Akhmediev Breathers and Peregrine Solitary Waves in a Quadratic Medium

Abstract: We investigate the formation of optical localized nonlinear structures, evolving upon a non-zero background plane wave, in a dispersive quadratic medium. We show the existence of quadratic Akhmediev breathers and Peregrine solitary waves, in the regime of cascading second-harmonic generation. This finding opens a novel path for the excitation of extreme rogue waves and for the description of modulation instability in quadratic nonlinear optics.