Title: 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.