Two-color walking Peregrine solitary waves

We study the extreme localization of light, evolving upon a
non-zero background, in two-color parametric wave interaction
in nonlinear quadratic media. We report the existence
of quadratic Peregrine solitary waves, in the presence
of significant group-velocity mismatch between the waves
(or Poynting vector beam walk-off), in the regime of cascading
second-harmonic generation. This finding opens a novel
path for the experimental demonstration of extreme rogue
waves in ultrafast quadratic nonlinear optics.