Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber

The resonant interaction of an optical field with two-level doping ions in a cryogenic
optical fiber is investigated within the framework of nonlinear Schrödinger and Maxwell-Bloch
equations. We present explicit fundamental rational rogue wave solutions in the context of
self-induced transparency for the coupled optical and matter waves. It is exhibited that the
optical wave component always features a typical Peregrine-like structure, while the matter waves
involve more complicated yet spatiotemporally balanced amplitude distribution. The existence
and stability of these rogue waves is then confirmed by numerical simulations, and they are shown
to be excited amid the onset of modulation instability. These solutions can also be extended,
using the same analytical framework, to include higher-order dispersive and nonlinear effects,
highlighting their universality.