Rogue wave formation by accelerated solitons at an optical event horizon

Abstract

Rogue waves, by definition, are rare events of extreme amplitude, but at the same time they are frequent in the sense that they can exist in a wide range of physical contexts. While many mechanisms have been demonstrated to explain the appearance of rogue waves in various specific systems, there is no known generic mechanism or general set of criteria shown to rule their appearance. Presupposing only the existence of a nonlinear Schrödinger-type equation together with a concave dispersion profile around a zero dispersion wavelength we demonstrate that solitons may experience acceleration and strong reshaping due to the interaction with continuum radiation, giving rise to extreme-value phenomena. The mechanism is independent of the optical Raman effect. A strong increase of the peak power is accompanied by a mild increase of the pulse energy and carrier frequency, whereas the photon number of the soliton remains practically constant. This reshaping mechanism is particularly robust and is naturally given in optics in the supercontinuum generation process.