Super chirped rogue waves in optical fibers

Abstract

The super rogue wave dynamics in optical fibers are investigated within the framework of a generalized nonlinear Schrödinger equation containing group-velocity dispersion, Kerr and quintic nonlinearity, and self-steepening effect. In terms of the explicit rogue wave solutions up to the third order, we show that, for a rogue wave solution of order n, it can be shaped up as a single super rogue wave state with its peak amplitude 2n + 1 times the background level, which results from the superposition of n(n + 1)/2 Peregrine solitons. Particularly, we demonstrate that these super rogue waves involve a frequency chirp that is also localized in both time and space. The robustness of the super chirped rogue waves against white-noise perturbations as well as the possibility of generating them in a turbulent field is numerically confirmed, which anticipates their accessibility to experimental observation.

Peregrine Solitons Beyond the Threefold Limit and Their Two-Soliton Interactions

“…Moreover, the interaction of such two PS states can create a spikelike rogue wave of extremely high peak amplitude (nearly 15-fold for certain given parameters). Our result is different from the deterministic colliding events of ordinary solitons [33][34][35], which could also yield a hump of very high amplitude, yet predictable. We confirm numerically that these high-amplitude PS solutions are robust and can be excited amid the onset of MI.…”

Recent progress on optical rogue waves in fiber lasers: status, challenges, and perspectives

“…RWs have been obtained in several optical configurations, such as the photonic crystals, 185 the optical fibers, 186 and the SC generation. 45 Recently, the generation of 2-D optical RWs in the presence of turbulence with the interaction of optical vortices was demonstrated by Gibson et al, 187 which indicates the optical vortices can induce the generation of RWs.…”

Peregrine Solitons on a Periodic Background in the Vector Cubic-Quintic Nonlinear Schrödinger Equation

“…We should point out that the Lax pair Eq. 3 takes the same form as used in the scalar CQ-NLS equation [42], except that the Q is now defined by a 3 × 3 matrix. The subsequent Darboux dressing operation is straightforward.…”

“…In this paper, we present an in-depth study of the formation of Peregrine solitons on a periodic background, within the framework of the vector cubic-quintic NLS (CQ-NLS) equation, which is a two-component version of the scalar NLS-type Gerdjikov-Ivanov equation [42]. As will be shown, this model has included the necessary ingredients such as group-velocity dispersion (GVD), Kerr nonlinearity, quintic nonlinearity, and self-steepening, which could provide more accurate descriptions for realistic rogue waves met in complex systems, as compared to the simple Manakov model [43,44] and to the vector Gerdjikov-Ivanov equation [45].…”