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

Abstract

Abstract: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.

Super chirped rogue waves in optical fibers

“…It is time and space dependent, and hence would lead the rogue waves to undergo a frequency shift (or chirping) during evolution. Such a chirping effect does not exist in many integrable systems, e.g., in the NLS equation [37], in the Maxwell-Bloch system [25], and in the Manakov system [59,62]. For this reason, our super rogue wave solutions discussed here can be termed super chirped rogue waves, to show distinction.…”

“…As it can mimic realistic extreme wave events, the Peregrine soliton has become a popular prototype of rogue waves in many areas [5,23]. Recent studies reveal that Peregrine solitons are universal solutions of majority of integrable models [24][25][26], not peculiar to the NLS equation, and have many interesting variants of emergence such as dark Peregrine solitons [27], anomalous Peregrine solitons [28], and chirped Peregrine solitons [29]. Of particular interest is the chirped Peregrine soliton, which can possess an extra doubly localized chirp while keeping the intensity features of the original Peregrine soliton.…”

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

“…The fact that this PS may involve a peak amplitude higher than threefold is very intriguing, as no such case occurs in integrable systems known so far [12,[21][22][23][24][25]48]. We attribute this unique amplitude property to the coupling between field components and to the coupling between space and time.…”

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

“…To answer this question, we perform extensive numerical simulations with respect to our analytical solutions (Eq. 5), using an efficient code based on the exponential time differencing Crank-Nicolson (ETDCN) scheme with Padé approximation [60,61]. Here we present merely two sets of numerical results, for a typical set of system parameters σ 1, c 1/4, a 1 8/9, a 2 4 5 √ /9, Figures 4A,B.…”