Controlled giant rogue waves in nonlinear fiber optics

We show the existence of self-similar giant rogue waves in a tapered graded-index nonlinear fiber and analytically illustrate their amplification in a rather small spatiotemporal domain by controlled manipulation of the phase. Our exact analysis takes recourse to the large manifold of available tapering profiles in conjunction with appropriate gain functions, which are allowed by the dynamical equation governing the tapered graded-index nonlinear fiber. The fact that these profiles and gain functions provide a wide class of boundary conditions makes them particularly relevant for transient rogue waves, which manifest rather rarely.

Figure 1

(a) Profiles of tapering function, width, and quadratic phase function, given by Eq. (14) for $n=1$. Panels (b) and (c), respectively, show the intensity profiles for first- and second-order self-similar optical rogue waves.

Figure 2

Profiles of tapering, width, and quadratic phase function, respectively, for $n=1$. Curve A corresponds to the profile given by Eq. (14) and curves B, C, and D correspond to the generalized class for different values of $c$: $c=0.1$, $c=1$, and $c=10$, respectively.

Figure 3

Evolution of first-order self-similar optical rogue waves for generalized tapering: (a) $c=0.1$, (b) $c=1$, and (c) $c=10$. The parameters used in the plots are $C_{02}=0.3$, $X_0=0.0$, and ${\zeta }_0=0.0$.

Figure 4

Evolution of second-order self-similar optical rogue waves for generalized tapering: (a) $c=0.1$, (b) $c=1$, and (c) $c=10$. The parameters used in the plots are $C_{02}=0.3$, $X_0=0.0$, and ${\zeta }_0=0.0$.