Modulational instability in optical fibers with randomly kicked normal dispersion

Abstract

We study modulational instability (MI) in optical fibers with random group velocity dispersion (GVD) generated by sharply localized perturbations of a normal GVD fiber that are either randomly or periodically placed along the fiber and that have random strength. This perturbation leads to the appearance of low frequency MI side lobes that grow with the strength of the perturbations, whereas they are faded by randomness in their position. If the random perturbations exhibit a finite average value, they can be compared with periodically perturbed fibers, where Arnold tongues appear. In that case, increased randomness in the strengths of the variations tends to affect the Arnold tongues less than increased randomness in their positions.

Stochastic modulational instability in the nonlinear Schrödinger equation with colored random dispersion

“…As in Ref. [21], the MI of stochastic origin is related to the growth rate of the second moment. The eigenvalues of the matrix in Eq.…”

“…We aim at studying the MI problem in a class of random-GVD fibers that is both experimentally accessible and theoretically tractable. In [21], we studied the case of a GVD perturbed by randomly located sharp and large kicks. Two different families of random processes were chosen to generate their mutual spacing and amplitude.…”

Large Modulational Instability Gain in Random Dispersion-Managed Fibers

“…Following [2,4], Eq. ( 1) is linearized around the continuous wave solution U 0 (z) = √ P exp(iγPz) and the resulting system for sideband phase-quadrature variables (x 1 , x 2 ) is written as a product of random matrices, depending on the random variables ∆L n .…”

“…Large random fluctuations of GVD were studied in Ref. [4], in the form of localised abrupt changes (kicks) around an average normal GVD. We apply the method developed in our previous work to compute the MI gain in a DM system where the length of each segment fluctuates randomly with a certain probability distribution.…”

Random telegraph dispersion management: modulational instability

“…In the late 90s, the white noise process (an exactly solvable model) was considered [9,[13][14][15]. Only recently different random processes were considered: localized GVD kicks [16] or coloured processes of low-pass or band-pass type [17].…”