Abstract

Modulational instability (MI) refers to the growth of an initial weak perturbation at the expense of a plane wave in a dispersive or diffractive nonlinear medium [1]. In the context of optical fibers, temporal MI in the anomalous group-velocity dispersion (GVD) regime has been extensively studied in recent years for its potential application in high-repetition rate ultrashort pulse train generation [2] and ultrafast optical switching [3]. The domain of MI may be extended to the normal GVD regime by means of a feedback loop [4] or exploiting cross-phase modulation (XPM) [5,6]. In the latter case, the simultaneous presence of two copropagating beams can also lead to a more complex behaviour in comparison with the scalar case [7]. The aim of this paper is to give a quantitative understanding of the nonlinear dynamics (i.e. past the early stage of exponential sidebands growth) of MI induced by XPM between linearly polarized beams copropagating along the principal axes of a high-birefringence fiber, both weakly perturbed. At first, for the sake of clarity, we will recall the well known linear stability analysis of the system and then introduce a finite dimensional truncation leading to an intricate system of Ordinary Differential Equations (ODE’s). Finally, introducing some approximations supported by numerical results and physical considerations, we will obtain an exactly solvable set of ODE's, which is analogous to the one derived in [7] for a different initial condition.

© 1993 Optical Society of America