Stability of bound states near the zero-dispersion wavelength in optical fibers

Abstract

The propagation of weakly nonlinear pulses near the zero-dispersion wavelength (ZDW) in optical fibers is governed by a modified nonlinear Schr\"odinger (NLS) equation with a third-order-derivative dispersive term. This equation is known to admit steady, multihump bound states that would require less peak power to launch than an ordinary NLS soliton pulse of comparable duration and with carrier wavelength in the anomalous dispersion regime. Here, the stability of the two-hump bound state for which third-order dispersion is most significant is examined. Linear stability analysis indicates the presence of a mild instability with ${O(10}^{\ensuremath{-}2})$ growth rate. Numerical solutions of the modified NLS equation, however, reveal that, under certain conditions, nonlinearity has a stabilizing effect, permitting two-hump pulses to propagate for long distances without collapsing. Depending on the type of perturbation, a perturbed bound state evolves to a neighboring state with carrier frequency shifted either towards or away from the ZDW. The evolution of more general pulse profiles near the ZDW is also considered and the effect of fiber loss is discussed.