Dynamics of Solitary Wave Pulses Near the Zero-Dispersion Wavelength in Optical Fibers

Abstract

Abstract : To counteract the effects of dispersion in the transmission of signals in optical fibers, it is desirable to use nonlinear wave pulses in the form of solitary waves which feature a perfect balance of dispersion and nonlinearity and are known to be possible in the anomalous dispersion regime. Near the zero-dispersion wavelength (ZDW), the borderline between normal and anomalous dispersion, however, dispersive effects are relatively weak and it would seem most efficient to operate there, assuming that one can launch solitary wave pulses close to the ZDW. Accordingly, the question of existence of such pulses and their stability to frequency and amplitude modulations has been examined. While no single hump solitary waves are possible near the ZDW, a countable infinitely of symmetric, locally confined bound states having more than one hump have been found, both analytically in terms of a novel perturbation technique, and numerically by a shooting procedure. The stability of the two hump bound state closest to the ZDW has also been examined. Linear stability analysis indicates the presence of a mild instability. Numerical simulations, however, reveal that, under certain conditions, nonlinearity has a stabilizing effect, permitting two hump pulses to propagate for long distances without collapsing. Finally, the effect of higher-order dispersion on solitary pulses in the anomalous dispersion regime away from the ZDW has been studied. It has been demonstrated that these pulses emit radiation in general. This can be an important issue when dealing with pulses of relatively short duration, in the femtosecond range.