Solitons Near the Zero Dispersion Point of Optical Fibers.

We study the propagation of nonlinear optical pulses at and near the zero dispersion point of single mode fibers. In the anomalous dispersion regime, the balance between second order dispersion and nonlinearity (the Kerr effect) results in solitons, pulses that propagate without distortion. At the zero dispersion point, third order dispersion balances nonlinearity. We observed numerically that initial pulses split into two parts on either side of the zero dispersion point in the frequency domain. The pulse shifted inside the anomalous dispersion regime is a soliton with small third order dispersion as perturbation. We determine numerically the criteria for this perturbed "soliton" to propagate. The power required to launch such a "soliton" is substantially lower than that of the conventional solitons in the anomalous regime because of the smaller dispersion present. We then study the effect of small third order dispersion on the conventional solitons. We find that radiation is excited at a frequency proportional to 1/ beta. The parameter beta is proportional to the ratio of third order dispersion coefficient to second order dispersion coefficient. For the fundamental soliton, this resonance frequency can be calculated using a perturbation method called "asymptotic beyond all orders." The radiation rate is shown to be exponentially small (proportional to exp(-1/ beta)). Hence, the energy which this fundamental soliton loses through radiation decreases sharply as one moves away from the zero dispersion point. Higher order solitons (also known as breathers) are found to break up into their constituent solitons after certain threshold values of beta are reached. To study the feasibility of soliton propagation near the zero dispersion point, the effect of zero dispersion point fluctuation due to axial variation of fiber parameters is investigated. It is shown both analytically and numerically that in the practical regime of parameters where the correlation length scale of the fluctuation is much shorter than both the second order and third order dispersion scale length, soliton propagation in the vicinity of the zero dispersion point is possible.