PULSE-PROPAGATION IN A NONLINEAR-OPTICAL FIBER WITH PERIODICALLY MODULATED DISPERSION - VARIATIONAL APPROACH

Stimulated by recent numerical results, an analytical approximation is developed for the dispersion management (pulse propagation in periodi cally modulated nonlinear optical fibers with piecewise constant dispe rsion). The approximation is based on the Gaussian ansatz. The dynamic s of the pulse are reduced to a two-dimensional map. An explicit solut ion for a fixed point of the map can be found when the nonlinearity is weak as compared to the strongly modulated dispersion, and when the d ispersion is, effectively, rapidly oscillating along the fiber. In the former case, the main result is the calculation of a mean value of th e dispersion coefficient which is necessary to compensate the weak non linearity, which is of obvious interest for pulse communications in di spersion-compensated linear fibers. In the latter case, the width of t he pulse performs small oscillations around a mean value. This mean wi dth is found for a given energy of the pulse, provided that the mean d ispersion is nonzero, and it is shown that the corresponding solution is unique and stable.