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 periodically modulated nonlinear optical fibers with piecewise constant dispersion). The approximation is based on the Gaussian ansatz. The dynamics of the pulse are reduced to a two-dimensional map. An explicit solution 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 dispersion is, effectively, rapidly oscillating along the fiber. In the former case, the main result is the calculation of a mean value of the dispersion coefficient which is necessary to compensate the weak nonlinearity, which is of obvious interest for pulse communications in dispersion-compensated linear fibers. In the latter case, the width of the pulse performs small oscillations around a mean value. This mean width is found for a given energy of the pulse, provided that the mean dispersion is nonzero, and it is shown that the corresponding solution is unique and stable.