Impulse response of nonlinear Schrödinger equation and its implications for pre-dispersed fiber-optic communication systems

In the presence of pre-dispersion, an exact solution of nonlinear Schrödinger equation (NLSE) is derived for impulse input. The phase factor of the exact solution is obtained in a closed form using the exponential integral. The nonlinear interaction among periodically placed impulses launched at the input is investigated, and the condition under which these pulses do not exchange energy is examined. It is found that if the complex weights of the impulses at the input have a secant-hyperbolic envelope and a proper chirp factor, they will propagate over long distances without exchanging energy. To describe their interaction, a discrete version of NLSE is derived. The derived equation is a form of discrete self-trapping (DST) equation, which is found to admit fundamental and higher order soliton solutions in the presence of high pre-dispersion. Nonlinear eigenmodes derived here may be useful for description of signal propagation and nonlinear interaction in highly pre-dispersion fiber-optic systems.