Dispersion-managed optical fiber systems with zero Hamiltonian

The dynamics of nonlinear pulse propagation in optical fibers is governed by the famous nonlinear Schrodinger equation (NLSE), in which the group-velocity dispersion and self-phase modulation form a basic set of optical processes describing a broad range of realistic physical situations. In this work, by means of variational formalism for the NLSE, we derive exact analytical expressions for the variational equations corresponding to the amplitude, width and chirp of the pulse in terms of initial pulse parameters, fiber parameters and the distance of propagation of the pulse; under the condition when the Hamiltonian of the system is zero. Then, for Gaussian and hyperbolic secant ansatz, we check the validity of the obtained analytical results to describe pulse propagation in optical fiber. As a practical application of our results, we consider the design of the DM fiber systems and we derive an analytical expression for the Gordon-Haus jitter.