On dynamics of elliptic solitons in lossy optical fibers

By exploiting the theory of electromagnetic waves from Maxwell's equations, the damped nonlinear Schrodinger (DNLS) equation is shown to govern the evolution of nonlinear periodic optical signals in a lossy optical fiber. These optical periodic pulses are mainly generated by the classical process of modulational instability (MI) in which nonlinearity is balanced by chromatic dispersion in the anomalous regime, with the linear loss generally suppressing the existence of soliton trains during propagation down the lossy fiber. When the periodic optical wave trains are subjected to weak external perturbations, this leads to the exposure of some internal modes of the system which are bound states solutions of the first order Lame equation. These modes generally characterize various fundamental background excitations that co-propagate with the optical periodic signals in the fiber. Direct numerical simulations of the DNLS amplitude equation depict the exponential decrease in the amplitude and corresponding increase in the width of the wave trains during propagation. Power lasers are used in order to compensate for fiber losses; this is realized via time-division multiplexing of optical pulses which are periodically pumped into the lossy fiber at regular distances within the framework of a distributed amplification scheme. This leads to the regular energy restoration in the lossy fiber as a result of the interactions between the energized multiplexed light signals (generated by the power lasers) and the propagating damped optical pulses, hence ensuring effective transmission over long distances.