Pulse Propagation in Nonlinear Optical Fibers using Phase-Sensitive Amplifiers

摘要

A mathematical model for pulse propagation in a nonlinear fiber-opticcommunications line is presented where linear loss in the fiber is balanced by a chain of periodically-spaced, phase-sensitive amplifiers (PSAs). A multiple scale analysis is employed to average over the strong, rapidly-varying, and periodic perturbations to the governing nonlinear Schrodinger equation (NLS). The analysis indicates that the averaged evolution is governed by a fourth-order nonlinear diffusion equation which evolves on a length scale much greater than that of the typical soliton period. In a particular limit, stable steady-state hyperbolic secant solutions of the averaged equation are analytically found to exist provided a minimum amount of over-amplification is supplied. Further, arbitrary initial conditions within a wide stability region exponentially decay onto the steady-state. Outside of this analytic regime, extensive numerical simulations indicate that soliton-like steady-states exist and act as exponential attractors for a wide region of parameter space. These simulations also show that the averaged evolution is quite accurate in modeling the full NLS with loss and phase-sensitive gain. The bifurcation structure of the fourth-order equation is explored. A subcritical bifurcation from the trivial solution is found to occur for a specific over-amplification value. Further, a limit point, or fold, is also found which connects the stable branch of solutions with the unstable branch from the subcritical bifurcation. The bifurcation structure can be further explored in parameter space with the use of AUTO which is capable of tracking steady-state solutions for a wide range of parameters.