Long-distance pulse propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers

We analyze pulse propagation in a nonlinear optical fiber in which linear loss in the fiber is balanced by a chain of periodically spaced, phase-sensitive, degenerate parametric amplifiers. Our analysis shows that no pulse evolution occurs over a soliton period owing to attenuation in the quadrature orthogonal to the amplified quadrature. Evidence is presented that indicates that stable pulse solutions exist on length scales much longer than the soliton period. These pulses are governed by a nonlinear fourth-order evolution equation, which describes the exponential decay of arbitrary initial pulses (within the stability regime) onto stable, steady-state, solitonlike pulses.