Pulse propagation in nonlinear optical fiber lines that employ phase-sensitive parametric amplifiers

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Abstract
Recently we proposed using periodically spaced, phase-sensitive optical parametric amplifiers to balance linear loss in a nonlinear fiber-optic communication line [Opt. Lett. 18, 803 (1993)]. We present a detailed analysis of pulse propagation in such a fiber line. Our analysis and numerical simulations show that the length scale over which the pulse evolution occurs is significantly increased beyond a soliton period. This is because of the attenuation of phase variations across the pulse’s profile by the amplifiers. Analytical evidence is presented that indicates that stable pulse evolution occurs on length scales much longer than the soliton period. This is confirmed through extensive numerical simulation, and the region of stable pulse propagation is found. The average evolution of such pulses is governed by a fourth-order nonlinear diffusion equation, which describes the exponential decay of arbitrary initial pulses into stable, steady-state, solitonlike pulses.