Abstract
Analysis of the nonlinear Schrödinger (NLS) equation and jump conditions governing pulse propagation in a nonlinear optical fiber with periodically-spaced, phase-sensitive parametric amplifiers (PSAs) shows that the averaged pulse evolution is governed by a fourth-order nonlinear diffusion equation similar to the Kuramoto-Sivashinsky and Swift-Hohenberg equations. A consequence of this diffusive dynamics is that dispersive radiation from evolving pulses is almost totally eliminated, and stable optical pulses propagate over long distances without deformation. Here the asymptotic derivation of this averaged fourth-order equation is reviewed, and comparisons are given between numerical solutions of the averaged equation and the full NLS equation with PSAs. It is shown that the main difference between the two computations is due to a small amount of high-frequency dispersive radiation. The numerical requirements for resolving these high-frequency components is also discussed.Key wordsnonlinear Schrödinger (NLS) equationsolitonsoptical fibersphase-sensitive optical parametric amplifierspseudo-spectral methodsAMS(MOS) subject classifications35Q5135Q5565M7035C20
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