Abstract

Chirped-pulse propagation under periodic amplification is considered on the basis of the variational method, and the resulting pulse-shape chaotic oscillations are studied. The system of equations governing the evolution of the parameter functions is nonintegrable and is solved by the canonical perturbation method and the construction of local approximate invariants embracing all the essential features of the phase-space dynamics. The latter provide useful guidelines for choosing the appropriate launching-pulse width and chirp for stable propagation for each specific transmission-link configuration. This fact is supported by comparison of the analytic results with the respective numerical ones of the exact dynamical system obtained by the variational method and by the direct integration of the nonlinear Schrödinger equation as well. The structure of the chaotic layer between the two distinct modes of behavior of a propagating pulse, namely, breathing and spreading/decaying, is also investigated qualitatively by utilizing Melnikov’s method. Examples from technologically realistic configurations are given for 4–14-ps pulses and for amplification periods of 40–100 km.

© 2002 Optical Society of America

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