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The multiple-scale averaging and dynamics of dispersion-managed optical solitons

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Abstract

Multiple-scale averaging is applied to the nonlinear Schrödinger equation with rapidly varying coefficients, and use the results to analyze pulse propagation in an optical fiber when a periodic dispersion map is employed. The effects of fiber loss and repeated amplification are taken into account by use of a coordinate transformation to relate the pulse dynamics in lossy fibers to that in equivalent lossless fibers. Second-order averaging leads to a general evolution equation that is applicable to both return-to-zero (soliton) and non-return-to-zero encoding schemes. The resulting equation is then applied to the specific case of solitons, and an asymptotic theory for the pulse dynamics is developed. Based upon the theory, a simple and effective design of two-step dispersion maps that are advantageous for wavelength-division-multiplexed soliton transmission is proposed. Theuse of these specifically designed dispersion maps allows simultaneous minimization of dispersive radiation in several different channels.

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Authors and Affiliations

  1. Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Illinois, 60208–3125, U.S.A

    Tian-Shiang Yang & William L. Kath

  2. Division of Electronic Engineering and Computer Science, Aston University, Birmingham, B4 7ET, U.K

    Sergei K. Turitsyn

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  1. Tian-Shiang Yang
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  2. William L. Kath
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  3. Sergei K. Turitsyn
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Yang, TS., Kath, W.L. & Turitsyn, S.K. The multiple-scale averaging and dynamics of dispersion-managed optical solitons. Journal of Engineering Mathematics 36, 163–184 (1999). https://doi.org/10.1023/A:1004554209222

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