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Waveguide Mode Interactions. Coupled Nonlinear Schrödinger Equations

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Waveguide Propagation of Nonlinear Waves

Part of the book series: Springer Series on Atomic, Optical, and Plasma Physics ((SSAOPP,volume 109))

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Abstract

The waveguide modes, specified by a transverse variable profile, propagate with velocity determined by the joint matter–waveguide dispersion. Any nonlinearity will lead to mode interaction, and in the case of wavepackets this will be described approximately by the coupled nonlinear Schrödinger (CNS) equations. The theory and numerical solutions is presented below.

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References

  1. G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, London, 1997)

    MATH  Google Scholar 

  2. C.R. Menyuk, Nonlinear pulse propagation in birefringent optical fibers. IEEE J. Quantum Electron 23(2), 174–176 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  3. S.J. Garth, C. Pask, Nonlinear effects in elliptical-core few-mode optical fiber. J. Opt. Soc. Am. B 9, 243 (1992)

    Article  ADS  Google Scholar 

  4. Q. Chang, E. Jia, W. Sun, Difference schemes for solving the generalized nonlinear Schrödinger equation. J. Comp. Phys. 148, 397 (1999)

    Article  ADS  Google Scholar 

  5. M.S. Ismail, S.Z. Alamri, Highly accurate finite difference method for coupled nonlinear Schrödinger equation. Int. J. Comput. Math. 81, 333 (2004)

    Article  MathSciNet  Google Scholar 

  6. F. Ivanauska, M. Radziunas, On convergence and stability of the explicit difference method for solution of nonlinear Schrödinger equations. SIAM J. Numer. Anal. 36, 1466 (1999)

    Article  MathSciNet  Google Scholar 

  7. J. Sun, X. Gu, Z. Ma, Numerical study of the soliton waves of the coupled nonlinear Schrödinger system. Phys. D 196, 311 (2004)

    Article  MathSciNet  Google Scholar 

  8. A. Kurtinaitis, F. Ivanauskas, Finite difference solution methods for a system of the nonlinear Schrödinger equations. Nonlinear Anal. Model. Control 9, 247 (2004)

    MathSciNet  MATH  Google Scholar 

  9. L. Wu, DuFort-Frankel type methods for linear and nonlinear Schrödinger equations. SIAM J. Numer. Anal. 33, 1526 (1996)

    Article  MathSciNet  Google Scholar 

  10. W. Dai, An unconditionally stable three-level explicit difference scheme for the Schrödinger equation with a variable coefficient. SIAM J. Numer. Anal. 29, 174 (1992)

    Article  MathSciNet  Google Scholar 

  11. A.A. Halim, S.P. Kshevetskii, S.B. Leble, Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system. Int. J. Math. Math. Sci. 63, 3979 (2002)

    MathSciNet  MATH  Google Scholar 

  12. A.A. Halim, S.P. Kshevetskii, S.B. Leble, Numerical integration of a coupled Kortweg-de Vries system. Comp. Math. App. 45, 581 (2003)

    Article  Google Scholar 

  13. A.W. Snyder, W.R. Young, Modes of optical waveguides. J. Opt. Soc. Am. A 3, 297 (1978)

    Article  Google Scholar 

  14. S.B. Leble, B. Reichel, Mode interaction in multi-mode optical fibers with Kerr effect (2005), arxiv:physics/0502122

  15. J.D. Hoffman, Numerical Methods for Engineers and Scientists, 2nd edn. Marcell Dekker (2001)

    Google Scholar 

  16. S.B. Leble, B. Reichel, On convergence and stability of a numerical scheme of coupled nonlinear Schrödinger equations. Comput. Math. Appl. 55, 745–759 (2008)

    Article  MathSciNet  Google Scholar 

  17. K. Porsezian, Soliton models in resonant and nonresonant optical fibers. Pramana J. Phys. 57, 1003 (2001)

    Article  ADS  Google Scholar 

  18. P.V. Mamyshev, S.V. Chemikov, E.M. Dianov, Generation of fundamental soliton trains for high-bit-rate optical fiber communication lines. IEEE J. QE 27, 2347 (1991)

    Article  Google Scholar 

  19. S. Novikov, S.V. Manakov, L.P. Pitaevskii, V.E. Zakharov, Theory of Solitons. The Inverse Scattering Method (Springer, Berlin, 1984)

    MATH  Google Scholar 

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Correspondence to Sergey Leble .

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Leble, S. (2019). Waveguide Mode Interactions. Coupled Nonlinear Schrödinger Equations. In: Waveguide Propagation of Nonlinear Waves. Springer Series on Atomic, Optical, and Plasma Physics, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-030-22652-7_4

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