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Nonlinear Waves in Optical Waveguides and Soliton Theory Applications

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Optical Solitons

Part of the book series: Lecture Notes in Physics ((LNP,volume 613))

Abstract

Starting with dielectric slab as a waveguide, we discuss the formal aspects of a derivation of model (soliton equations) reducing the description of the threedimensional electromagnetic wave. The link to the novel experiments in planar dielectric guides is shown. The derivation we consider as an asymptotic in a small parameter that embed the soliton equation into a general physical model. The resulting system is coupled NS (c NS). Then we go to the nonlinear resonance description; N-wave interactions. Starting from general theory and integration by dressing method arising from Darboux transformation (DT) techniques. Going to linear resonance, we study N-level Maxwell-Bloch (MB) equations with rescaling. Integrability and solutions and perturbation theory of MB equations is treated again via DT approach. The solution of the Manakov system (the cNS with equal nonlinear constants) is integrated by the same Zakharov-Shabat (ZS) problem. The case of non reduced MB equation integrability is discussed in the context of the general quantum Liouville-von Neumann (LvN) evolution equation as associated ZS problem.

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Author information

Authors and Affiliations

  1. Faculty of Applied Physics and Mathematics, Technical University of Gdańsk, ul. G.Narutowicza, 11/12, 80-952, Gdańsk-Wrzeszcz, Poland

    S. B. Leble

  2. Theoretical Physics Department, Kaliningrad State University, Al.Nevsky st.,14, 236041, Kaliningrad, Russia

    S. B. Leble

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  1. S. B. Leble
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Editors and Affiliations

  1. Raman School of Physics, Pondicherry University, 605014, Kalapet, Pondicherry, India

    K. Porsezian

  2. Department of Physics Kalapet, Cochin University of Science and Technology, 682022, Kochi, India

    V. C. Kuriakose

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Leble, S.B. (2002). Nonlinear Waves in Optical Waveguides and Soliton Theory Applications. In: Porsezian, K., Kuriakose, V.C. (eds) Optical Solitons. Lecture Notes in Physics, vol 613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36141-3_4

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  • DOI: https://doi.org/10.1007/3-540-36141-3_4

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  • Print ISBN: 978-3-540-00155-3

  • Online ISBN: 978-3-540-36141-1

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