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Comparison of Solutions of the General Nonlinear Amplitude Equation and a Modified Schrӧdinger Equation

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Journal of Russian Laser Research Aims and scope

Abstract

We review the dynamics of narrow and broad-band optical pulses in nonlinear dispersive media. A major problem that arises during the development of theoretical models, which describe accurately and correctly the behavior of these pulses, is the limited application of the nonlinear Schrӧdinger equation. It describes very well the evolution of nanosecond and picosecond laser pulses. However, when we investigate the propagation of femtosecond and attosecond light pulses, it is necessary to use the more general nonlinear amplitude equation. We show that in this equation two additional terms are included and they have a significant impact on the phase of the pulse. We perform numerical simulations and show the temporal shift of the position of fundamental solitons. This effect depends on the initial duration of the laser pulses. To clarify the influence of the additional terms on the parameters of the optical pulses, we consider the nonlinear amplitude equation, which is a modified nonlinear Schrӧdinger equation.

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Authors and Affiliations

  1. Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradsko shossee, 1784, Sofia, Bulgaria

    A. M. Dakova, L. M. Kovachev & V. I. Slavchev

  2. Faculty of Physics, University of Plovdiv “Paisii Hilendarski”, 24 Tsar Asen Street, 4000, Plovdiv, Bulgaria

    D. Y. Dakova

Authors
  1. A. M. Dakova
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  2. D. Y. Dakova
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  3. L. M. Kovachev
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  4. V. I. Slavchev
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Correspondence to A. M. Dakova.

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Dakova, A.M., Dakova, D.Y., Kovachev, L.M. et al. Comparison of Solutions of the General Nonlinear Amplitude Equation and a Modified Schrӧdinger Equation. J Russ Laser Res 37, 155–163 (2016). https://doi.org/10.1007/s10946-016-9555-y

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  • DOI: https://doi.org/10.1007/s10946-016-9555-y

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