Wave localization in two dimensional parabolic periodic refractive index profiles: a 4th order Runge–Kutta study

  • M. Solaimani
  • B. Farnam
  • M. Ghalandari
  • S. Z. SeyedShirazi


In this work, we have studied the wave localization in a two dimensional parabolic periodic refractive index profile. Our calculations have been performed by developing a 4th order Runge–Kutta method. Effects of different parameters in refractive index profile and incident wave shape on the wave intensity and shape in the future are shown. Effects of the mentioned parameters on localization degree and total momentum of the system are also investigated. We find different parameters change intervals within which the excitation disperses. Thus no bound state is possible. Finally, we show when a bound state is present.


Wave localization 4th order Runge Kutta method Two dimensional parabolic periodic refractive index profile 



We are grateful for Qom University of Technology supports.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • M. Solaimani
    • 1
  • B. Farnam
    • 2
  • M. Ghalandari
    • 1
  • S. Z. SeyedShirazi
    • 2
  1. 1.Department of Physics, Faculty of ScienceQom University of TechnologyQomIran
  2. 2.Department of Mathematics, Faculty of ScienceQom University of TechnologyQomIran

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