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
Article
  • 16 Downloads

Abstract

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.

Keywords

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

Notes

Acknowledgements

We are grateful for Qom University of Technology supports.

References

  1. Caplan, R.M., Carretero-Gonzalez, R.: Numerical stability of explicit Runge–Kutta finite-difference schemes for the nonlinear Schrödinger equation. Appl. Numer. Math. 71, 24–40 (2013)MathSciNetCrossRefMATHGoogle Scholar
  2. Dauxois, T., Peyrard, M.: Physics of Solitons. Cambridge University Press, Cambridge (2005)MATHGoogle Scholar
  3. Devillard, P., Dunlop, F., Souillard, B.: Localization of gravity waves on a channel with a random bottom. J. Fluid Mech. 186, 521–538 (1988)ADSCrossRefMATHGoogle Scholar
  4. Eisenberg, H.S., Silberberg, Y., Morandotti, R., Aitchison, J.S.: Diffraction management. Phys. Rev. Lett. 85, 1863–1866 (2000)ADSCrossRefGoogle Scholar
  5. Gautam, S., Angom, D.: Phase separation of binary condensates in harmonic and lattice potentials. J. Phys. B At. Mol. Opt. Phys. 44, 025302 (2011)ADSCrossRefGoogle Scholar
  6. Ghalandari, M., Solaimani, M.: Spatial soliton propagation through waveguides: rectangular and parabolic rectangular index profile. Opt. Quant. Electron. 48, 514 (2016)CrossRefGoogle Scholar
  7. Lee, P.A., Ramakrishnan, T.V.: Disordered electronic systems. Rev. Mod. Phys. 57, 287–337 (1985)ADSCrossRefGoogle Scholar
  8. Lifshits, I.M., Gredeskul, A.S., Pastur, L.A.: Introduction to the Theory of Disordered Systems. Wiley, New York (1988)Google Scholar
  9. Lundquist, P.B., Andersen, D.R., Swartzlander Jr., G.A.: Asymptotic behavior of the self-defocusing nonlinear Schrödinger equation for piecewise constant initial conditions. J. Opt. Soc. Am. B 12, 698–703 (1995)ADSCrossRefGoogle Scholar
  10. Morandotti, R., Eisenberg, H.S., Silberberg, Y., Sorel, M., Aitchison, J.S.: Self-focusing and defocusing in waveguide arrays. Phys. Rev. Lett. 86, 3296–3299 (2001)ADSCrossRefGoogle Scholar
  11. Rong-Pei, Z., Xi-Jun, Y., Tao, F.: Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method. Chin. Phys. B 21, 030202 (2012)CrossRefGoogle Scholar
  12. Schwartz, T., Bartal, G., Fishman, S., Segev, M.: Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007)ADSCrossRefGoogle Scholar
  13. Seyed Shirazi, S.Z., Solaimani, M., Farnam, B., Ghalandari, M., Aleomraninejad, S.M.A.: Spatial soliton propagation through a triangular waveguide: a Runge Kutta study. Optik 129, 200–206 (2017)ADSCrossRefGoogle Scholar
  14. Shapiro, S.A., Hubral, P.: Elastic Waves in Random Media. Springer, Berlin (1999)Google Scholar
  15. Sheng, P.: Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena. Academic Press, San Diego (1995)Google Scholar
  16. Tang, X.-Y., Kant Shukla, P.: Solution of the one-dimensional spatially inhomogeneous cubic-quintic nonlinear Schrödinger equation with an external potential. Phys. Rev. A 76, 013612 (2007)ADSCrossRefGoogle Scholar
  17. Xie, S.-S., Li, G.-X., Yi, S.: Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation. Comput. Methods Appl. Mech. Eng. 198, 1052–1060 (2009)ADSCrossRefMATHGoogle Scholar

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

Personalised recommendations