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Multi-step Iterative Algorithm for Mathematical Modeling of Light Bullets in Anisotropic Media

  • Irina G. ZakharovaEmail author
  • Aleksey A. Kalinovich
  • Maria V. Komissarova
  • Sergey V. Sazonov
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

To perform an analytical and numerical investigation of optical bullets in a focusing bulk waveguide with quadratic nonlinearity we use the well-known quasi-optical approach. We give an approximate soliton solution representing a two-component light bullet. To investigate numerically the regimes of the formation and propagation of two-component optical bullets we construct a conservative difference scheme. To realize the multi-dimensional nonlinear difference scheme we propose a multi-step effective iterative solver. This method allows us to carry out an accurate and efficient modeling of the considered processes.

Keywords

Multi-step algorithm Light bullets 
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References

  1. 1.
    Kivshar, Y.S., Agrawal, G.: Optical Solitons: From Fibers to Photonic Crystals. Academic press, Cambridge (2003)Google Scholar
  2. 2.
    Karamzin, Y.N., Sukhorukov, A.P.: Nonlinear interaction of diffracting light beams in a medium with quadratic nonlinearity; focusing of beams and limiting the efficiency of optical frequency converters. Eksp Zh. Teor. Fiz. 20, 734 (1974)Google Scholar
  3. 3.
    Kanashov, A.A., Rubenchik, A.M.: On diffraction and dispersion effect on three wave interaction. Phys. D 4, 122 (1981)CrossRefGoogle Scholar
  4. 4.
    Malomed, B.A., Drummond, P., He, H., et al.: Spatiotemporal solitons in multidimensional optical media with a quadratic nonlinearity. Phys. Rev. E 56, 4725 (1997)CrossRefGoogle Scholar
  5. 5.
    Skryabin, D.V., Firth, W.J.: Generation and stability of optical bullets in quadratic nonlinear media. Opt. Commun. 148, 79 (1998)CrossRefGoogle Scholar
  6. 6.
    McLeod, R., Wagner, K., Blair, S.: (3+1)-dimensional optical soliton dragging logic. Phys. Rev. A 52, 3254 (1995)CrossRefGoogle Scholar
  7. 7.
    McDonald, G.D., et al.: Bright solitonic matter-wave interferometer. Phys. Rev. Lett. 113, 013002 (2014)CrossRefGoogle Scholar
  8. 8.
    Sazonov, S.V., Mamaikin, M.S., Komissarova, M.V., Zakharova, I.G.: Planar light bullets under conditions of second-harmonic generation. Phys. Rev. E 96, 022208 (2017)CrossRefGoogle Scholar
  9. 9.
    Sazonov, S.V., Mamaikin, M.S., Zakharova, I.G., Komissarova, M.V.: Planar spatiotemporal solitons in a quadratic nonlinear medium. Phys. Wave Phenom. 25, 83 (2017)CrossRefGoogle Scholar
  10. 10.
    Samarskii, A.A.: The Theory of Difference Schemes Marcel. Dekker Inc., New York (2001)CrossRefGoogle Scholar
  11. 11.
    Karamzin, Y.N.: Difference schemes for calculating the three-frequency interactions of electromagnetic waves in a non-linear medium with quadratic polarization. USSR Comput. Math. Math. Phys. 14(4), 236–241 (1974)CrossRefGoogle Scholar
  12. 12.
    Ciegis, R., Mirinavicius, A., Radziunas, M.: Comparison of split step solvers for multidimensional Schrödinger problems. Comput. Methods Appl. Math. 13(1), 237–250 (2013)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Gaspar, F.J., Rodrigo, C., Ciegis, R., Mirinavicius, A.: Comparison of solvers for 2D Schrodinger problems. Int. J. Numer. Anal. Model. 11(1), 131–147 (2014)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Trofimov, V.A., Loginova, M.M.: Difference scheme for the problem of femtosecond pulse interaction with semiconductor in the case of nonlinear electron mobility. J. Comput. Math. Math. Phys. 45(12), 2185–2196 (2005)zbMATHGoogle Scholar
  15. 15.
    Shizgal, B.: Spectral Methods in Chemistry and Physics. SC. Springer, Dordrecht (2015).  https://doi.org/10.1007/978-94-017-9454-1CrossRefzbMATHGoogle Scholar
  16. 16.
    Drummond, P.D.: Central partial difference propagation algorithms. Comput. Phys. Commun. 29, 211 (1983)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Agrawal, G.: Nonlinear Fiber Optics, 5th edn. Academic press, Cambridge (2012)zbMATHGoogle Scholar
  18. 18.
    Trofimov, V.A., Loginova, M.M., Egorenkov, V.A.: Influence of external electric field on laser- induced wave process occurring in semiconductor under the femtosecond pulse acting. In: Proceedings of SPIE, vol. 9127, p. 912709 (2014)Google Scholar
  19. 19.
    Trofimov, V.A., Loginova, M.M., Egorenkov, V.A.: New two-step iteration process for solving the semiconductor plasma generation problem with arbitrary BC in 2D case. WIT Trans. Model. Simul. 59 (2015).  https://doi.org/10.2495/CMEM150081
  20. 20.
    Antoine, X., Besse, C.: Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrodinger equation. J. Comput. Phys. 188, 157–175 (2003)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Irina G. Zakharova
    • 1
    Email author
  • Aleksey A. Kalinovich
    • 1
  • Maria V. Komissarova
    • 1
  • Sergey V. Sazonov
    • 1
    • 2
  1. 1.Faculty of PhysicsM.V. Lomonosov Moscow State UniversityLeninskie GoryRussia
  2. 2.National Research Centre “Kurchatov Istitute”MoscowRussia

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