Spatiotemporal Complex Geometrical Optics (CGO) of N 3D Interacting Asymmetric Gaussian Wave Packets in Nonlinear Medium - CGO as the Simplest and Efficient Method for Spatiotemporal Evolution

Pawel Berczynski, Slawomir Marczynski

2015

Abstract

The complex geometrical optics (CGO) was applied for the spatiotemporal evolution of arbitrary number of 3D mutually incoherent (with different carrier frequencies) Gaussian wave packets (GWPs) interacting and propagating in a nonlinear medium of Kerr type. The CGO reduced description of the propagation of the beam, the pulse and the wave packet to complex ordinary differential equations (ODE) This leads to exceptionally fast numerical algorithms. We observed high efficiency of the CGO method to compute interactions of arbitrary number of 3D Gaussian wave packets propagating in a nonlinear (anomalous) dispersive medium of the Kerr type. The derived CGO equations were compared with equations obtained by the variational method. CGO described the Gaussian beam propagation in free space as well as the Gaussian pulse spreading in the linear anomalous dispersive medium more illustratively than both the Fourier transform method and the Fresnel diffraction integral method. The spatiotemporal CGO has been proven to be a method more practical than the spectral analysis, the variational method, the method of moments and the method of the generalized eikonal approximation. Complementary to the presented results, an on-line CGO solver, implemented in Javascript, is freely available at the authors’ website: http://slawek.ps.pl/odelia.html.

References

  1. S. A. Akhmanov, A. P. Sukhorukov, R. V. Khokhlov. Selffocusing and light diffraction in nonlinear medium. Soviet Phys. Uspekhi 10, 609-636 (1968).
  2. D. Anderson. Variational approach to nonlinear pulse propagation in optical fibers. Physical Review A, vol. 27, No. 6, pp. 3135-3145, (1983).
  3. J. A. Arnaud,. Beams and Fiber Optics, Academic Press, New York, (1976).
  4. P. Berczynski and Yu. A. Kravtsov. Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eikonal form of complex geometrical optics, Phys. Lett. A, 331, 265-268 (2004).
  5. P. Berczynski. Complex geometrical optics of nonlinear inhomogeneous fibres. Journal of Optics 13 035707 (2011).
  6. P. Berczynski. Complex geometrical optics of inhomogeneous and nonlinear saturable media, Optics Communications 295, 208-218, (2013).
  7. P. Berczynski and S. Marczynski. Chapter One: Gaussian Beam Propagation in Inhomogeneous Nonlinear Media: Description in Ordinary Differential Equations by Complex Geometrical Optics. Advances in Imaging and Electron Physics, (Edited by Peter W. Hawkes), Vol. 185, ISBN: 978-0-12-800144-8, Pages 1-111, (2014).
  8. M. Born, E. Wolf. Principles of Optics, New York: Pergamon, (1959).
  9. S. Choudhary, L. B. Felsen. Analysis of Gaussian beam propagation and diffraction by inhomogeneous wave tracking. Proceedings of the IEEE, vol. 62, No.11, (1974).
  10. G. A. Deschamps. Gaussian beam as a bundle of complex rays. Electron. Lett., 7(23), 684-685, (1971).
  11. G. A. Deschamps and P. E Mast,. Beam tracing and applications. In: Proc. Symp. Quasi-Optics, pp. 379-395, Polytechnic Press, New York, (1964).
  12. L. Felsen. Evanescent waves. J. Opt. Soc. Am., vol. 66, No. 8, p. 751-754, (1976).
  13. Ch. Jirauschek, U. Morgner, F. X. Kartner, Variational analysis of spatiotemporal pulse dynamics in dispersive Kerr media, pp 1716-17-21, J.Opt.Soc.Am. B 19, Vol. 19, No. 7, (2002).
  14. M. Kline and I. Kay. Electromagnetic theory and Geometrical Optics. Pure and Applied Mathematics, A Series of Texts and Monographs Edited by R. Courant, L. Bers and J. Stoker, vol.12, John Wiley and Sons, Inc. (1965).
  15. H. Kogelnik, On the Propagation of Gaussian Beams of Light Through Lenslike Media Including those with a Loss or Gain Variation. Applied Optics, 4(12), 1562 - 1569, (1965).
  16. Yu A. Kravtsov N. Y. Zhu. Theory of diffraction: Heuristic Approaches, Alpha Science International, ISBN 1842653725, (2009).
  17. Yu. A. Kravtsov, Complex rays and complex caustics, Radiophys. Quantum Electronics 10, 719-730, (1967).
  18. R. K. Luneburg,. Mathematical Theory of Optics. University of California Press, Berkeley and Los Angeles, (1964).
  19. E. G. Sauter. Nonlinear Optics. John Wiley&Son, p. 1-214, NY 10158-0012, published in Canada, (1996).
  20. A. Sommerfeld. Optics, Lectures on theoretical physics, vol. 4, New York: Academic Press, (1964).
  21. S. N. Vlasov, V. A. Petrischev and V. I. Talanov. Averaged description of wave beams in linear and nonlinear media (The method of moments), Radiofizika, vol. 14, No. 9, pp. 1353-1363, (1971).
  22. S. Yap, B. Quek and K. Low. Generalized eikonal approximation. 1. Propagation of electromagnetic pulse in a linear dispersive medium, 2. Propagation of stationary electromagnetic waves in linear and nonlinear media, JOSA A, vol. 15, 2725-2729; vol.15, 2720-2724, (1998).
Download


Paper Citation


in Harvard Style

Berczynski P. and Marczynski S. (2015). Spatiotemporal Complex Geometrical Optics (CGO) of N 3D Interacting Asymmetric Gaussian Wave Packets in Nonlinear Medium - CGO as the Simplest and Efficient Method for Spatiotemporal Evolution . In Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS, ISBN 978-989-758-092-5, pages 53-60. DOI: 10.5220/0005291600530060


in Bibtex Style

@conference{photoptics15,
author={Pawel Berczynski and Slawomir Marczynski},
title={Spatiotemporal Complex Geometrical Optics (CGO) of N 3D Interacting Asymmetric Gaussian Wave Packets in Nonlinear Medium - CGO as the Simplest and Efficient Method for Spatiotemporal Evolution},
booktitle={Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,},
year={2015},
pages={53-60},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005291600530060},
isbn={978-989-758-092-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 1: PHOTOPTICS,
TI - Spatiotemporal Complex Geometrical Optics (CGO) of N 3D Interacting Asymmetric Gaussian Wave Packets in Nonlinear Medium - CGO as the Simplest and Efficient Method for Spatiotemporal Evolution
SN - 978-989-758-092-5
AU - Berczynski P.
AU - Marczynski S.
PY - 2015
SP - 53
EP - 60
DO - 10.5220/0005291600530060