• NEWS
  • CURRENT ISSUE
  • CONTACT
GET_pdf delibra

Volume 14 (1) 2008, 13-19

Propagation Technique for Ultrashort Pulses II: Numerical Methods to Solve the Pulse Propagation Equation

Cao Long V. 1, Hung Nguyen Viet 2, Trippenbach Marek 3, Khoa Dinh Xuan 4

1Institute of Physics, University of Zielona Góra
Podgórna 50, 65-246 Zielona Góra, Poland
e-mail: V.CaoLong@if.uz.zgora.pl
2Soltan Institute for Nuclear Studies
Hoża 69, 00-681 Warsaw, Poland
e-mail: hungvn@fuw.edu.pl
3Department of Physics, Warsaw University
Hoża 69, 00-681 Warsaw, Poland
e-mail: matri@fuw.edu.pl
4Vinh University, Nghe An, Vietnam
e-mail: khoadhv@yahoo.co

Received:

Recived: 16 November 2007; revised: 12 May 2008; published online: 18 June 2008

DOI:   10.12921/cmst.2008.14.01.13-19

OAI:   oai:lib.psnc.pl:641

Abstract:

We presented the numerical technique to approximately solve the pulse propagation equation. Two efficient methods for this problem, the Split-Step Fourier and the fourth order Runge-Kutta methods are considered. Their high accuracy are shown by comparison with analytical solutions in some particular situations. Our numerical experiments are implemented for soliton propagation and interacting high order solitons. We also numerically investigate an important technique to create ultrashort pulses, which is known as the pulse compression. It is based on high order soliton propagation in Kerr media when the effect of stimulated Raman scattering is taken into account.

Key words:

Kerr medium, propagation, ultrashort pulse

References:

[1] G. P. Agrawal, Nonlinear Fiber Optics, Academic, San Diego, 2003.
[2] Cao Long Van, Dinh Xuan Khoa and Marek Trippenbach, Introduction to Nonlinear Optics, Vinh 2003.
[3] U. Bandelow, A. Demircan and M. Kesting, Simulation of Pulse Propagation in Nonlinear Optical Fibers, WIAS, 2003.
[4] Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals, Academic Press, San Diego, 2003.
[5] Cao Long Van, Nguyen Viet Hung, Marek Trippenbach and Dinh Xuan Khoa, Propagation technique for ultrashort pulses I.
[6] P. L. Francois, J. Opt. Soc. Am. B8, 276-293 (1991).
[7] G. M. Muslu and H. A. Erbay, Mathematics and Computers in Simulation 67, 581-595 (2005).
[8] M. S. Ozyaici, J. Optoelectronics and Advanced Materials 6, 71-76 (2004).
[9] G. P. Agrawal, Opt. Lett. 15, 224-226 (1990).
[10] G. H. Shiraz, P. Shum and N. Nagata, IEEE J. Quantum Electron. 31, 190- 200 (1995).
[11] W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in Fortran 77 – The Art of Scientific Computing, Cambridge University Press, 1992.
[12] J. D. Hoffman, Numerical Methods for Engineers and Scientists, Marcel Dekker, 2001.
[13] L. Debnath, Nonlinear partial differential equations for scietists and engineers, Birkhauser, 1997.
[14] T. Hohage and F. Schmidt, On the Numerical Solution of Nonlinear Schrödinger Type Equations in Fiber Optics, Berlin, 2002.
[15] Cao Long Van, Marek Trippenbach, Dinh Xuan Khoa, Nguyen Viet Hung and Phan Xuan Anh, Conference on Theoretical Physics, Sam Son, Vietnam, 12-14 August 2003; Journal of Science, Vinh University 1A, 50 (2003).
[16] R. S. Tasgal, Y. B. Band, private communication, 2003.
[17] M. Gedalin, T. C. Scott and Y. B. Band, Phys. Rev. Lett. 78, 448-451 (1997).
[18] A. L. Maimistov and A. M. Basharov, Nonlinear optical waves, Kluwer Academic, 1999.
[19] Cao Long Van, Nguyen Viet Hung, Marek Trippenbach, Dinh Xuan Khoa, Propagation technique for ultrashort pulses III.

  • JOURNAL MENU

    • AIMS AND SCOPE
    • EDITORS
    • EDITORIAL BOARD
    • NOTES FOR AUTHORS
    • CONTACT
    • IAN SNOOK PRIZES 2015
    • IAN SNOOK PRIZES 2016
    • IAN SNOOK PRIZES 2017
  • GALLERY

    vol_19_04_2013
    vol_19_03_2013
    volume_19_2_2013
    volume_19_1_2013
    vol_sp_2_2010
    vol_sp_2006
    vol_sp_1_2010
    vol_16_01_2010
    vol_18_2_2012
    vol_18_01_2012
    vol_17_01_02_2011
    vol_16_02_2010
    vol_15_02_2009
    vol_15_01_2009
    vol_14_02_2008
    vol_14_01_2008
    vol_13_02_2007
    vol_13_01_2007
    vol_12_02_2006
    vol_12_01_2006
    vol_11_02_2005
    vol_11_01_2005
  • CURRENT ISSUE

  • MANUSCRIPT SUBMISSION

    • SUBMIT A MANUSCRIPT
  • FUTURE ISSUES

    • ACCEPTED PAPERS
  • ALL ISSUES

    • 2018
      • Volume 24 (4)
      • Volume 24 (3)
      • Volume 24 (2)
      • Volume 24 (1)
    • 2017
      • Volume 23 (4)
      • Volume 23 (3)
      • Volume 23 (2)
      • Volume 23 (1)
    • 2016
      • Volume 22 (4)
      • Volume 22 (3)
      • Volume 22 (2)
      • Volume 22 (1)
    • 2015
      • Volume 21 (4)
      • Volume 21 (3)
      • Volume 21 (2)
      • Volume 21 (1)
    • 2014
      • Volume 20 (4)
      • Volume 20 (3)
      • Volume 20 (2)
      • Volume 20 (1)
    • 2013
      • Volume 19 (4)
      • Volume 19 (3)
      • Volume 19 (2)
      • Volume 19 (1)
    • 2012
      • Volume 18 (2)
      • Volume 18 (1)
    • 2011
      • Volume 17 (1-2)
    • 2010
      • Volume SI (2)
      • Volume SI (1)
      • Volume 16 (2)
      • Volume 16 (1)
    • 2009
      • Volume 15 (2)
      • Volume 15 (1)
    • 2008
      • Volume 14 (2)
      • Volume 14 (1)
    • 2007
      • Volume 13 (2)
      • Volume 13 (1)
    • 2006
      • Volume SI (1)
      • Volume 12 (2)
      • Volume 12 (1)
    • 2005
      • Volume 11 (2)
      • Volume 11 (1)
    • 2004
      • Volume 10 (2)
      • Volume 10 (1)
    • 2003
      • Volume 9 (1)
    • 2002
      • Volume 8 (2)
      • Volume 8 (1)
    • 2001
      • Volume 7 (2)
      • Volume 7 (1)
    • 2000
      • Volume 6 (1)
    • 1999
      • Volume 5 (1)
    • 1998
      • Volume 4 (1)
    • 1997
      • Volume 3 (1)
    • 1996
      • Volume 2 (1)
      • Volume 1 (1)
    • OLDER ISSUES
  • DATABASES

    • ARTICLES BASE
    • AUTHORS BASE
  • NEWS
  • CURRENT ISSUE
  • CONTACT

Institute of Bioorganic Chemistry Polish Academy of Sciences
Poznań Supercomputing and Networking Center

61-704 Poznań, Z. Noskowskiego 12/14
phone: (+48 61) 858-20-03
fax: (+48 61) 858-21-51