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:
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.
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:
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.
