Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-25T05:23:12.271Z Has data issue: false hasContentIssue false
  • English
  • Français

Radiation reduction of optical solitons resulting from higher order dispersion terms in the nonlinear Schrödinger equation

Published online by Cambridge University Press:  05 December 2005

ROBERT BEECH  and
FREDERICK OSMAN
ROBERT BEECH
Affiliation:
School of Quantitative Methods & Mathematical Sciences, University of Western Sydney, Penrith South DC, Australia
FREDERICK OSMAN
Affiliation:
School of Quantitative Methods & Mathematical Sciences, University of Western Sydney, Penrith South DC, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper will present the nonlinearity and dispersion effects involved in propagation of optical solitons, which can be understood by using a numerical routine to solve the nonlinear Schrödinger equation (NLSE). Here, Mathematica v5© (Wolfram, 2003) is used to explore in depth several features of optical solitons formation and propagation. These numerical routines were implemented through the use of Mathematica v5© and the results give a very clear idea of this interesting and important practical phenomenon. It is hoped that this work will open up an important new approach to the cause, effect, and correction of interference from secondary radiation found in the uses of soliton waves in lasers and in optical fiber telecommunication. It is believed that these results will be of considerable use in any work or research in this field and in self-focusing properties of the soliton (Osman et al., 2004a, 2004b; Hora, 1991). In a previous paper on this topic (Beech & Osman, 2004), it was shown that solitons of NLSE radiate. This paper goes on from there to show that these radiations only occur in solitons derived from cubic, or odd-numbered higher orders of NLSE, and that there are no such radiations from solitons of quadratic, or even-numbered higher order of NLSE. It is anticipated that this will stimulate research into practical means to control or eliminate such radiations.

Keywords

Higher order dispersionHigher order of NLSENonlinear Schrödinger equation (NLSE)Soliton radiationsSolitons
Type
Workshop on Fast High Density Plasma Blocks Driven By Picosecond Terawatt Lasers
Information
Laser and Particle Beams , Volume 23 , Issue 4 , October 2005 , pp. 483 - 502
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Akhmediev, N.N. & Ankiewicz, A. (1997). Solitons, Nonlinear Pulses And Beams. Canberra: Chapman & Hall.
Beech, R. & Osman, F. (2004). Breaking and Self-Focusing Properties of Korteweg de Vries Solitons. Proc. IMS2004, Banff, Canada.
Drazin, G. & Johnson, R.S. (1990). Solitons: An Introduction. Cambridge: Cambridge University Press.
Hora, H. (2004). Developments in inertial fusion energy and beam fusion at magnetic confinement. Laser Part. Beams 22, 69–74.Google Scholar
Hora, H. (1991). Plasmas at High Temperature and Density. Heidelberg: Springer.
Karpman, V.I. (1998). Evolution of solitons described by higher-order nonlinear Schrödinger equations. Phy. Lett. A 244, 397–400.Google Scholar
Karpman, V.I. & Shagalow, A.G. (1999). Evolution of solitons described by higher-order nonlinear Schrödinger equation. II. Numerical investigation. Phys. Lett. A 254, 319–324.Google Scholar
Osman, F., Castillo, R. & Hora, H. (2000). Focusing and Defocusing of the Nonlinear Paraxial Equation at Laser Plasma Interaction. Laser Part. Beams 18, 73.Google Scholar
Osman, F., Cang, Yu., Hora, H., Evans, P., Cao, L.H., Liu, H., He, X.T., Badziak, J., Parys, A.B., Wolowski, J., Woryna, E., Jungwirth, K., Kraliova, B., Kraska, J., Laska, L., Pfeifer, M., Rohlena, K., Skala, J. & Ullschmied, J. (2004a). Two-Fluid Computations to Skin Layer Acceleration. Laser Part. Beams 22, 83–88.Google Scholar
Osman, F., Beech, R. & Hora, H. (2004b). Solutions of the nonlinear paraxial equation due to laser-plasma interactions. Laser Part. Beams 22, 69–74.Google Scholar
Wolfram, S. (2003). The Mathematica Book. Champaign, IL: Wolfram Media.
Zakharov, V.E. & Shabat, A.B. (1972). Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62.Google Scholar