Skip to main content
SpringerLink
Log in

Beam propagation in a linear or nonlinear lens-like medium usingABCD ray matrices: the method of moments

  • ABCD Law, Propagation and Higher Order Moments
  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

We derive exact expressions for the evolution of the second order moment of the intensity distribution of an arbitrary beam propagating in a nonlinear Kerr medium with a quadratic index profile. The results can be recast in terms of theABCD matrix formalism after introducing a generalized complex radius of curvature,Q(z). Various definitions of the beam quality factor are introduced. Numerical simulations reveal the interest of this approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. SIMON, N. MUKUNDA and E. C. G. SUDARSHAN,Opt. Commun. 65 (1988) 322.

    Google Scholar 

  2. S. LAVI, R. PROCHASKA and E. KEREN,Appl. Opt. 27 (1988) 3696.

    Google Scholar 

  3. M. J. BASTIAANS,Optik 82 (1989) 173.

    Google Scholar 

  4. F. GORI, M. SANTARSIERO and A. SONA,Opt. Commun. 82, (1991) 197.

    Google Scholar 

  5. A. T. FRIBERG, A. VASARA and J. TURUNEN,Phys. Rev. A43 (1991) 7079.

    Google Scholar 

  6. S. N. VLASOV, V. A. PETRISHCHEV and V. I. TALANOV,Radiophys. Quantum Electron. 14 (1971) 1062.

    Google Scholar 

  7. B. R. SUYDAM,IEEE J. Quantum Electron. QE-11 (1975) 225.

    Google Scholar 

  8. P.-A. BÉLANGER,Opt. Lett. 16 (1991) 196.

    Google Scholar 

  9. G. P. AGRAWAL,Nonlinear Fiber Optics (Academic Press, Boston, Massachusetts, 1989).

    Google Scholar 

  10. S. A. AKHMANOV, R. V. KHOKHLOV and A. P. SUKHORUKOV, inLaser Handbook, edited by F. T. Arecchia and E. O. Schulz-Dubois (North-Holland, Amsterdam, 1972 p. 1151.

    Google Scholar 

  11. A. E. SIEGMAN,IEEE J. Quantum Electron. QE-27 (1991) 1146.

    Google Scholar 

  12. P. A. BÉLANGER,Opt. Commun. 67 (1988) 369.

    Google Scholar 

  13. A. E. SIEGMAN,Proc. Soc. Photo-Opt. Instrum. Engng. 1224 (1990) 2.

    Google Scholar 

  14. J. H. MARBURGER,Prog. Quantum Electron. 4 (1975) 36.

    Google Scholar 

  15. Y. R. SHEN, —ibid. 4 (1975) 1.

    Google Scholar 

  16. A. YARIV,Quantum Electronics, 3rd Edn (Wiley, New York, 1989).

    Google Scholar 

  17. P.-A. BÉLANGER and C. PARÉ,Appl. Opt. 22 (1983) 1293.

    Google Scholar 

  18. A. YARIV and P. YEH,Opt. Commun. 27 (1978) 295.

    Google Scholar 

  19. R. Y. CHIAO, E. GARMIRE and C. H. TOWNES,Phys. Rev. Lett. 13 (1964) 479.

    Google Scholar 

  20. H. A. HAUS,Appl. Phys. Lett. 8 (1966) 128.

    Google Scholar 

  21. D. ANDERSON, M. BONNEDAL and M. LISAK,Phys. Fluids 22 (1979) 1838.

    Google Scholar 

  22. L. GAGNON and C. PARÉ,J. Opt. Soc. Am. A8 (1991) 601.

    Google Scholar 

  23. Y. CHEN,Opt. Commun. 82 (1991) 255.

    Google Scholar 

  24. J. F. LAM, B. LIPPMANN and F. TAPPERT, —ibid. 15 (1975) 419.

    Google Scholar 

  25. J. M. SOTO-CRESPO, D. R. HEATLY, E. M. WRIGHT and N. N. AKHMEDIEV,Phys. Rev. A44 (1991) 636.

    Google Scholar 

  26. M. D. FEIT and J. A. FLECK,J. Opt. Soc. Am. B 5 (1988) 633.

    Google Scholar 

  27. J. T. MANASSAH, P. L. BALDEK and R. R. ALFANO,Opt. Lett. 13 (1988) 589.

    Google Scholar 

  28. M. KARLSSON, D. ANDERSON and M. DESAIX, —ibid. 17 (1992) 22.

    Google Scholar 

  29. C. PARÉ and P.-A. BÉLANGER,IEEE J. Quantum Electron. QE-28 (1992) 355.

    Google Scholar 

  30. L. GAGNON,J. Opt. Soc. Am. B7 (1990) 1098 and references therein.

    Google Scholar 

  31. L. GAGNON and P. WINTERNITZ,Phys. Rev. A39 (1989) 296.

    Google Scholar 

  32. J. A. GIANNINI and R. I. JOSEPH,Phys. Lett. A160 (1991) 363.

    Google Scholar 

  33. V. E. ZAKHAROV and A. B. SHABAT,Soviet Phys. JETP 34 (1972) 62.

    Google Scholar 

  34. R. MARTINEZ-HERRERO and P. M. MEJIAS,Opt. Commun. 85 (1991) 162.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Equipe Laser et Optique Guidée, (COPL) Département de Physique, Université Laval, G1K 7P4, Sainte-Foy, Québec, Canada

    C. Paré & P. -A. Bélanger

Authors
  1. C. Paré
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. -A. Bélanger
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

An Invited Paper

Rights and permissions

Reprints and permissions

About this article

Cite this article

Paré, C., Bélanger, P.A. Beam propagation in a linear or nonlinear lens-like medium usingABCD ray matrices: the method of moments. Opt Quant Electron 24, S1051–S1070 (1992). https://doi.org/10.1007/BF01588605

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01588605

Keywords

Search

Navigation