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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. SIMON, N. MUKUNDA and E. C. G. SUDARSHAN,Opt. Commun. 65 (1988) 322.
S. LAVI, R. PROCHASKA and E. KEREN,Appl. Opt. 27 (1988) 3696.
M. J. BASTIAANS,Optik 82 (1989) 173.
F. GORI, M. SANTARSIERO and A. SONA,Opt. Commun. 82, (1991) 197.
A. T. FRIBERG, A. VASARA and J. TURUNEN,Phys. Rev. A43 (1991) 7079.
S. N. VLASOV, V. A. PETRISHCHEV and V. I. TALANOV,Radiophys. Quantum Electron. 14 (1971) 1062.
B. R. SUYDAM,IEEE J. Quantum Electron. QE-11 (1975) 225.
P.-A. BÉLANGER,Opt. Lett. 16 (1991) 196.
G. P. AGRAWAL,Nonlinear Fiber Optics (Academic Press, Boston, Massachusetts, 1989).
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.
A. E. SIEGMAN,IEEE J. Quantum Electron. QE-27 (1991) 1146.
P. A. BÉLANGER,Opt. Commun. 67 (1988) 369.
A. E. SIEGMAN,Proc. Soc. Photo-Opt. Instrum. Engng. 1224 (1990) 2.
J. H. MARBURGER,Prog. Quantum Electron. 4 (1975) 36.
Y. R. SHEN, —ibid. 4 (1975) 1.
A. YARIV,Quantum Electronics, 3rd Edn (Wiley, New York, 1989).
P.-A. BÉLANGER and C. PARÉ,Appl. Opt. 22 (1983) 1293.
A. YARIV and P. YEH,Opt. Commun. 27 (1978) 295.
R. Y. CHIAO, E. GARMIRE and C. H. TOWNES,Phys. Rev. Lett. 13 (1964) 479.
H. A. HAUS,Appl. Phys. Lett. 8 (1966) 128.
D. ANDERSON, M. BONNEDAL and M. LISAK,Phys. Fluids 22 (1979) 1838.
L. GAGNON and C. PARÉ,J. Opt. Soc. Am. A8 (1991) 601.
Y. CHEN,Opt. Commun. 82 (1991) 255.
J. F. LAM, B. LIPPMANN and F. TAPPERT, —ibid. 15 (1975) 419.
J. M. SOTO-CRESPO, D. R. HEATLY, E. M. WRIGHT and N. N. AKHMEDIEV,Phys. Rev. A44 (1991) 636.
M. D. FEIT and J. A. FLECK,J. Opt. Soc. Am. B 5 (1988) 633.
J. T. MANASSAH, P. L. BALDEK and R. R. ALFANO,Opt. Lett. 13 (1988) 589.
M. KARLSSON, D. ANDERSON and M. DESAIX, —ibid. 17 (1992) 22.
C. PARÉ and P.-A. BÉLANGER,IEEE J. Quantum Electron. QE-28 (1992) 355.
L. GAGNON,J. Opt. Soc. Am. B7 (1990) 1098 and references therein.
L. GAGNON and P. WINTERNITZ,Phys. Rev. A39 (1989) 296.
J. A. GIANNINI and R. I. JOSEPH,Phys. Lett. A160 (1991) 363.
V. E. ZAKHAROV and A. B. SHABAT,Soviet Phys. JETP 34 (1972) 62.
R. MARTINEZ-HERRERO and P. M. MEJIAS,Opt. Commun. 85 (1991) 162.
Author information
Authors and Affiliations
Additional information
An Invited Paper
Rights 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
Issue Date:
DOI: https://doi.org/10.1007/BF01588605