Abstract

We present results from a novel variational method for the study of beam propagation in a Kerr medium with nonlinear absorption. This new method combines the variational method and a nonlinear absorption equation and gives a concise expression for the combination. The results obtained with this method show good quantitative agreement with numerical solutions obtained with the finite-difference method. It is shown that the variational method takes much less time than a numerical simulation with the finite-difference method for analysis of beam propagation in a thick medium with nonlinear absorption and nonlinear refraction. The new method makes detailed analysis of beam propagation in a Kerr medium with nonlinear absorption very simple and fast.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2001 (1)

D. Anderson, M. Lisak, and A. Berntson, Pramana J. Phys. 57, 917 (2001).
[CrossRef]

1998 (1)

S. C. Cerda, S. B. Cavalcanti, and J. M. Hickmann, Eur. J. Phys. D 1, 313 (1998).
[CrossRef]

1997 (1)

1993 (1)

1992 (1)

1991 (2)

M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. A 8, 2082 (1991).

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1989 (1)

1983 (2)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

D. Anderson, Opt. Commun. 48, 107 (1983).
[CrossRef]

Anderson, D.

D. Anderson, M. Lisak, and A. Berntson, Pramana J. Phys. 57, 917 (2001).
[CrossRef]

M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. A 8, 2082 (1991).

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

D. Anderson, Opt. Commun. 48, 107 (1983).
[CrossRef]

Berntson, A.

D. Anderson, M. Lisak, and A. Berntson, Pramana J. Phys. 57, 917 (2001).
[CrossRef]

Cavalcanti, S. B.

S. C. Cerda, S. B. Cavalcanti, and J. M. Hickmann, Eur. J. Phys. D 1, 313 (1998).
[CrossRef]

Cerda, S. C.

S. C. Cerda, S. B. Cavalcanti, and J. M. Hickmann, Eur. J. Phys. D 1, 313 (1998).
[CrossRef]

Desaix, M.

M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. A 8, 2082 (1991).

Gross, B.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Hermann, J. A.

Hickmann, J. M.

S. C. Cerda, S. B. Cavalcanti, and J. M. Hickmann, Eur. J. Phys. D 1, 313 (1998).
[CrossRef]

Lisak, M.

D. Anderson, M. Lisak, and A. Berntson, Pramana J. Phys. 57, 917 (2001).
[CrossRef]

M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. A 8, 2082 (1991).

Manassah, J. T.

McDuff, R. G.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, Opt. Lett. 14, 955 (1989).
[CrossRef] [PubMed]

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Eur. J. Phys. D (1)

S. C. Cerda, S. B. Cavalcanti, and J. M. Hickmann, Eur. J. Phys. D 1, 313 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Opt. Soc. Am. A (1)

M. Desaix, D. Anderson, and M. Lisak, J. Opt. Soc. Am. A 8, 2082 (1991).

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

D. Anderson, Opt. Commun. 48, 107 (1983).
[CrossRef]

Opt. Eng. (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Pramana J. Phys. (1)

D. Anderson, M. Lisak, and A. Berntson, Pramana J. Phys. 57, 917 (2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Open-aperture Z-scan curves for different medium lengths, scaled by Rayleigh length. Curves a; l=1; curves b, l=2; curves c, l=4. Solid curves, results of the variational method; dotted curves, results of the numerical simulation.

Fig. 2
Fig. 2

Open-aperture Z-scan curves for different values of the nonlinear refractive index, scaled by ZnSe’s refractive-index value. Curves a, n2=-1; curves b, n2=0; curves c, n2=1. Solid and dashed curves are as defined in Fig. 1.

Fig. 3
Fig. 3

Open-aperture Z-scan curves for different two-photon absorption coefficients, scaled by ZnSe’s value. Curves a, α2=1/2; curves b, α2=1; curves c, α2=2. Solid and dashed curves are as defined in Fig. 1.

Fig. 4
Fig. 4

Computational times taken by the two methods for different medium lengths. The medium length is scaled by Rayleigh length z0, and the time is in seconds. The parameters used are the same as those of ZnSe. Inset, computation time as a function of the number of computation steps in the r direction, where L=10z0; the other parameters are the same as those of ZnSe’s.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

1rrrEr-2ikEz+2n2k2n0E2E=0,
L=rEr2-ikrEE*z-E*Ez-n2k2n0rE4,
Er,z=Azexp-r22a2z+ibzr2,
δ0-Ldrdz=0.
ddza2A2=0, a2A2=a02A02,
b=-k2adadz,
d2adz2-1k2a31-n2a2A2k22n0=0.
1rrrEr-2ikEz-iki=1nαiE2i-1E+2n2k2n0E2E=0,
dE2/dz=-i=1nαiE2i.
da2A2dz=-a2i=1nA2ii.

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