Abstract

We discuss a numerical method based on Lanczos reduction of modeling nonparaxial propagation of a cylindrical symmetric beam. To illustrate the performance and demonstrate the significant difference between nonparaxial and paraxial beams, we consider Gaussian beam propagation in two different settings.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]

1994 (2)

1992 (2)

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

B. Hermansson, D. Yevick, W. Bardyszewski, and M. Glasner, J. Lightwave Technol. 10, 772 (1992).
[CrossRef]

1991 (1)

1989 (1)

1986 (1)

T. Park and J. Light, J. Chem. Phys. 85, 5870 (1986); V. Druskin and L. Knizhnerman, Radio Sci. 29, 937 (1994).
[CrossRef]

1979 (1)

1972 (1)

1970 (1)

V. I. Talanov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 11, 199 (1970) [JETP Lett. 11, 303 (1970)].

Bardyszewski, W.

B. Hermansson, D. Yevick, W. Bardyszewski, and M. Glasner, J. Lightwave Technol. 10, 772 (1992).
[CrossRef]

Carter, W. H.

Feit, M. D.

Fleck, J. A.

Glasner, M.

B. Hermansson, D. Yevick, W. Bardyszewski, and M. Glasner, J. Lightwave Technol. 10, 772 (1992).
[CrossRef]

Hermansson, B.

B. Hermansson, D. Yevick, W. Bardyszewski, and M. Glasner, J. Lightwave Technol. 10, 772 (1992).
[CrossRef]

Law, C. T.

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

Light, J.

T. Park and J. Light, J. Chem. Phys. 85, 5870 (1986); V. Druskin and L. Knizhnerman, Radio Sci. 29, 937 (1994).
[CrossRef]

Park, T.

T. Park and J. Light, J. Chem. Phys. 85, 5870 (1986); V. Druskin and L. Knizhnerman, Radio Sci. 29, 937 (1994).
[CrossRef]

Ratowsky, R. P.

Sehmi, N. S.

N. S. Sehmi, Large Order Structural Eigenanalysis for Finite Element Systems (Halsted, New York, 1989), pp. 48–69.

Swartzlander, G. A.

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

Talanov, V. I.

V. I. Talanov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 11, 199 (1970) [JETP Lett. 11, 303 (1970)].

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1996), pp. 46–57.

Yevick, D.

D. Yevick, Opt. Quantum Electron. 26, S185 (1994).
[CrossRef]

B. Hermansson, D. Yevick, W. Bardyszewski, and M. Glasner, J. Lightwave Technol. 10, 772 (1992).
[CrossRef]

Appl. Opt. (1)

J. Chem. Phys. (1)

T. Park and J. Light, J. Chem. Phys. 85, 5870 (1986); V. Druskin and L. Knizhnerman, Radio Sci. 29, 937 (1994).
[CrossRef]

J. Lightwave Technol. (1)

B. Hermansson, D. Yevick, W. Bardyszewski, and M. Glasner, J. Lightwave Technol. 10, 772 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

D. Yevick, Opt. Quantum Electron. 26, S185 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef]

Zh. Eksp. Teor. Fiz. Pis’ma Red. (1)

V. I. Talanov, Zh. Eksp. Teor. Fiz. Pis’ma Red. 11, 199 (1970) [JETP Lett. 11, 303 (1970)].

Other (2)

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, New York, 1996), pp. 46–57.

N. S. Sehmi, Large Order Structural Eigenanalysis for Finite Element Systems (Halsted, New York, 1989), pp. 48–69.

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Figures (3)

Fig. 1
Fig. 1

Normalized peak intensity of a Gaussian beam in a gradient-index fiber versus normalized propagation distance Z. Inset, profiles (both original size and 4× original) at Z=0.25 (near the focus) for paraxial (analytical) and nonparaxial calculations.

Fig. 2
Fig. 2

Relative error ϵZ of paraxial and nonparaxial calculations versus half divergence angle θ1/2 for Gaussian beams of various sizes propagating in free space for Z=0.1.

Fig. 3
Fig. 3

Relative error ϵZ versus half divergence angle θ1/2 under the same conditions as for Fig. 2, except that Z=5.

Equations (9)

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

-12kw022ψZ2+iψZ=Hψ.
iψZ=Hψ,
ψR,ZψR,Z=p=-N/2+1N/2cpZexp-iβpZexp-iβpZupR,
ψ¯Z+ΔZ=exp-H̲ΔZψ¯Z.
βp=-4z0k1-1+βp/2z0k1/2.
limR0 1RψR=2ψR2R=0.
ψeR,Z=12f20exp-q2/4f2×exp-i2pZ/f2J0qR/fqdq,
p=1-q21/2q21-iq2-11/2q2>1.
ϵZ=0LϕψR,Z-ψeR,Z2dR0LϕψeR,Z2dR,

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