Abstract

It is shown that the propagation of a temporal pulse in a single-mode optical fiber is mathematically equivalent to Fresnel diffraction of a spatial beam. A time-domain Collett–Wolf equivalence theorem applies to pulse propagation in fibers.

© 1982 Optical Society of America

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References

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  1. E. Collett, E. Wolf, “Is complete spatial coherence necessary for the generation of highly directional light beams?” Opt. Lett. 2, 27–29 (1978).
    [CrossRef] [PubMed]
  2. See, e.g., J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  3. This is obtained by taking the inverse Fourier transform of the transfer function H(ω) reported in Refs. 4 and 5.
  4. F. P. Kapron, D. B. Keck, “Pulse transmission through a dielectric optical waveguide,” Appl. Opt. 10, 1519–1523 (1971).
    [CrossRef] [PubMed]
  5. D. Marcuse, “Pulse distortion in single-mode fibers,” Appl. Opt. 19, 1653–1660 (1980).
    [CrossRef] [PubMed]
  6. B. E. A. Saleh, “Intensity distribution due to a partially coherent field and the Collett–Wolf equivalence theorem in the Fresnel zone,” Opt. Commun. 30, 135–138 (1979).
    [CrossRef]
  7. See, e.g., A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1976), Chap. 3.
  8. C. Lin, H. Kogelnik, L. G. Cohen, “Optical pulse equalization and low dispersion transmission in single-mode fibers in 1.3–1.7-μm spectral region,” Opt. Lett. 5, 476–478 (1980).
    [CrossRef] [PubMed]

1980 (2)

1979 (1)

B. E. A. Saleh, “Intensity distribution due to a partially coherent field and the Collett–Wolf equivalence theorem in the Fresnel zone,” Opt. Commun. 30, 135–138 (1979).
[CrossRef]

1978 (1)

1971 (1)

Cohen, L. G.

Collett, E.

Goodman, J. W.

See, e.g., J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Kapron, F. P.

Keck, D. B.

Kogelnik, H.

Lin, C.

Marcuse, D.

Saleh, B. E. A.

B. E. A. Saleh, “Intensity distribution due to a partially coherent field and the Collett–Wolf equivalence theorem in the Fresnel zone,” Opt. Commun. 30, 135–138 (1979).
[CrossRef]

Wolf, E.

Yariv, A.

See, e.g., A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1976), Chap. 3.

Appl. Opt. (2)

Opt. Commun. (1)

B. E. A. Saleh, “Intensity distribution due to a partially coherent field and the Collett–Wolf equivalence theorem in the Fresnel zone,” Opt. Commun. 30, 135–138 (1979).
[CrossRef]

Opt. Lett. (2)

Other (3)

See, e.g., A. Yariv, Introduction to Optical Electronics (Holt, Rinehart and Winston, New York, 1976), Chap. 3.

See, e.g., J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

This is obtained by taking the inverse Fourier transform of the transfer function H(ω) reported in Refs. 4 and 5.

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Equations (10)

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h ( r ) exp ( j π λ z r 2 ) .
h ( t ) exp ( j 1 2 β ¨ z t 2 ) ,
I 0 ( r ) = U i * ( r 1 ) U i ( r 2 ) γ ( r 1 r 2 ) × h * ( r r 1 ) h ( r r 2 ) d r 1 d r 2 ,
U i ( r ) exp ( r 2 / 4 σ s 2 ) , γ ( r ) exp ( r 2 / 2 σ c 2 ) ,
I 0 ( r ) exp [ r 2 / 2 σ 2 ( z ) ]
σ 2 ( z ) = σ s 2 + ( λ 2 π ) 2 ( 1 σ s 2 + 1 σ c 2 ) z 2 .
I 0 ( t ) = U i * ( t 1 ) U i ( t 2 ) γ ( t 1 t 2 ) × h * ( t t 1 ) h ( t t 2 ) d t 1 d t 2 ,
U i ( t ) exp ( t 2 / 4 σ s 2 ) , γ ( t ) exp ( t 2 / 2 σ c 2 ) ,
I 0 ( t ) exp [ t 2 / 2 σ 2 ( z ) ]
σ 2 ( z ) = σ s 2 + ( β ¨ ) 2 ( 1 σ s 2 + 1 σ c 2 ) z 2 .

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