Abstract

The wavelengths of minimum dispersion in step-index monomode fibers are evaluated quite rigorously. These results are compared with those obtained when certain approximations used by several authors are introduced into the course of the calculation. Furthermore, a comparison is made between the wavelengths of minimum dispersion obtained when dispersive data measured by different authors are used for the evaluation.

© 1983 Optical Society of America

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References

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  1. W. L. Mammel, L. G. Cohen, Appl. Opt. 21, 699 (1982).
    [CrossRef] [PubMed]
  2. K. Jurgensen, Appl. Opt. 17, 2412 (1978).
    [CrossRef] [PubMed]
  3. H.-G. Unger, AEU Arch. Electron. Übertragungstech. Electron. Commun. 31, 518 (1977).
  4. M. Miyagi, S. Nishida, Appl. Opt. 18, 678 (1979).
    [CrossRef] [PubMed]
  5. D. Gloge, Appl. Opt. 10, 2442 (1971).
    [CrossRef] [PubMed]
  6. K. Jurgensen, Appl. Opt. 18, 1259 (1979).
    [CrossRef] [PubMed]
  7. K. I. White, B. P. Nelson, Electron. Lett. 15, 396 (1979).
    [CrossRef]
  8. C. T. Chang, Appl. Opt. 18, 2516 (1979).
    [CrossRef] [PubMed]
  9. H.-D. Rudolph, E.-G. Neumann, Nachrichtentech. Z. 29, 328 (1976).
  10. S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, in Technical Digest, First International Conference on Integrated Optics and Optical Fiber Communications (IECE, Tokyo, 1977).
  11. J. W. Fleming, Electron. Lett. 14, 326 (1978).
    [CrossRef]
  12. N. Shibata, S. Shibata, T. Edahiro, Electron. Lett. 17, 311 (1981).
  13. D. N. Payne, A. H. Hartog, Electron. Lett. 13, 627 (1977).
    [CrossRef]

1982 (1)

1981 (1)

N. Shibata, S. Shibata, T. Edahiro, Electron. Lett. 17, 311 (1981).

1979 (4)

1978 (2)

K. Jurgensen, Appl. Opt. 17, 2412 (1978).
[CrossRef] [PubMed]

J. W. Fleming, Electron. Lett. 14, 326 (1978).
[CrossRef]

1977 (2)

D. N. Payne, A. H. Hartog, Electron. Lett. 13, 627 (1977).
[CrossRef]

H.-G. Unger, AEU Arch. Electron. Übertragungstech. Electron. Commun. 31, 518 (1977).

1976 (1)

H.-D. Rudolph, E.-G. Neumann, Nachrichtentech. Z. 29, 328 (1976).

1971 (1)

Chang, C. T.

Cohen, L. G.

Edahiro, T.

N. Shibata, S. Shibata, T. Edahiro, Electron. Lett. 17, 311 (1981).

Fleming, J. W.

J. W. Fleming, Electron. Lett. 14, 326 (1978).
[CrossRef]

Gloge, D.

Hartog, A. H.

D. N. Payne, A. H. Hartog, Electron. Lett. 13, 627 (1977).
[CrossRef]

Izawa, T.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, in Technical Digest, First International Conference on Integrated Optics and Optical Fiber Communications (IECE, Tokyo, 1977).

Jurgensen, K.

Kobayashi, S.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, in Technical Digest, First International Conference on Integrated Optics and Optical Fiber Communications (IECE, Tokyo, 1977).

Mammel, W. L.

Miyagi, M.

Nelson, B. P.

K. I. White, B. P. Nelson, Electron. Lett. 15, 396 (1979).
[CrossRef]

Neumann, E.-G.

H.-D. Rudolph, E.-G. Neumann, Nachrichtentech. Z. 29, 328 (1976).

Nishida, S.

Payne, D. N.

D. N. Payne, A. H. Hartog, Electron. Lett. 13, 627 (1977).
[CrossRef]

Rudolph, H.-D.

H.-D. Rudolph, E.-G. Neumann, Nachrichtentech. Z. 29, 328 (1976).

Shibata, N.

N. Shibata, S. Shibata, T. Edahiro, Electron. Lett. 17, 311 (1981).

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, in Technical Digest, First International Conference on Integrated Optics and Optical Fiber Communications (IECE, Tokyo, 1977).

Shibata, S.

N. Shibata, S. Shibata, T. Edahiro, Electron. Lett. 17, 311 (1981).

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, in Technical Digest, First International Conference on Integrated Optics and Optical Fiber Communications (IECE, Tokyo, 1977).

Unger, H.-G.

H.-G. Unger, AEU Arch. Electron. Übertragungstech. Electron. Commun. 31, 518 (1977).

White, K. I.

K. I. White, B. P. Nelson, Electron. Lett. 15, 396 (1979).
[CrossRef]

AEU Arch. Electron. Übertragungstech. Electron. Commun. (1)

H.-G. Unger, AEU Arch. Electron. Übertragungstech. Electron. Commun. 31, 518 (1977).

Appl. Opt. (6)

Electron. Lett. (4)

J. W. Fleming, Electron. Lett. 14, 326 (1978).
[CrossRef]

N. Shibata, S. Shibata, T. Edahiro, Electron. Lett. 17, 311 (1981).

D. N. Payne, A. H. Hartog, Electron. Lett. 13, 627 (1977).
[CrossRef]

K. I. White, B. P. Nelson, Electron. Lett. 15, 396 (1979).
[CrossRef]

Nachrichtentech. Z. (1)

H.-D. Rudolph, E.-G. Neumann, Nachrichtentech. Z. 29, 328 (1976).

Other (1)

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, in Technical Digest, First International Conference on Integrated Optics and Optical Fiber Communications (IECE, Tokyo, 1977).

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Figures (6)

Fig. 1
Fig. 1

Wavelength of minimum dispersion vs GeO2 concentration in the core.

Fig. 2
Fig. 2

Wavelength of minimum dispersion vs V. C = GeO2 concentration in the core.

Fig. 3
Fig. 3

GeO2 concentration in the core C and core diameter 2a for fibers with minimum dispersion at λ ̂ = 1.3 μ m.

Fig. 4
Fig. 4

GeO2 concentration in the core C and core diameter 2a for fibers with minimum dispersion at λ ̂ = 1.55 μ m.

Fig. 5
Fig. 5

Accuracy of wavelength of minimum dispersion obtained with different approximations: A, approximation of Rudolph and Neumann,9 Eq. (13), vertical bars denote range of validity of this approximation; B, approximation of the eigenvalue equation, Eq. (14); C, approximation of Eq. (11). GeO2 concentration in the core is 7.9 mole %.

Fig. 6
Fig. 6

Wavelength of minimum dispersion obtained with refractive-index data measured by different authors: a, Kobayashi,10C = 7.9 mole % GeO2 in the core; b, Fleming,11 interpolated to 7.9 mole %; c, Shimata,12 interpolated to 7.9 mole %.

Equations (21)

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n = c / υ ,
n ( λ ) = n λ 0 + n λ 0 ( λ λ 0 ) + ½ n λ 0 ( λ λ 0 ) 2 + n λ 0 ( λ λ 0 ) 3 + ,
2 τ = ( 2 a ) 2 + ( 2 τ s ) 2 ,
n = β / k = [ n 2 2 + b ( n 1 2 n 2 2 ) ] 1 / 2 ,
b = w 2 / V 2 ,
w = a ( β 2 k 2 n 2 2 ) 1 / 2 ,
u = a ( k 2 n 1 2 β 2 ) 1 / 2 ,
V = ( u 2 + w 2 ) 1 / 2 = a k ( n 1 2 n 2 2 ) 1 / 2 ,
J 0 u J 1 = 1 u 2 + 1 2 ( 1 + n 2 2 n 1 2 ) ( K 0 w K 1 + 1 w 2 ) ( + ) [ 1 4 ( 1 n 2 2 n 1 2 ) 2 ( K 0 w K 1 + 1 w 2 ) 2 + ( 1 u 2 + 1 w 2 ) 2 ( 1 n 2 2 n 1 2 ) u 2 + w 2 u 2 w 4 ] 1 / 2 ,
( n ) λ ̂ = 0 ,
n n 2 + b ( n 1 n 2 ) n 1 ( 1 b ) ( n 1 n 2 )
w 1.1428 V 0.9960
b 1.3060 2.2765 / V + 0.9920 / V 2 .
J 0 u J 1 K 0 w K 1
n = ( n 2 ) / 2 n ( n 2 ) 12 / 4 n 3 .
n = ( n 2 2 + b δ ) 1 / 2 ;
( n 2 ) = 2 n 2 n 2 + b δ + b δ ;
( n 2 ) = 2 n 2 n 2 2 + 2 n 2 n 2 + b δ + 2 b δ + b δ ;
n i 2 1 = m = 1 3 a i , m λ 2 λ 2 b i , m .
δ A ( λ ) C ,
( n 1 n 2 ) / n 1 5 = B ( λ ) C ,

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