Abstract

Exact numerical solutions for the LP01 propagating mode of the scalar wave equation are used to calculate propagation constants in single-mode fibers with arbitrary refractive-index profiles. The procedure is used to correlate predicted chromatic dispersion properties of single-mode fibers based on interferometrically measured profiles with direct transmission measurements vs wavelength. Resulting waveguide dispersion effects are used to design single-mode fibers that have minimum chromatic dispersion at desired wavelengths within the 1.3–1.6-μm region.

© 1980 Optical Society of America

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  1. T. Miya, Y. Terunuma, T. Hosaka, T. Miyashita, Electron. Lett. 15, 106 (1979).
    [CrossRef]
  2. L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
    [CrossRef] [PubMed]
  3. C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978).
    [CrossRef]
  4. D. N. Payne, A. H. Hartog, Electron. Lett. 13, 627 (1977).
    [CrossRef]
  5. L. G. Cohen, C. Lin, W. G. French, Electron. Lett. 15, 334 (1979).
    [CrossRef]
  6. K. Okamoto, T. Okoshi, IEEE Trans. Microwave Theory Tech. 24, 416 (1976).
    [CrossRef]
  7. J. W. Fleming, Electron. Lett. 14, 326 (1978).
    [CrossRef]
  8. L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
    [CrossRef]
  9. G. W. Tasker, W. G. French, J. R. Simpson, P. Kaiser, H. M. Presby, Appl. Opt. 17, 1836 (1978).
    [CrossRef] [PubMed]
  10. H. M. Presby, D. Marcuse, H. W. Astle, Appl. Opt. 17, 2209 (1978).
    [CrossRef] [PubMed]
  11. S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, “Refractive-Index Dispersion of Doped Fused Silica,” Technical Digest, IEEE Japan International Conference on Integrated Optics and Optical Fiber Communication (1977), pp. 309–312, Tokyo, Japan.
  12. H. M. Presby, I. P. Kaminow, Appl. Opt. 15, 3029 (1976).
    [CrossRef] [PubMed]
  13. D. Gloge, Appl. Opt. 10, 2442 (1971).
    [CrossRef] [PubMed]
  14. D. Gloge, IEEE Trans. Microwave Theory Tech. 23, 106 (1975).
    [CrossRef]
  15. D. Marcuse, Appl. Opt. 18, 2930 (1979).
    [CrossRef] [PubMed]

1979 (3)

T. Miya, Y. Terunuma, T. Hosaka, T. Miyashita, Electron. Lett. 15, 106 (1979).
[CrossRef]

L. G. Cohen, C. Lin, W. G. French, Electron. Lett. 15, 334 (1979).
[CrossRef]

D. Marcuse, Appl. Opt. 18, 2930 (1979).
[CrossRef] [PubMed]

1978 (5)

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978).
[CrossRef]

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

L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
[CrossRef]

G. W. Tasker, W. G. French, J. R. Simpson, P. Kaiser, H. M. Presby, Appl. Opt. 17, 1836 (1978).
[CrossRef] [PubMed]

H. M. Presby, D. Marcuse, H. W. Astle, Appl. Opt. 17, 2209 (1978).
[CrossRef] [PubMed]

1977 (2)

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

L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

1976 (2)

H. M. Presby, I. P. Kaminow, Appl. Opt. 15, 3029 (1976).
[CrossRef] [PubMed]

K. Okamoto, T. Okoshi, IEEE Trans. Microwave Theory Tech. 24, 416 (1976).
[CrossRef]

1975 (1)

D. Gloge, IEEE Trans. Microwave Theory Tech. 23, 106 (1975).
[CrossRef]

1971 (1)

Astle, H. W.

Cohen, L. G.

L. G. Cohen, C. Lin, W. G. French, Electron. Lett. 15, 334 (1979).
[CrossRef]

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978).
[CrossRef]

L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
[CrossRef]

L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

Fleming, J. W.

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

Foertmeyer, V. A.

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978).
[CrossRef]

French, W. G.

L. G. Cohen, C. Lin, W. G. French, Electron. Lett. 15, 334 (1979).
[CrossRef]

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978).
[CrossRef]

G. W. Tasker, W. G. French, J. R. Simpson, P. Kaiser, H. M. Presby, Appl. Opt. 17, 1836 (1978).
[CrossRef] [PubMed]

Gloge, D.

D. Gloge, IEEE Trans. Microwave Theory Tech. 23, 106 (1975).
[CrossRef]

D. Gloge, Appl. Opt. 10, 2442 (1971).
[CrossRef] [PubMed]

Hartog, A. H.

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

Hosaka, T.

T. Miya, Y. Terunuma, T. Hosaka, T. Miyashita, Electron. Lett. 15, 106 (1979).
[CrossRef]

Izawa, T.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, “Refractive-Index Dispersion of Doped Fused Silica,” Technical Digest, IEEE Japan International Conference on Integrated Optics and Optical Fiber Communication (1977), pp. 309–312, Tokyo, Japan.

Kaiser, P.

Kaminow, I. P.

Kobayashi, S.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, “Refractive-Index Dispersion of Doped Fused Silica,” Technical Digest, IEEE Japan International Conference on Integrated Optics and Optical Fiber Communication (1977), pp. 309–312, Tokyo, Japan.

Lin, C.

L. G. Cohen, C. Lin, W. G. French, Electron. Lett. 15, 334 (1979).
[CrossRef]

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978).
[CrossRef]

L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
[CrossRef]

L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

Marcuse, D.

Miya, T.

T. Miya, Y. Terunuma, T. Hosaka, T. Miyashita, Electron. Lett. 15, 106 (1979).
[CrossRef]

Miyashita, T.

T. Miya, Y. Terunuma, T. Hosaka, T. Miyashita, Electron. Lett. 15, 106 (1979).
[CrossRef]

Okamoto, K.

K. Okamoto, T. Okoshi, IEEE Trans. Microwave Theory Tech. 24, 416 (1976).
[CrossRef]

Okoshi, T.

K. Okamoto, T. Okoshi, IEEE Trans. Microwave Theory Tech. 24, 416 (1976).
[CrossRef]

Payne, D. N.

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

Presby, H. M.

Shibata, N.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, “Refractive-Index Dispersion of Doped Fused Silica,” Technical Digest, IEEE Japan International Conference on Integrated Optics and Optical Fiber Communication (1977), pp. 309–312, Tokyo, Japan.

Shibata, S.

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, “Refractive-Index Dispersion of Doped Fused Silica,” Technical Digest, IEEE Japan International Conference on Integrated Optics and Optical Fiber Communication (1977), pp. 309–312, Tokyo, Japan.

Simpson, J. R.

Tasker, G. W.

Terunuma, Y.

T. Miya, Y. Terunuma, T. Hosaka, T. Miyashita, Electron. Lett. 15, 106 (1979).
[CrossRef]

Appl. Opt. (6)

Electron. Lett. (5)

T. Miya, Y. Terunuma, T. Hosaka, T. Miyashita, Electron. Lett. 15, 106 (1979).
[CrossRef]

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

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978).
[CrossRef]

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

L. G. Cohen, C. Lin, W. G. French, Electron. Lett. 15, 334 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. G. Cohen, C. Lin, IEEE J. Quantum Electron. QE-14, 855 (1978).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

K. Okamoto, T. Okoshi, IEEE Trans. Microwave Theory Tech. 24, 416 (1976).
[CrossRef]

D. Gloge, IEEE Trans. Microwave Theory Tech. 23, 106 (1975).
[CrossRef]

Other (1)

S. Kobayashi, S. Shibata, N. Shibata, T. Izawa, “Refractive-Index Dispersion of Doped Fused Silica,” Technical Digest, IEEE Japan International Conference on Integrated Optics and Optical Fiber Communication (1977), pp. 309–312, Tokyo, Japan.

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Figures (5)

Fig. 1
Fig. 1

Refractive-index profile measured for a sample from 1.04-mm diam tip of a preform.

Fig. 2
Fig. 2

Chromatic dispersion vs wavelength for four fibers drawn from same preform. Fibers 1, 2, 3, 4 have core diameters of 7, 5.2, 4.8, and 4 μm, respectively. Solid curves are results of transmission measurements, and dashed curves are numerical predictions.

Fig. 3
Fig. 3

Numerically predicted waveguide and material dispersion are plotted separately vs wavelength for fibers 1, 2, 3, 4. Material dispersion curve applies to all four fibers. Remaining waveguide dispersion curves include material dispersion effects through wavelength dependence of core and cladding refractive indices.

Fig. 4
Fig. 4

Numerically predicted waveguide dispersion with and without material dispersion effects are plotted vs wavelength. Dashed curves include material effects. Solid curves exclude material effects and were calculated by neglecting refractive-index wavelength dependence.

Fig. 5
Fig. 5

Design curves for single-mode fibers with minimum chromatic dispersion at any selected wavelength between 1.33 and 1.75 μm. Calculations were made for two preforms with peak core– cladding index differences, Δn = 0.012 and 0.018. ○ data points are results of measurements in fibers with Δn = 0.012.

Equations (12)

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1 R d dR ( R d Φ dR ) + [ k 2 ( R ) β 2 ] Φ ( R ) = 0 ,
Φ ( 0 ) = 1 ; Φ ( 0 ) = 0 ;
r = R / a E ( r ) = Φ ( R ) Δ = n 0 2 n c 2 / 2 n 0 2 V 2 = 2 Δ k 0 2 a 2 β 2 = k 0 2 ( 1 2 Δ B 2 ) = k 0 2 1 a 2 ( V 2 B 2 ) k 2 ( R ) = k 0 2 [ 1 2 Δ N ( r ) ]
1 r d dr ( r dE d r ) + V 2 [ B 2 N ( r ) ] E ( r ) = 0 ,
E ( 0 ) = 1 ; E ( 0 ) = 0 ,
E ( 1 ) E ( 1 ) = V ( 1 B 2 ) 1 / 2 K 0 [ V ( 1 B 2 ) 1 / 2 ] K 0 [ V ( 1 B 2 ) 1 / 2 ] ,
τ = λ 2 L 2 π c dB d λ ,
dB d λ = 1 2 β | dk 0 2 d λ 1 a 2 d ( V 2 B 2 ) d ( V 2 ) d ( V 2 ) d λ | ,
d ( k 0 2 ) d λ = ( 2 π ) 2 d d λ ( n 0 2 λ 2 ) ,
d ( V 2 ) d λ = ( 2 π a ) 2 d d λ ( n 0 2 n c 2 λ 2 ) .
n 2 = 1 + i = 1 3 A i λ 2 ( λ 2 l i 2 ) .
D = 1 L d τ d λ ,

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