Abstract

Optical signals transmitted through cladded glass fibers are subject to delay distortion because of (1) dispersion in the material, (2) dispersion caused by the waveguide characteristic, and (3) delay differences between modes. We isolate these effects and evaluate their significance for cases of practical interest. These concern fibers in which the refractive index of the cladding is only slightly lower than that of the core.

© 1971 Optical Society of America

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References

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  1. D. Williams, K. C. Kao, Proc. IEEE 56, 197 (1968).
    [CrossRef]
  2. W. A. Gambling, P. J. R. Laybourn, M. D. Lee, Electron. Lett. 6, 364 (1970).
    [CrossRef]
  3. H. J. Heyke, “Optical Pulse Transmission in Cladded Fibers With Imperfections,” presented at the Conference on Trunk Telecommunications by Guided Waves, 29 Sept.–2 Oct., 1970, London.
  4. D. Gloge, M. A. Dunguay, W. J. Hansen, A. R. Tynes, “Light Pulse Distortion in Dispersive Glass Fibers Measured with a Picosecond Gate,” presented at the 1971 IEEE/OSA Conference on Laser Engineering and Applications, 2–4 June, 1971, Washington, D.C.
  5. W. A. Gambling, P. J. R. Laybourn, Electron. Lett. 6, 661 (1970).
    [CrossRef]
  6. P. J. R. Laybourn, Electron. Lett. 4, 507 (1968).
    [CrossRef]
  7. F. P. Kapron, D. B. Keck, Appl. Opt. 10, 1519 (1971).
    [CrossRef] [PubMed]
  8. R. B. Dyott, J. R. Stern, “Group Delay in Glass Fiber Waveguide,” presented at the Conference on Trunk Telecommunication by Guided Waves, 29 Sept.–2 Oct., 1970, London.
  9. A. W. Snyder, IEEE Trans. Microwave Theory Techniques MTT-17, 1130 (1969).
    [CrossRef]
  10. D. Gloge, Appl. Opt. 10, 2252 (1971).
    [CrossRef] [PubMed]
  11. C. G. B. Garrett, D. E. McCumber, Phys. Rev. 1, 305 (1970).

1971 (2)

1970 (3)

C. G. B. Garrett, D. E. McCumber, Phys. Rev. 1, 305 (1970).

W. A. Gambling, P. J. R. Laybourn, M. D. Lee, Electron. Lett. 6, 364 (1970).
[CrossRef]

W. A. Gambling, P. J. R. Laybourn, Electron. Lett. 6, 661 (1970).
[CrossRef]

1969 (1)

A. W. Snyder, IEEE Trans. Microwave Theory Techniques MTT-17, 1130 (1969).
[CrossRef]

1968 (2)

D. Williams, K. C. Kao, Proc. IEEE 56, 197 (1968).
[CrossRef]

P. J. R. Laybourn, Electron. Lett. 4, 507 (1968).
[CrossRef]

Dunguay, M. A.

D. Gloge, M. A. Dunguay, W. J. Hansen, A. R. Tynes, “Light Pulse Distortion in Dispersive Glass Fibers Measured with a Picosecond Gate,” presented at the 1971 IEEE/OSA Conference on Laser Engineering and Applications, 2–4 June, 1971, Washington, D.C.

Dyott, R. B.

R. B. Dyott, J. R. Stern, “Group Delay in Glass Fiber Waveguide,” presented at the Conference on Trunk Telecommunication by Guided Waves, 29 Sept.–2 Oct., 1970, London.

Gambling, W. A.

W. A. Gambling, P. J. R. Laybourn, Electron. Lett. 6, 661 (1970).
[CrossRef]

W. A. Gambling, P. J. R. Laybourn, M. D. Lee, Electron. Lett. 6, 364 (1970).
[CrossRef]

Garrett, C. G. B.

C. G. B. Garrett, D. E. McCumber, Phys. Rev. 1, 305 (1970).

Gloge, D.

D. Gloge, Appl. Opt. 10, 2252 (1971).
[CrossRef] [PubMed]

D. Gloge, M. A. Dunguay, W. J. Hansen, A. R. Tynes, “Light Pulse Distortion in Dispersive Glass Fibers Measured with a Picosecond Gate,” presented at the 1971 IEEE/OSA Conference on Laser Engineering and Applications, 2–4 June, 1971, Washington, D.C.

Hansen, W. J.

D. Gloge, M. A. Dunguay, W. J. Hansen, A. R. Tynes, “Light Pulse Distortion in Dispersive Glass Fibers Measured with a Picosecond Gate,” presented at the 1971 IEEE/OSA Conference on Laser Engineering and Applications, 2–4 June, 1971, Washington, D.C.

Heyke, H. J.

H. J. Heyke, “Optical Pulse Transmission in Cladded Fibers With Imperfections,” presented at the Conference on Trunk Telecommunications by Guided Waves, 29 Sept.–2 Oct., 1970, London.

Kao, K. C.

D. Williams, K. C. Kao, Proc. IEEE 56, 197 (1968).
[CrossRef]

Kapron, F. P.

Keck, D. B.

Laybourn, P. J. R.

W. A. Gambling, P. J. R. Laybourn, M. D. Lee, Electron. Lett. 6, 364 (1970).
[CrossRef]

W. A. Gambling, P. J. R. Laybourn, Electron. Lett. 6, 661 (1970).
[CrossRef]

P. J. R. Laybourn, Electron. Lett. 4, 507 (1968).
[CrossRef]

Lee, M. D.

W. A. Gambling, P. J. R. Laybourn, M. D. Lee, Electron. Lett. 6, 364 (1970).
[CrossRef]

McCumber, D. E.

C. G. B. Garrett, D. E. McCumber, Phys. Rev. 1, 305 (1970).

Snyder, A. W.

A. W. Snyder, IEEE Trans. Microwave Theory Techniques MTT-17, 1130 (1969).
[CrossRef]

Stern, J. R.

R. B. Dyott, J. R. Stern, “Group Delay in Glass Fiber Waveguide,” presented at the Conference on Trunk Telecommunication by Guided Waves, 29 Sept.–2 Oct., 1970, London.

Tynes, A. R.

D. Gloge, M. A. Dunguay, W. J. Hansen, A. R. Tynes, “Light Pulse Distortion in Dispersive Glass Fibers Measured with a Picosecond Gate,” presented at the 1971 IEEE/OSA Conference on Laser Engineering and Applications, 2–4 June, 1971, Washington, D.C.

Williams, D.

D. Williams, K. C. Kao, Proc. IEEE 56, 197 (1968).
[CrossRef]

Appl. Opt. (2)

Electron. Lett. (3)

W. A. Gambling, P. J. R. Laybourn, M. D. Lee, Electron. Lett. 6, 364 (1970).
[CrossRef]

W. A. Gambling, P. J. R. Laybourn, Electron. Lett. 6, 661 (1970).
[CrossRef]

P. J. R. Laybourn, Electron. Lett. 4, 507 (1968).
[CrossRef]

IEEE Trans. Microwave Theory Techniques (1)

A. W. Snyder, IEEE Trans. Microwave Theory Techniques MTT-17, 1130 (1969).
[CrossRef]

Phys. Rev. (1)

C. G. B. Garrett, D. E. McCumber, Phys. Rev. 1, 305 (1970).

Proc. IEEE (1)

D. Williams, K. C. Kao, Proc. IEEE 56, 197 (1968).
[CrossRef]

Other (3)

R. B. Dyott, J. R. Stern, “Group Delay in Glass Fiber Waveguide,” presented at the Conference on Trunk Telecommunication by Guided Waves, 29 Sept.–2 Oct., 1970, London.

H. J. Heyke, “Optical Pulse Transmission in Cladded Fibers With Imperfections,” presented at the Conference on Trunk Telecommunications by Guided Waves, 29 Sept.–2 Oct., 1970, London.

D. Gloge, M. A. Dunguay, W. J. Hansen, A. R. Tynes, “Light Pulse Distortion in Dispersive Glass Fibers Measured with a Picosecond Gate,” presented at the 1971 IEEE/OSA Conference on Laser Engineering and Applications, 2–4 June, 1971, Washington, D.C.

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Figures (3)

Fig. 1
Fig. 1

Reractive index n and group index N = d(kn)/dk as a function of frequency for fused silica (SiO2) and the Schott glasses K9 and SSK1.

Fig. 2
Fig. 2

Waveguide parameter b and its derivatives d(vb)/dv and vd2(vb)/dv2 as a function of the normalized frequency v.

Fig. 3
Fig. 3

Dispersion coefficient kd2(kn)/dk2 as a function of frequency for fused silica (SiO2) and the Schott glasses K9 and SSK1.

Equations (22)

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τ = ( 1 / c ) ( d β / d k ) ,
d β / d k = d ( k n ) / d k = N ,
u = a ( k 2 n 1 2 - β 2 ) 1 2
w = a ( β 2 - k 2 n 2 2 ) 1 2 ,
v = ( u 2 + w 2 ) 1 2
b = 1 - u 2 / v 2 .
v = a k ( n 1 2 - n 2 2 ) 1 2
b = ( β 2 / k 2 - n 2 2 ) / ( n 1 2 - n 2 2 ) .
β = k ( n 2 2 + ( n 1 2 - n 2 2 ) b ) 1 2 .
d β / d k = { n 2 N 2 + [ b + 1 2 v ( d b / d v ) ] ( n 1 N 1 - n 2 N 2 ) } / [ n 2 2 + ( n 1 2 - n 2 2 ) b ] 1 2 ,
d β / d k = N 2 + ( N 1 + N 2 ) b + ½ [ ( n 1 / n 2 ) N 1 - N 2 ] v ( d b / d v ) .
( n 1 - n 2 ) / n 2 ( N 1 - N 2 ) / N 2 1 ,
d β / d k = N 2 + ( N 1 - N 2 ) [ d ( v b ) / d v ] .
d ( v b ) / d v 1 + ( u 2 / v 2 ) 1 + ( m / M )
T = ( 1 / c ) [ N 1 + ( N 1 - N 2 ) ( m / M ) ] .
s = Δ F / ( d τ / d f ) = Δ ( 1 / c ) k ( d 2 β / d k 2 )
k ( d 2 β / d k 2 ) = k ( d N 2 / d k ) + k [ d ( N 1 - N 2 ) / d k ] [ d ( v b ) / d v ] + [ ( N 1 2 - N 2 2 ) / ( n 1 + n 2 ) ] v [ d 2 ( v b ) / d v 2 ] .
s = ( Δ / c ) { k ( d N 2 / d k ) + ( N 1 - N 2 ) v [ d 2 ( v b ) / d v 2 ] } .
v / [ d 2 ( v b ) / d v 2 ] - 2 ( u 2 / v 2 ) - 2 ( m / M ) .
s Δ ( 1 / c ) [ k ( d N 2 / d k ) - 2 ( m / M ) ( N 1 - N 2 ) ] .
( T 2 + L 2 s 2 ) 1 2
T 2 + { [ ( L / T ) ( d 2 β / d ω 2 ) ] 2 } 1 2

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