Abstract

The material dispersion of a parabolic graded-index fiber can be completely characterized through numerical aperture measurements. The relation between the dispersion slope and wavelength of zero dispersion is discussed for single-mode fibers, and the corresponding relation for material dispersion in multimode fibers is presented. Then the effective wavelength of zero material dispersion in a multimode fiber is expressed in terms of a quantity that resembles a numerical aperture. Formulas relating that quantity to measured numerical apertures are derived in the Appendix. Starting with just numerical aperture measurements, therefore, one may determine the effective wavelength of zero material dispersion and effective material dispersion slope for a multimode fiber.

© 1990 Optical Society of America

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References

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  1. L. G. Cohen, C. Lin, “Pulse Delay Measurements in the Zero Dispersion Wavelength Region for Optical Fibers,” Appl. Opt. 16, 3136–3139 (1977).
    [CrossRef] [PubMed]
  2. C. Lin, W. French, “A Near IR Raman Oscillator Tuneable from 1.07 to 1.3 μ,” Appl. Phys. Lett. 39, 666–668 (1979).
    [CrossRef]
  3. B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, “Phase Shift Technique for the Measurement of Chromatic Dispersion in Optical Fibers Using LEDs,” IEEE J. Quantum Electron. QE-18, 1509–1515 (1982).
    [CrossRef]
  4. P. J. Vella, P. M. Garel-Jones, R. S. Lowe, “Measurement of Chromatic Dispersion of Long Spans of Single-Mode Fibre: a Factory and Field Test Method,” Electron. Lett. 20, 167–168 (1984).
    [CrossRef]
  5. M. J. Saunders, W. B. Gardner, “Precision Interferometric Measurement of Dispersion in Short Single Mode Fibers,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1984), p. 123.
  6. L. Oksanen, S. J. Halme, “Interferometric Dispersion Measurement in Single-Mode Fibers with a Numerical Method to Extract the Group Delays from the Measured Visibility Curves,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1984), p. 127.
  7. J. Yamada, “Simple Dispersion Measurement of a Long-Span, Single-Mode Fiber Using the Longitudinal Mode Spacing of a Semiconductor Laser,” Opt. Quantum Electron. 14, 183–187 (1982).
    [CrossRef]
  8. C. Lin, A. R. Tynes, A. Tomita, P. L. Liu, “Pulse Delay Measurements in Single-Mode Fibers Using Picosecond InGaAsP Injection Lasers in the 1–3 μm Spectral Region,” Bell Syst. Tech. J. 62, 457–462 (1983).
  9. D. W. Schicketanz, C. K. Eoll, “Dispersion Measurement Using Only Two Wavelengths,” Electron. Lett. 22, 209–211 (1986).
    [CrossRef]
  10. C. K. Eoll, T. Goldring, T. R. Lucas, “Efficient Solution of Maxwell’s Equations for Optical Fibers with Arbitrary Refractive-Index Profiles,” Opt. Lett. 12, 841–843 (1987).
    [CrossRef] [PubMed]
  11. W. H. Hatton, M. Nishimura, W. Haltiwanger, “New Field Measurement System for Single Mode Fiber Dispersion Utilizing Wavelength Division Multiplexing Technique,” in Proceedings, Thirty-Fourth International Wire and Cable Symposium (1985), p. 142.
  12. J. W. Fleming, “Dispersion in GeO2–SiO2 Glasses,” Appl. Opt. 23, 4486–4493 (1984).
    [CrossRef] [PubMed]
  13. D. W. Schicketanz, W. S. Jackman, “Effective Fiber Bandwidth in LED Based Systems,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1986), p. 93.
  14. S. Geckeler, Optical Fiber Transmission Systems (Artech House, Norwood, MA, 1987).

1987 (1)

1986 (1)

D. W. Schicketanz, C. K. Eoll, “Dispersion Measurement Using Only Two Wavelengths,” Electron. Lett. 22, 209–211 (1986).
[CrossRef]

1984 (2)

J. W. Fleming, “Dispersion in GeO2–SiO2 Glasses,” Appl. Opt. 23, 4486–4493 (1984).
[CrossRef] [PubMed]

P. J. Vella, P. M. Garel-Jones, R. S. Lowe, “Measurement of Chromatic Dispersion of Long Spans of Single-Mode Fibre: a Factory and Field Test Method,” Electron. Lett. 20, 167–168 (1984).
[CrossRef]

1983 (1)

C. Lin, A. R. Tynes, A. Tomita, P. L. Liu, “Pulse Delay Measurements in Single-Mode Fibers Using Picosecond InGaAsP Injection Lasers in the 1–3 μm Spectral Region,” Bell Syst. Tech. J. 62, 457–462 (1983).

1982 (2)

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, “Phase Shift Technique for the Measurement of Chromatic Dispersion in Optical Fibers Using LEDs,” IEEE J. Quantum Electron. QE-18, 1509–1515 (1982).
[CrossRef]

J. Yamada, “Simple Dispersion Measurement of a Long-Span, Single-Mode Fiber Using the Longitudinal Mode Spacing of a Semiconductor Laser,” Opt. Quantum Electron. 14, 183–187 (1982).
[CrossRef]

1979 (1)

C. Lin, W. French, “A Near IR Raman Oscillator Tuneable from 1.07 to 1.3 μ,” Appl. Phys. Lett. 39, 666–668 (1979).
[CrossRef]

1977 (1)

Cohen, L. G.

Costa, B.

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, “Phase Shift Technique for the Measurement of Chromatic Dispersion in Optical Fibers Using LEDs,” IEEE J. Quantum Electron. QE-18, 1509–1515 (1982).
[CrossRef]

Eoll, C. K.

Fleming, J. W.

French, W.

C. Lin, W. French, “A Near IR Raman Oscillator Tuneable from 1.07 to 1.3 μ,” Appl. Phys. Lett. 39, 666–668 (1979).
[CrossRef]

Gardner, W. B.

M. J. Saunders, W. B. Gardner, “Precision Interferometric Measurement of Dispersion in Short Single Mode Fibers,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1984), p. 123.

Garel-Jones, P. M.

P. J. Vella, P. M. Garel-Jones, R. S. Lowe, “Measurement of Chromatic Dispersion of Long Spans of Single-Mode Fibre: a Factory and Field Test Method,” Electron. Lett. 20, 167–168 (1984).
[CrossRef]

Geckeler, S.

S. Geckeler, Optical Fiber Transmission Systems (Artech House, Norwood, MA, 1987).

Goldring, T.

Halme, S. J.

L. Oksanen, S. J. Halme, “Interferometric Dispersion Measurement in Single-Mode Fibers with a Numerical Method to Extract the Group Delays from the Measured Visibility Curves,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1984), p. 127.

Haltiwanger, W.

W. H. Hatton, M. Nishimura, W. Haltiwanger, “New Field Measurement System for Single Mode Fiber Dispersion Utilizing Wavelength Division Multiplexing Technique,” in Proceedings, Thirty-Fourth International Wire and Cable Symposium (1985), p. 142.

Hatton, W. H.

W. H. Hatton, M. Nishimura, W. Haltiwanger, “New Field Measurement System for Single Mode Fiber Dispersion Utilizing Wavelength Division Multiplexing Technique,” in Proceedings, Thirty-Fourth International Wire and Cable Symposium (1985), p. 142.

Jackman, W. S.

D. W. Schicketanz, W. S. Jackman, “Effective Fiber Bandwidth in LED Based Systems,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1986), p. 93.

Lin, C.

C. Lin, A. R. Tynes, A. Tomita, P. L. Liu, “Pulse Delay Measurements in Single-Mode Fibers Using Picosecond InGaAsP Injection Lasers in the 1–3 μm Spectral Region,” Bell Syst. Tech. J. 62, 457–462 (1983).

C. Lin, W. French, “A Near IR Raman Oscillator Tuneable from 1.07 to 1.3 μ,” Appl. Phys. Lett. 39, 666–668 (1979).
[CrossRef]

L. G. Cohen, C. Lin, “Pulse Delay Measurements in the Zero Dispersion Wavelength Region for Optical Fibers,” Appl. Opt. 16, 3136–3139 (1977).
[CrossRef] [PubMed]

Liu, P. L.

C. Lin, A. R. Tynes, A. Tomita, P. L. Liu, “Pulse Delay Measurements in Single-Mode Fibers Using Picosecond InGaAsP Injection Lasers in the 1–3 μm Spectral Region,” Bell Syst. Tech. J. 62, 457–462 (1983).

Lowe, R. S.

P. J. Vella, P. M. Garel-Jones, R. S. Lowe, “Measurement of Chromatic Dispersion of Long Spans of Single-Mode Fibre: a Factory and Field Test Method,” Electron. Lett. 20, 167–168 (1984).
[CrossRef]

Lucas, T. R.

Mazzoni, D.

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, “Phase Shift Technique for the Measurement of Chromatic Dispersion in Optical Fibers Using LEDs,” IEEE J. Quantum Electron. QE-18, 1509–1515 (1982).
[CrossRef]

Nishimura, M.

W. H. Hatton, M. Nishimura, W. Haltiwanger, “New Field Measurement System for Single Mode Fiber Dispersion Utilizing Wavelength Division Multiplexing Technique,” in Proceedings, Thirty-Fourth International Wire and Cable Symposium (1985), p. 142.

Oksanen, L.

L. Oksanen, S. J. Halme, “Interferometric Dispersion Measurement in Single-Mode Fibers with a Numerical Method to Extract the Group Delays from the Measured Visibility Curves,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1984), p. 127.

Puleo, M.

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, “Phase Shift Technique for the Measurement of Chromatic Dispersion in Optical Fibers Using LEDs,” IEEE J. Quantum Electron. QE-18, 1509–1515 (1982).
[CrossRef]

Saunders, M. J.

M. J. Saunders, W. B. Gardner, “Precision Interferometric Measurement of Dispersion in Short Single Mode Fibers,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1984), p. 123.

Schicketanz, D. W.

D. W. Schicketanz, C. K. Eoll, “Dispersion Measurement Using Only Two Wavelengths,” Electron. Lett. 22, 209–211 (1986).
[CrossRef]

D. W. Schicketanz, W. S. Jackman, “Effective Fiber Bandwidth in LED Based Systems,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1986), p. 93.

Tomita, A.

C. Lin, A. R. Tynes, A. Tomita, P. L. Liu, “Pulse Delay Measurements in Single-Mode Fibers Using Picosecond InGaAsP Injection Lasers in the 1–3 μm Spectral Region,” Bell Syst. Tech. J. 62, 457–462 (1983).

Tynes, A. R.

C. Lin, A. R. Tynes, A. Tomita, P. L. Liu, “Pulse Delay Measurements in Single-Mode Fibers Using Picosecond InGaAsP Injection Lasers in the 1–3 μm Spectral Region,” Bell Syst. Tech. J. 62, 457–462 (1983).

Vella, P. J.

P. J. Vella, P. M. Garel-Jones, R. S. Lowe, “Measurement of Chromatic Dispersion of Long Spans of Single-Mode Fibre: a Factory and Field Test Method,” Electron. Lett. 20, 167–168 (1984).
[CrossRef]

Vezzoni, E.

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, “Phase Shift Technique for the Measurement of Chromatic Dispersion in Optical Fibers Using LEDs,” IEEE J. Quantum Electron. QE-18, 1509–1515 (1982).
[CrossRef]

Yamada, J.

J. Yamada, “Simple Dispersion Measurement of a Long-Span, Single-Mode Fiber Using the Longitudinal Mode Spacing of a Semiconductor Laser,” Opt. Quantum Electron. 14, 183–187 (1982).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. Lin, W. French, “A Near IR Raman Oscillator Tuneable from 1.07 to 1.3 μ,” Appl. Phys. Lett. 39, 666–668 (1979).
[CrossRef]

Bell Syst. Tech. J. (1)

C. Lin, A. R. Tynes, A. Tomita, P. L. Liu, “Pulse Delay Measurements in Single-Mode Fibers Using Picosecond InGaAsP Injection Lasers in the 1–3 μm Spectral Region,” Bell Syst. Tech. J. 62, 457–462 (1983).

Electron. Lett. (2)

D. W. Schicketanz, C. K. Eoll, “Dispersion Measurement Using Only Two Wavelengths,” Electron. Lett. 22, 209–211 (1986).
[CrossRef]

P. J. Vella, P. M. Garel-Jones, R. S. Lowe, “Measurement of Chromatic Dispersion of Long Spans of Single-Mode Fibre: a Factory and Field Test Method,” Electron. Lett. 20, 167–168 (1984).
[CrossRef]

IEEE J. Quantum Electron. (1)

B. Costa, D. Mazzoni, M. Puleo, E. Vezzoni, “Phase Shift Technique for the Measurement of Chromatic Dispersion in Optical Fibers Using LEDs,” IEEE J. Quantum Electron. QE-18, 1509–1515 (1982).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

J. Yamada, “Simple Dispersion Measurement of a Long-Span, Single-Mode Fiber Using the Longitudinal Mode Spacing of a Semiconductor Laser,” Opt. Quantum Electron. 14, 183–187 (1982).
[CrossRef]

Other (5)

D. W. Schicketanz, W. S. Jackman, “Effective Fiber Bandwidth in LED Based Systems,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1986), p. 93.

S. Geckeler, Optical Fiber Transmission Systems (Artech House, Norwood, MA, 1987).

W. H. Hatton, M. Nishimura, W. Haltiwanger, “New Field Measurement System for Single Mode Fiber Dispersion Utilizing Wavelength Division Multiplexing Technique,” in Proceedings, Thirty-Fourth International Wire and Cable Symposium (1985), p. 142.

M. J. Saunders, W. B. Gardner, “Precision Interferometric Measurement of Dispersion in Short Single Mode Fibers,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1984), p. 123.

L. Oksanen, S. J. Halme, “Interferometric Dispersion Measurement in Single-Mode Fibers with a Numerical Method to Extract the Group Delays from the Measured Visibility Curves,” in Technical Digest, Symposium on Optical Fiber Measurements, Boulder, CO (1984), p. 127.

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Figures (2)

Fig. 1
Fig. 1

Dispersion slope at the wavelength of zero dispersion as a function of the wavelength of zero dispersion.

Fig. 2
Fig. 2

Power density distributions P(r,ϕ) and P(r) for parabolic graded-index fibers.

Tables (4)

Tables Icon

Table I Properties of Fibers Tested

Tables Icon

Table II Dispersion from Numerical Apertures

Tables Icon

Table III Dispersion from Relative Pulse Delays

Tables Icon

Table IV Effect of Launch Conditions Using Lasers

Equations (39)

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t g = A λ 2 + B + C λ - 2 .
D = 2 A λ - 2 C λ - 3 .
λ 0 4 = C / A ,
S 0 = 8 A .
D = S 0 4 ( λ - λ 0 4 λ - 3 ) .
λ 0 4 = λ 1 2 λ 2 2 { 1 - 8 Δ t / [ S 0 ( λ 1 2 - λ 2 2 ) ] } .
S 0 = 0.4695 - 0.2908 λ 0 ± 0.0015 ps / nm 2 km
S 0 = 0.1845 - 0.0662 λ 0 ± 0.0002 ps / nm 2 km
N . A . 2 = n 2 - n 2 2 .
λ 0 = 1.2728 + 0.0219 N . A . + 1.027 N . A . 2 ,
N . A . ( λ ) N . A . ( 0.600 ) = 1.0734 - 0.1616 λ + 0.0654 λ 2
λ 0 = 1.2728 + 0.0223 N . A . + 1.062 N . A . 2 .
0.95 N . A . 2 = ( N . A . short ) 2 - ( 0.533 N . A . long ) 2 ,
n 2 ( r ) - n 2 2 n 1 2 - n 2 2 = 1 - ( r r 0 ) 2
P ( r , ϕ ) = 2 π r 0 2 [ 1 - ( r r 0 ) 2 ] .
P ( r ) = 0 2 P ( r , ϕ ) r d ϕ ,
P ( r ) = 4 r r 0 2 [ 1 - ( r r 0 ) 2 ] .
r p = r 0 / 3 = 0.577 r 0 ,
r a = 8 r 0 / 15 = 0.533 r 0 .
n eff 2 = n 2 ( r a ) ;
n eff 2 = ( 1 - 0.533 2 ) n 1 2 + 0.533 2 n 2 2 .
P ( N . A . , ϕ ) = 2 π R ( N . A . 0 ) 2 [ 1 - ( N . A . N . A . 0 ) 2 ] ,
P ( N . A . ) = 0 2 π P ( N . A . , ϕ ) R sin θ d ϕ ,
P ( N . A . ) = 4 N . A . ( N . A . 0 ) 2 [ 1 - ( N . A . N . A . 0 ) 2 ] .
N . A . a = 0.533 N . A . 0 .
P ( N . A . a , ϕ ) P ( 0 , ϕ ) = 1 - 0.533 2 = 0.716.
P ( N . A . 5 % , ϕ ) P ( 0 , ϕ ) = 0.05 ,
N . A . 0 2 = N . A . 5 % 2 / 0.95.
N . A . 0 2 = n 1 2 - n 2 2 .
N . A . a 2 = n 1 2 - n eff 2 .
N . A . eff 2 = N . A . 0 2 - N . A . a 2 ,
N . A . eff 2 = n eff 2 - n 2 2 .
N . A . eff = 0.868 N . A . 5 % .
N . A . ¯ a 2 = n 1 2 - n ¯ eff 2 ,
N . A . ¯ a = 0.533 N . A . ¯ 0 .
N . A . eff 2 = N . A . 0 2 - N . A . ¯ a 2 ,
N . A . eff 2 = n ¯ eff 2 - n 2 2 ,
N . A . eff 2 = ( N . A . short ) 2 / 0.95 - ( 0.533 N . A . long ) 2 / 0.95.
N . A . eff 2 = ( N . A . short ) 2 / 0.95 - ( N . A . long 72 % ) 2 ,

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