Abstract

A Runge-Kutta procedure was used for investigating the dispersion characteristics of single-mode triangular- index fibers with a trench in the cladding. Numerical results on the total dispersion, its sensitivities to the core radius, wavelength, index difference variations, and its influence on the fiber’s bandwidth–length product are presented. Some interesting features, due to the presence of a trench, are pointed out. One salient feature is the appearance of dispersion flattening over a certain wavelength range near 1.55 μm for b/a = 2 and c/a > 2.7 (a = core radius, b = inner trench radius, c = outer trench radius) where the total dispersion is low, yielding a bandwidth–length product as high as 104 GHz · km. The presence of a trench has not been investigated previously.

© 1990 Optical Society of America

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  1. D. B. Keck, “Single-Mode Fibers Outperform Multimode Cables,” IEEE Spectrum 20, 30–37 (1983).
  2. D. Marcuse, “Interdependence of Waveguide and Material Dispersion,” Appl. Opt. 18, 2930–2932 (1979).
    [CrossRef] [PubMed]
  3. K. I. White, “Design Parameters for Dispersion-Shifted Triangular-Profile Single-mode Fibers,” Electron. Lett. 18, 725–727 (1982).
    [CrossRef]
  4. M. A. Saifi, S. J. Jang, L. G. Cohen, J. Stone, “Triangular-Profile Single-Mode Fiber,” Opt. Lett. 7, 43–45 (1982).
    [CrossRef] [PubMed]
  5. T. Moriyama, M. Miyamoto, M. Akiyama, R. Sanada, O. Fukuda, T. Miya, R. Chida, “Fabrication of Low Loss and Long Length VAD Fibers for 1.55 μm Wavelength Region,” in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982), pp. 31–35.
  6. A. D. Pearson, L. G. Cohen, W. A. Reed, J. T. Krause, E. A. Sigety, F. DiMarcello, A. G. Richardson, “Transmission, Splicing, and Cabling Performance of Dispersion-Shifted Single-Mode Fiber,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984), paper TUI5.
  7. B. J. Ainslie, C. R. Day, “A Review of Single-Mode Fibers with Modified Dispersion Characteristics,” IEEE/OSA J. Lightwave Technol. LT-4, 967–979 (1986).
    [CrossRef]
  8. D. M. Cooper, S. P. Craig, C. R. Day, B. J. Ainslie, “Multiple-Index Structures for Dispersion-Shifted Single-Mode Fibers,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD4.
  9. K. B. Chung, S. S. Choi, “Propagation Characteristics of a Triangular-Index Doubly Clad Monomode Fiber,” Electron. Lett. 21, 271–272 (1985).
    [CrossRef]
  10. T. D. Croft, J. E. Ritter, V. A. Bhagavatula, “Low Loss Dispersion-Shifted Fiber Manufactured by the OVD Process,” IEEE/OSA J. Lightwave Technol. LT-3, 931–934 (1985); Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD2.
    [CrossRef]
  11. A. Ghatak, K. Thyagarajan, “Graded-Index Optical Waveguides: a Review,” Prog. Opt. 18, 1–126 (1980).
    [CrossRef]
  12. G. L. Yip, Y. H. Ahmew, “Propagation Characteristics of Radially Inhomogeneous Optical Fiber,” Electron. Lett. 10, 37–38(1974).
    [CrossRef]
  13. Y. H. Ahmew, “Propagation Characteristics of the Self-Focusing Fiber Waveguide,” M. Eng. Thesis, Electrical Engineering Dept. McGill U. (1973).
  14. A. Ralston, H. S. Wilf, Mathematical Methods for Digital Computers (Wiley, New York, 1960), pp. 111–120.
  15. S. Gill, “A Process for the Step by Step Integration of Differential Equations in an Automatic Digital Computing Machine,” Proc. Cambridge Philos. Soc. 47, 96–108 (1951).
    [CrossRef]
  16. U. C. Paek, G. E. Peterson, A. Carnevale, “Dispersionless Single-Mode Lightguides with α Index Profiles,” Bell Syst. Tech. J. 60, 583–598 (1981).
  17. C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, MA, 1984), Chap. 4.
  18. J. W. Fleming, “Material Dispersion in Lightguide Glasses,” Electron. Lett. 14, 326–328 (1978).
    [CrossRef]
  19. S. J. Jang, L. G. Cohen, W. L. Mammel, M. A. Saifi, “Experimental Verification of Ultra-Wide Bandwidth Spectra in Doubly-Clad Single-Mode Fiber,” Bell Syst. Tech. J. 61, 385–390 (1982).
  20. L. G. Cohen, W. A. Mammel, S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. QE-18, 49–53 (1982).
    [CrossRef]
  21. P.-L. Francois, “Tolerance Requirements for Dispersion Free Single-Mode Fiber Design: Influence of Geometrical Parameters, Dopant Diffusion, and Axial Dip,” IEEE J. Quantum Electron. QE-18, 1490–1499 (1982).
    [CrossRef]
  22. L. G. Cohen, W. A. Mammel, S. Lumish, “Tailoring the Shapes of Dispersion Spectra to Control Bandwidths in Single-Mode Fibers,” Opt. Lett. 7, 183–185 (1982).
    [CrossRef] [PubMed]
  23. M. Y. El-Ibiary, “Parameter Optimization in Graded-Index Dispersion-Shifted Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-4, 364–367 (1986).
    [CrossRef]
  24. K. Ogawa, “Analysis of Mode-Partition Noise in Laser System,” IEEE J. Quantum Electron. QE-18, 849–855 (1982).
    [CrossRef]

1986 (2)

B. J. Ainslie, C. R. Day, “A Review of Single-Mode Fibers with Modified Dispersion Characteristics,” IEEE/OSA J. Lightwave Technol. LT-4, 967–979 (1986).
[CrossRef]

M. Y. El-Ibiary, “Parameter Optimization in Graded-Index Dispersion-Shifted Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-4, 364–367 (1986).
[CrossRef]

1985 (2)

K. B. Chung, S. S. Choi, “Propagation Characteristics of a Triangular-Index Doubly Clad Monomode Fiber,” Electron. Lett. 21, 271–272 (1985).
[CrossRef]

T. D. Croft, J. E. Ritter, V. A. Bhagavatula, “Low Loss Dispersion-Shifted Fiber Manufactured by the OVD Process,” IEEE/OSA J. Lightwave Technol. LT-3, 931–934 (1985); Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD2.
[CrossRef]

1983 (1)

D. B. Keck, “Single-Mode Fibers Outperform Multimode Cables,” IEEE Spectrum 20, 30–37 (1983).

1982 (7)

K. I. White, “Design Parameters for Dispersion-Shifted Triangular-Profile Single-mode Fibers,” Electron. Lett. 18, 725–727 (1982).
[CrossRef]

K. Ogawa, “Analysis of Mode-Partition Noise in Laser System,” IEEE J. Quantum Electron. QE-18, 849–855 (1982).
[CrossRef]

M. A. Saifi, S. J. Jang, L. G. Cohen, J. Stone, “Triangular-Profile Single-Mode Fiber,” Opt. Lett. 7, 43–45 (1982).
[CrossRef] [PubMed]

L. G. Cohen, W. A. Mammel, S. Lumish, “Tailoring the Shapes of Dispersion Spectra to Control Bandwidths in Single-Mode Fibers,” Opt. Lett. 7, 183–185 (1982).
[CrossRef] [PubMed]

S. J. Jang, L. G. Cohen, W. L. Mammel, M. A. Saifi, “Experimental Verification of Ultra-Wide Bandwidth Spectra in Doubly-Clad Single-Mode Fiber,” Bell Syst. Tech. J. 61, 385–390 (1982).

L. G. Cohen, W. A. Mammel, S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. QE-18, 49–53 (1982).
[CrossRef]

P.-L. Francois, “Tolerance Requirements for Dispersion Free Single-Mode Fiber Design: Influence of Geometrical Parameters, Dopant Diffusion, and Axial Dip,” IEEE J. Quantum Electron. QE-18, 1490–1499 (1982).
[CrossRef]

1981 (1)

U. C. Paek, G. E. Peterson, A. Carnevale, “Dispersionless Single-Mode Lightguides with α Index Profiles,” Bell Syst. Tech. J. 60, 583–598 (1981).

1980 (1)

A. Ghatak, K. Thyagarajan, “Graded-Index Optical Waveguides: a Review,” Prog. Opt. 18, 1–126 (1980).
[CrossRef]

1979 (1)

1978 (1)

J. W. Fleming, “Material Dispersion in Lightguide Glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

1974 (1)

G. L. Yip, Y. H. Ahmew, “Propagation Characteristics of Radially Inhomogeneous Optical Fiber,” Electron. Lett. 10, 37–38(1974).
[CrossRef]

1951 (1)

S. Gill, “A Process for the Step by Step Integration of Differential Equations in an Automatic Digital Computing Machine,” Proc. Cambridge Philos. Soc. 47, 96–108 (1951).
[CrossRef]

Ahmew, Y. H.

G. L. Yip, Y. H. Ahmew, “Propagation Characteristics of Radially Inhomogeneous Optical Fiber,” Electron. Lett. 10, 37–38(1974).
[CrossRef]

Y. H. Ahmew, “Propagation Characteristics of the Self-Focusing Fiber Waveguide,” M. Eng. Thesis, Electrical Engineering Dept. McGill U. (1973).

Ainslie, B. J.

B. J. Ainslie, C. R. Day, “A Review of Single-Mode Fibers with Modified Dispersion Characteristics,” IEEE/OSA J. Lightwave Technol. LT-4, 967–979 (1986).
[CrossRef]

D. M. Cooper, S. P. Craig, C. R. Day, B. J. Ainslie, “Multiple-Index Structures for Dispersion-Shifted Single-Mode Fibers,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD4.

Akiyama, M.

T. Moriyama, M. Miyamoto, M. Akiyama, R. Sanada, O. Fukuda, T. Miya, R. Chida, “Fabrication of Low Loss and Long Length VAD Fibers for 1.55 μm Wavelength Region,” in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982), pp. 31–35.

Bhagavatula, V. A.

T. D. Croft, J. E. Ritter, V. A. Bhagavatula, “Low Loss Dispersion-Shifted Fiber Manufactured by the OVD Process,” IEEE/OSA J. Lightwave Technol. LT-3, 931–934 (1985); Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD2.
[CrossRef]

Carnevale, A.

U. C. Paek, G. E. Peterson, A. Carnevale, “Dispersionless Single-Mode Lightguides with α Index Profiles,” Bell Syst. Tech. J. 60, 583–598 (1981).

Chida, R.

T. Moriyama, M. Miyamoto, M. Akiyama, R. Sanada, O. Fukuda, T. Miya, R. Chida, “Fabrication of Low Loss and Long Length VAD Fibers for 1.55 μm Wavelength Region,” in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982), pp. 31–35.

Choi, S. S.

K. B. Chung, S. S. Choi, “Propagation Characteristics of a Triangular-Index Doubly Clad Monomode Fiber,” Electron. Lett. 21, 271–272 (1985).
[CrossRef]

Chung, K. B.

K. B. Chung, S. S. Choi, “Propagation Characteristics of a Triangular-Index Doubly Clad Monomode Fiber,” Electron. Lett. 21, 271–272 (1985).
[CrossRef]

Cohen, L. G.

M. A. Saifi, S. J. Jang, L. G. Cohen, J. Stone, “Triangular-Profile Single-Mode Fiber,” Opt. Lett. 7, 43–45 (1982).
[CrossRef] [PubMed]

S. J. Jang, L. G. Cohen, W. L. Mammel, M. A. Saifi, “Experimental Verification of Ultra-Wide Bandwidth Spectra in Doubly-Clad Single-Mode Fiber,” Bell Syst. Tech. J. 61, 385–390 (1982).

L. G. Cohen, W. A. Mammel, S. Lumish, “Tailoring the Shapes of Dispersion Spectra to Control Bandwidths in Single-Mode Fibers,” Opt. Lett. 7, 183–185 (1982).
[CrossRef] [PubMed]

L. G. Cohen, W. A. Mammel, S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. QE-18, 49–53 (1982).
[CrossRef]

A. D. Pearson, L. G. Cohen, W. A. Reed, J. T. Krause, E. A. Sigety, F. DiMarcello, A. G. Richardson, “Transmission, Splicing, and Cabling Performance of Dispersion-Shifted Single-Mode Fiber,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984), paper TUI5.

Cooper, D. M.

D. M. Cooper, S. P. Craig, C. R. Day, B. J. Ainslie, “Multiple-Index Structures for Dispersion-Shifted Single-Mode Fibers,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD4.

Craig, S. P.

D. M. Cooper, S. P. Craig, C. R. Day, B. J. Ainslie, “Multiple-Index Structures for Dispersion-Shifted Single-Mode Fibers,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD4.

Croft, T. D.

T. D. Croft, J. E. Ritter, V. A. Bhagavatula, “Low Loss Dispersion-Shifted Fiber Manufactured by the OVD Process,” IEEE/OSA J. Lightwave Technol. LT-3, 931–934 (1985); Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD2.
[CrossRef]

Day, C. R.

B. J. Ainslie, C. R. Day, “A Review of Single-Mode Fibers with Modified Dispersion Characteristics,” IEEE/OSA J. Lightwave Technol. LT-4, 967–979 (1986).
[CrossRef]

D. M. Cooper, S. P. Craig, C. R. Day, B. J. Ainslie, “Multiple-Index Structures for Dispersion-Shifted Single-Mode Fibers,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD4.

DiMarcello, F.

A. D. Pearson, L. G. Cohen, W. A. Reed, J. T. Krause, E. A. Sigety, F. DiMarcello, A. G. Richardson, “Transmission, Splicing, and Cabling Performance of Dispersion-Shifted Single-Mode Fiber,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984), paper TUI5.

El-Ibiary, M. Y.

M. Y. El-Ibiary, “Parameter Optimization in Graded-Index Dispersion-Shifted Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-4, 364–367 (1986).
[CrossRef]

Fleming, J. W.

J. W. Fleming, “Material Dispersion in Lightguide Glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

Francois, P.-L.

P.-L. Francois, “Tolerance Requirements for Dispersion Free Single-Mode Fiber Design: Influence of Geometrical Parameters, Dopant Diffusion, and Axial Dip,” IEEE J. Quantum Electron. QE-18, 1490–1499 (1982).
[CrossRef]

Fukuda, O.

T. Moriyama, M. Miyamoto, M. Akiyama, R. Sanada, O. Fukuda, T. Miya, R. Chida, “Fabrication of Low Loss and Long Length VAD Fibers for 1.55 μm Wavelength Region,” in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982), pp. 31–35.

Gerald, C. F.

C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, MA, 1984), Chap. 4.

Ghatak, A.

A. Ghatak, K. Thyagarajan, “Graded-Index Optical Waveguides: a Review,” Prog. Opt. 18, 1–126 (1980).
[CrossRef]

Gill, S.

S. Gill, “A Process for the Step by Step Integration of Differential Equations in an Automatic Digital Computing Machine,” Proc. Cambridge Philos. Soc. 47, 96–108 (1951).
[CrossRef]

Jang, S. J.

M. A. Saifi, S. J. Jang, L. G. Cohen, J. Stone, “Triangular-Profile Single-Mode Fiber,” Opt. Lett. 7, 43–45 (1982).
[CrossRef] [PubMed]

S. J. Jang, L. G. Cohen, W. L. Mammel, M. A. Saifi, “Experimental Verification of Ultra-Wide Bandwidth Spectra in Doubly-Clad Single-Mode Fiber,” Bell Syst. Tech. J. 61, 385–390 (1982).

Keck, D. B.

D. B. Keck, “Single-Mode Fibers Outperform Multimode Cables,” IEEE Spectrum 20, 30–37 (1983).

Krause, J. T.

A. D. Pearson, L. G. Cohen, W. A. Reed, J. T. Krause, E. A. Sigety, F. DiMarcello, A. G. Richardson, “Transmission, Splicing, and Cabling Performance of Dispersion-Shifted Single-Mode Fiber,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984), paper TUI5.

Lumish, S.

L. G. Cohen, W. A. Mammel, S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. QE-18, 49–53 (1982).
[CrossRef]

L. G. Cohen, W. A. Mammel, S. Lumish, “Tailoring the Shapes of Dispersion Spectra to Control Bandwidths in Single-Mode Fibers,” Opt. Lett. 7, 183–185 (1982).
[CrossRef] [PubMed]

Mammel, W. A.

L. G. Cohen, W. A. Mammel, S. Lumish, “Tailoring the Shapes of Dispersion Spectra to Control Bandwidths in Single-Mode Fibers,” Opt. Lett. 7, 183–185 (1982).
[CrossRef] [PubMed]

L. G. Cohen, W. A. Mammel, S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. QE-18, 49–53 (1982).
[CrossRef]

Mammel, W. L.

S. J. Jang, L. G. Cohen, W. L. Mammel, M. A. Saifi, “Experimental Verification of Ultra-Wide Bandwidth Spectra in Doubly-Clad Single-Mode Fiber,” Bell Syst. Tech. J. 61, 385–390 (1982).

Marcuse, D.

Miya, T.

T. Moriyama, M. Miyamoto, M. Akiyama, R. Sanada, O. Fukuda, T. Miya, R. Chida, “Fabrication of Low Loss and Long Length VAD Fibers for 1.55 μm Wavelength Region,” in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982), pp. 31–35.

Miyamoto, M.

T. Moriyama, M. Miyamoto, M. Akiyama, R. Sanada, O. Fukuda, T. Miya, R. Chida, “Fabrication of Low Loss and Long Length VAD Fibers for 1.55 μm Wavelength Region,” in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982), pp. 31–35.

Moriyama, T.

T. Moriyama, M. Miyamoto, M. Akiyama, R. Sanada, O. Fukuda, T. Miya, R. Chida, “Fabrication of Low Loss and Long Length VAD Fibers for 1.55 μm Wavelength Region,” in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982), pp. 31–35.

Ogawa, K.

K. Ogawa, “Analysis of Mode-Partition Noise in Laser System,” IEEE J. Quantum Electron. QE-18, 849–855 (1982).
[CrossRef]

Paek, U. C.

U. C. Paek, G. E. Peterson, A. Carnevale, “Dispersionless Single-Mode Lightguides with α Index Profiles,” Bell Syst. Tech. J. 60, 583–598 (1981).

Pearson, A. D.

A. D. Pearson, L. G. Cohen, W. A. Reed, J. T. Krause, E. A. Sigety, F. DiMarcello, A. G. Richardson, “Transmission, Splicing, and Cabling Performance of Dispersion-Shifted Single-Mode Fiber,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984), paper TUI5.

Peterson, G. E.

U. C. Paek, G. E. Peterson, A. Carnevale, “Dispersionless Single-Mode Lightguides with α Index Profiles,” Bell Syst. Tech. J. 60, 583–598 (1981).

Ralston, A.

A. Ralston, H. S. Wilf, Mathematical Methods for Digital Computers (Wiley, New York, 1960), pp. 111–120.

Reed, W. A.

A. D. Pearson, L. G. Cohen, W. A. Reed, J. T. Krause, E. A. Sigety, F. DiMarcello, A. G. Richardson, “Transmission, Splicing, and Cabling Performance of Dispersion-Shifted Single-Mode Fiber,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984), paper TUI5.

Richardson, A. G.

A. D. Pearson, L. G. Cohen, W. A. Reed, J. T. Krause, E. A. Sigety, F. DiMarcello, A. G. Richardson, “Transmission, Splicing, and Cabling Performance of Dispersion-Shifted Single-Mode Fiber,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984), paper TUI5.

Ritter, J. E.

T. D. Croft, J. E. Ritter, V. A. Bhagavatula, “Low Loss Dispersion-Shifted Fiber Manufactured by the OVD Process,” IEEE/OSA J. Lightwave Technol. LT-3, 931–934 (1985); Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD2.
[CrossRef]

Saifi, M. A.

M. A. Saifi, S. J. Jang, L. G. Cohen, J. Stone, “Triangular-Profile Single-Mode Fiber,” Opt. Lett. 7, 43–45 (1982).
[CrossRef] [PubMed]

S. J. Jang, L. G. Cohen, W. L. Mammel, M. A. Saifi, “Experimental Verification of Ultra-Wide Bandwidth Spectra in Doubly-Clad Single-Mode Fiber,” Bell Syst. Tech. J. 61, 385–390 (1982).

Sanada, R.

T. Moriyama, M. Miyamoto, M. Akiyama, R. Sanada, O. Fukuda, T. Miya, R. Chida, “Fabrication of Low Loss and Long Length VAD Fibers for 1.55 μm Wavelength Region,” in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982), pp. 31–35.

Sigety, E. A.

A. D. Pearson, L. G. Cohen, W. A. Reed, J. T. Krause, E. A. Sigety, F. DiMarcello, A. G. Richardson, “Transmission, Splicing, and Cabling Performance of Dispersion-Shifted Single-Mode Fiber,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984), paper TUI5.

Stone, J.

Thyagarajan, K.

A. Ghatak, K. Thyagarajan, “Graded-Index Optical Waveguides: a Review,” Prog. Opt. 18, 1–126 (1980).
[CrossRef]

Wheatley, P. O.

C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, MA, 1984), Chap. 4.

White, K. I.

K. I. White, “Design Parameters for Dispersion-Shifted Triangular-Profile Single-mode Fibers,” Electron. Lett. 18, 725–727 (1982).
[CrossRef]

Wilf, H. S.

A. Ralston, H. S. Wilf, Mathematical Methods for Digital Computers (Wiley, New York, 1960), pp. 111–120.

Yip, G. L.

G. L. Yip, Y. H. Ahmew, “Propagation Characteristics of Radially Inhomogeneous Optical Fiber,” Electron. Lett. 10, 37–38(1974).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (2)

U. C. Paek, G. E. Peterson, A. Carnevale, “Dispersionless Single-Mode Lightguides with α Index Profiles,” Bell Syst. Tech. J. 60, 583–598 (1981).

S. J. Jang, L. G. Cohen, W. L. Mammel, M. A. Saifi, “Experimental Verification of Ultra-Wide Bandwidth Spectra in Doubly-Clad Single-Mode Fiber,” Bell Syst. Tech. J. 61, 385–390 (1982).

Electron. Lett. (4)

J. W. Fleming, “Material Dispersion in Lightguide Glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

K. B. Chung, S. S. Choi, “Propagation Characteristics of a Triangular-Index Doubly Clad Monomode Fiber,” Electron. Lett. 21, 271–272 (1985).
[CrossRef]

G. L. Yip, Y. H. Ahmew, “Propagation Characteristics of Radially Inhomogeneous Optical Fiber,” Electron. Lett. 10, 37–38(1974).
[CrossRef]

K. I. White, “Design Parameters for Dispersion-Shifted Triangular-Profile Single-mode Fibers,” Electron. Lett. 18, 725–727 (1982).
[CrossRef]

IEEE J. Quantum Electron. (3)

K. Ogawa, “Analysis of Mode-Partition Noise in Laser System,” IEEE J. Quantum Electron. QE-18, 849–855 (1982).
[CrossRef]

L. G. Cohen, W. A. Mammel, S. Lumish, “Dispersion and Bandwidth Spectra in Single-Mode Fibers,” IEEE J. Quantum Electron. QE-18, 49–53 (1982).
[CrossRef]

P.-L. Francois, “Tolerance Requirements for Dispersion Free Single-Mode Fiber Design: Influence of Geometrical Parameters, Dopant Diffusion, and Axial Dip,” IEEE J. Quantum Electron. QE-18, 1490–1499 (1982).
[CrossRef]

IEEE Spectrum (1)

D. B. Keck, “Single-Mode Fibers Outperform Multimode Cables,” IEEE Spectrum 20, 30–37 (1983).

IEEE/OSA J. Lightwave Technol. (3)

T. D. Croft, J. E. Ritter, V. A. Bhagavatula, “Low Loss Dispersion-Shifted Fiber Manufactured by the OVD Process,” IEEE/OSA J. Lightwave Technol. LT-3, 931–934 (1985); Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD2.
[CrossRef]

B. J. Ainslie, C. R. Day, “A Review of Single-Mode Fibers with Modified Dispersion Characteristics,” IEEE/OSA J. Lightwave Technol. LT-4, 967–979 (1986).
[CrossRef]

M. Y. El-Ibiary, “Parameter Optimization in Graded-Index Dispersion-Shifted Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-4, 364–367 (1986).
[CrossRef]

Opt. Lett. (2)

Proc. Cambridge Philos. Soc. (1)

S. Gill, “A Process for the Step by Step Integration of Differential Equations in an Automatic Digital Computing Machine,” Proc. Cambridge Philos. Soc. 47, 96–108 (1951).
[CrossRef]

Prog. Opt. (1)

A. Ghatak, K. Thyagarajan, “Graded-Index Optical Waveguides: a Review,” Prog. Opt. 18, 1–126 (1980).
[CrossRef]

Other (6)

Y. H. Ahmew, “Propagation Characteristics of the Self-Focusing Fiber Waveguide,” M. Eng. Thesis, Electrical Engineering Dept. McGill U. (1973).

A. Ralston, H. S. Wilf, Mathematical Methods for Digital Computers (Wiley, New York, 1960), pp. 111–120.

D. M. Cooper, S. P. Craig, C. R. Day, B. J. Ainslie, “Multiple-Index Structures for Dispersion-Shifted Single-Mode Fibers,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1985), paper WD4.

T. Moriyama, M. Miyamoto, M. Akiyama, R. Sanada, O. Fukuda, T. Miya, R. Chida, “Fabrication of Low Loss and Long Length VAD Fibers for 1.55 μm Wavelength Region,” in Technical Digest, Eighth European Conference on Optical Communication, Cannes (1982), pp. 31–35.

A. D. Pearson, L. G. Cohen, W. A. Reed, J. T. Krause, E. A. Sigety, F. DiMarcello, A. G. Richardson, “Transmission, Splicing, and Cabling Performance of Dispersion-Shifted Single-Mode Fiber,” in Technical Digest, Conference on Optical Fiber Communication (Optical Society of America, Washington, DC, 1984), paper TUI5.

C. F. Gerald, P. O. Wheatley, Applied Numerical Analysis (Addison-Wesley, Reading, MA, 1984), Chap. 4.

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Figures (8)

Fig. 1
Fig. 1

Refractive index profile of the fibers under study.

Fig. 2
Fig. 2

(a) Total dispersion as a function of wavelength for fibers 1–6. (b) Calculated sensitivity dD t / vs the normalized trench parameter c/a. (c) Total dispersion as a function of wavelength for fibers 7 and 8.

Fig. 3
Fig. 3

Total dispersion as a function of relative change in the core: (a) for fibers 1–6 and (b) for fiber 7 and 8.

Fig. 4
Fig. 4

(a) Larger core radius satisfying D t = 0 at 1.55 μm vs trench parameter b/a. (b) Total dispersion vs wavelength for fibers 9 and 10. (c) Total dispersion as a function of relative change in the core radius for fibers 9 and 10. (d) Smaller core radius as a function of b/a.

Fig. 5
Fig. 5

D t vs core radius a.

Fig. 6
Fig. 6

Sensitivity − o /da vs c/a.

Fig. 7
Fig. 7

Total dispersion vs relative change in (a) Δ1 and (b) Δ2.

Fig. 8
Fig. 8

Bandwidth–length product vs wavelength for fibers 1, 4, 5, and 6.

Tables (1)

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Table I Parameters of Fibers Under Study

Equations (15)

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F ( x ) = [ f 1 ( x ) f 2 ( x ) f 3 ( x ) f 4 ( x ) ] .
F 1 ( r , Φ , z , t ) = [ E z E Φ H z H Φ ] = [ x n f 1 ( x ) x n - 1 f 2 ( x ) i η 0 - 1 x n f 3 ( x ) i η 0 - 1 x n - 1 f 4 ( x ) ] exp i ( ω t - β z - n Φ ) ,
d F ( x ) d x = A ( x ) F ( x ) .
F ( x ) = B ( x , x o ) F ( x o ) ,
F ( k o a - ) = B ( k o a - , 0 ) F ( 0 ) .
D t = 1 L d t d λ = - λ c o d 2 U d λ 2 ,
d 2 U d λ 2 = - U ( λ + 2 Δ λ ) + 16 U ( λ + Δ λ ) - 30 U ( λ ) + 16 U ( λ - Δ λ ) - U ( λ - 2 Δ λ ) 12 ( Δ λ ) 2 + O ( Δ λ 4 ) .
n 2 - 1 = i = 1 3 a i λ 2 λ 2 - b i 2 ,
a 1 = 0.696750 , b 1 = 0.069066 , a 2 = 0.408218 , b 2 = 0.115662 , a 3 = 0.890815 , b 3 = 9.900559.
n 1 = n 2 / ( 1 - Δ 1 ) , n 3 = n 2 ( 1 - Δ 2 ) , n ( r ) = n 1 [ 1 - Δ 1 ( r / a ) ]             for 0 r a .
H c ( Ω , λ ) = 1 1 + ( L Ω σ s 2 4 | d D t d λ | ) 2 4 × exp { - ( L Ω σ s 2 D t 2 ) 2 [ 1 + ( L Ω σ s 2 4 | d D t d λ | ) 2 ] } ,
f BW · L = L Ω 2 π = 2.47 × 10 6 σ s 2 | d D t d λ |             GHz · km ,
( L Ω σ s 2 4 | d D t d λ | ) 2
f BW · L = L Ω 2 π = 375 σ s D t             GHz · km .
f BW · L 1 π arcsin ( 3 4 P 1 + P 2 P 1 P 2 ) D t σ + 1 2 d D t d λ σ 2 ( P 1 - P 2 ) / ( P 1 + P 2 ) ,

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