Abstract

An exhaustive and simple method for dispersion flattening in double-clad single-mode fibers is presented. The idea is to generate all such fibers with a certain cutoff wavelength and then find, by one-dimensional minimization and direct inspection, fibers yielding minimum dispersion. As examples, the root mean square chromatic dispersion over the wavelength range (1.25, 1.60 μm) is minimized for a W fiber and also for a triangular-index fiber with a depressed inner cladding. The material dispersion is included through a Sellmeier refractive-index formula. The full vector solution of Maxwell's equations is used. It is found, as is well known, that the W fiber is capable of dispersion flattening. The validity of the numerical results presented depends on the validity of the approximate refractive-index model used.

© 1994 Optical Society of America

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References

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  1. B. J. Ainslie, C. R. Day, “A review of single-mode fibers with modified dispersion characteristics,” J. Lightwave Technol. LT-4, 967–979 (1986).
    [Crossref]
  2. R. Lundin, “Minimization of the chromatic dispersion over a broad wavelength range in a single-mode optical fiber,” Appl. Opt. 32, 3241–3245 (1993).
    [Crossref] [PubMed]
  3. B. P. Nelson, K. J. Blow, N. J. Doran, “Synthesis of monomode fiber profiles using multivariate optimization,” Electron. Lett. 20, 704–705 (1984).
    [Crossref]
  4. G. Trommer, “Synthesis of monomode fiber profiles by solving a modified eigenvalue problem,” Electron. Lett. 21, 458–460 (1985).
  5. G. Trommer, “Synthesis of monomode fiber profiles by solving an almost linear system of algebraic equations,” Electron. Lett. 21, 727–729 (1985).
    [Crossref]
  6. P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, San Diego, Calif., 1981).
  7. K. Okamoto, T. Edahiro, A. Kawana, T. Miya, “Dispersion minimization in single-mode fibers over a wide spectral range,” Electron. Lett. 15, 729–731 (1979).
    [Crossref]
  8. H. R. D. Sunak, S. P. Bastien, “Universal single-mode dispersion-flattened fluoride fiber designed for optimum performance from 1.5 to 2.9 μm,” Electron. Lett. 24, 879–880 (1988).
    [Crossref]
  9. P. L. Francois, “Zero dispersion in attenuation optimized doubly clad fibers,” J. Lightwave Technol. LT-1, 26–37 (1983).
    [Crossref]
  10. L. G. Cohen, W. L. Mammel, S. J. Jang, “Low-loss quadruple clad single-mode lightguides with dispersion below 2 ps/km nm over the 1.28 μm–1.65 μm wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
    [Crossref]
  11. J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
    [Crossref]
  12. M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), pp. 243–245.
  13. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), pp. 878–879.
  14. R. Lundin, “A general power-series expansion method for exact analysis of the guided modes in an optical fiber,” J. Lightwave Technol. LT-4, 1617–1625 (1986).
    [Crossref]
  15. A. Safaai-Jazi, L. J. Lu, “Evaluation of chromatic dispersion in fibers,” Opt. Lett. 14, 760–762 (1989).
    [Crossref] [PubMed]

1993 (1)

1989 (1)

1988 (1)

H. R. D. Sunak, S. P. Bastien, “Universal single-mode dispersion-flattened fluoride fiber designed for optimum performance from 1.5 to 2.9 μm,” Electron. Lett. 24, 879–880 (1988).
[Crossref]

1986 (2)

B. J. Ainslie, C. R. Day, “A review of single-mode fibers with modified dispersion characteristics,” J. Lightwave Technol. LT-4, 967–979 (1986).
[Crossref]

R. Lundin, “A general power-series expansion method for exact analysis of the guided modes in an optical fiber,” J. Lightwave Technol. LT-4, 1617–1625 (1986).
[Crossref]

1985 (2)

G. Trommer, “Synthesis of monomode fiber profiles by solving a modified eigenvalue problem,” Electron. Lett. 21, 458–460 (1985).

G. Trommer, “Synthesis of monomode fiber profiles by solving an almost linear system of algebraic equations,” Electron. Lett. 21, 727–729 (1985).
[Crossref]

1984 (1)

B. P. Nelson, K. J. Blow, N. J. Doran, “Synthesis of monomode fiber profiles using multivariate optimization,” Electron. Lett. 20, 704–705 (1984).
[Crossref]

1983 (1)

P. L. Francois, “Zero dispersion in attenuation optimized doubly clad fibers,” J. Lightwave Technol. LT-1, 26–37 (1983).
[Crossref]

1982 (1)

L. G. Cohen, W. L. Mammel, S. J. Jang, “Low-loss quadruple clad single-mode lightguides with dispersion below 2 ps/km nm over the 1.28 μm–1.65 μm wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[Crossref]

1979 (1)

K. Okamoto, T. Edahiro, A. Kawana, T. Miya, “Dispersion minimization in single-mode fibers over a wide spectral range,” Electron. Lett. 15, 729–731 (1979).
[Crossref]

1978 (1)

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[Crossref]

Adams, M. J.

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), pp. 243–245.

Ainslie, B. J.

B. J. Ainslie, C. R. Day, “A review of single-mode fibers with modified dispersion characteristics,” J. Lightwave Technol. LT-4, 967–979 (1986).
[Crossref]

Bastien, S. P.

H. R. D. Sunak, S. P. Bastien, “Universal single-mode dispersion-flattened fluoride fiber designed for optimum performance from 1.5 to 2.9 μm,” Electron. Lett. 24, 879–880 (1988).
[Crossref]

Blow, K. J.

B. P. Nelson, K. J. Blow, N. J. Doran, “Synthesis of monomode fiber profiles using multivariate optimization,” Electron. Lett. 20, 704–705 (1984).
[Crossref]

Cohen, L. G.

L. G. Cohen, W. L. Mammel, S. J. Jang, “Low-loss quadruple clad single-mode lightguides with dispersion below 2 ps/km nm over the 1.28 μm–1.65 μm wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[Crossref]

Day, C. R.

B. J. Ainslie, C. R. Day, “A review of single-mode fibers with modified dispersion characteristics,” J. Lightwave Technol. LT-4, 967–979 (1986).
[Crossref]

Doran, N. J.

B. P. Nelson, K. J. Blow, N. J. Doran, “Synthesis of monomode fiber profiles using multivariate optimization,” Electron. Lett. 20, 704–705 (1984).
[Crossref]

Edahiro, T.

K. Okamoto, T. Edahiro, A. Kawana, T. Miya, “Dispersion minimization in single-mode fibers over a wide spectral range,” Electron. Lett. 15, 729–731 (1979).
[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, “Zero dispersion in attenuation optimized doubly clad fibers,” J. Lightwave Technol. LT-1, 26–37 (1983).
[Crossref]

Gill, P. E.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, San Diego, Calif., 1981).

Jang, S. J.

L. G. Cohen, W. L. Mammel, S. J. Jang, “Low-loss quadruple clad single-mode lightguides with dispersion below 2 ps/km nm over the 1.28 μm–1.65 μm wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[Crossref]

Kawana, A.

K. Okamoto, T. Edahiro, A. Kawana, T. Miya, “Dispersion minimization in single-mode fibers over a wide spectral range,” Electron. Lett. 15, 729–731 (1979).
[Crossref]

Lu, L. J.

Lundin, R.

R. Lundin, “Minimization of the chromatic dispersion over a broad wavelength range in a single-mode optical fiber,” Appl. Opt. 32, 3241–3245 (1993).
[Crossref] [PubMed]

R. Lundin, “A general power-series expansion method for exact analysis of the guided modes in an optical fiber,” J. Lightwave Technol. LT-4, 1617–1625 (1986).
[Crossref]

Mammel, W. L.

L. G. Cohen, W. L. Mammel, S. J. Jang, “Low-loss quadruple clad single-mode lightguides with dispersion below 2 ps/km nm over the 1.28 μm–1.65 μm wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[Crossref]

Miya, T.

K. Okamoto, T. Edahiro, A. Kawana, T. Miya, “Dispersion minimization in single-mode fibers over a wide spectral range,” Electron. Lett. 15, 729–731 (1979).
[Crossref]

Murray, W.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, San Diego, Calif., 1981).

Nelson, B. P.

B. P. Nelson, K. J. Blow, N. J. Doran, “Synthesis of monomode fiber profiles using multivariate optimization,” Electron. Lett. 20, 704–705 (1984).
[Crossref]

Okamoto, K.

K. Okamoto, T. Edahiro, A. Kawana, T. Miya, “Dispersion minimization in single-mode fibers over a wide spectral range,” Electron. Lett. 15, 729–731 (1979).
[Crossref]

Safaai-Jazi, A.

Sunak, H. R. D.

H. R. D. Sunak, S. P. Bastien, “Universal single-mode dispersion-flattened fluoride fiber designed for optimum performance from 1.5 to 2.9 μm,” Electron. Lett. 24, 879–880 (1988).
[Crossref]

Trommer, G.

G. Trommer, “Synthesis of monomode fiber profiles by solving a modified eigenvalue problem,” Electron. Lett. 21, 458–460 (1985).

G. Trommer, “Synthesis of monomode fiber profiles by solving an almost linear system of algebraic equations,” Electron. Lett. 21, 727–729 (1985).
[Crossref]

Wright, M. H.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, San Diego, Calif., 1981).

Appl. Opt. (1)

Electron. Lett. (7)

B. P. Nelson, K. J. Blow, N. J. Doran, “Synthesis of monomode fiber profiles using multivariate optimization,” Electron. Lett. 20, 704–705 (1984).
[Crossref]

G. Trommer, “Synthesis of monomode fiber profiles by solving a modified eigenvalue problem,” Electron. Lett. 21, 458–460 (1985).

G. Trommer, “Synthesis of monomode fiber profiles by solving an almost linear system of algebraic equations,” Electron. Lett. 21, 727–729 (1985).
[Crossref]

L. G. Cohen, W. L. Mammel, S. J. Jang, “Low-loss quadruple clad single-mode lightguides with dispersion below 2 ps/km nm over the 1.28 μm–1.65 μm wavelength range,” Electron. Lett. 18, 1023–1024 (1982).
[Crossref]

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[Crossref]

K. Okamoto, T. Edahiro, A. Kawana, T. Miya, “Dispersion minimization in single-mode fibers over a wide spectral range,” Electron. Lett. 15, 729–731 (1979).
[Crossref]

H. R. D. Sunak, S. P. Bastien, “Universal single-mode dispersion-flattened fluoride fiber designed for optimum performance from 1.5 to 2.9 μm,” Electron. Lett. 24, 879–880 (1988).
[Crossref]

J. Lightwave Technol. (3)

P. L. Francois, “Zero dispersion in attenuation optimized doubly clad fibers,” J. Lightwave Technol. LT-1, 26–37 (1983).
[Crossref]

R. Lundin, “A general power-series expansion method for exact analysis of the guided modes in an optical fiber,” J. Lightwave Technol. LT-4, 1617–1625 (1986).
[Crossref]

B. J. Ainslie, C. R. Day, “A review of single-mode fibers with modified dispersion characteristics,” J. Lightwave Technol. LT-4, 967–979 (1986).
[Crossref]

Opt. Lett. (1)

Other (3)

M. J. Adams, An Introduction to Optical Waveguides (Wiley, New York, 1981), pp. 243–245.

M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (National Bureau of Standards, Washington, D.C., 1964), pp. 878–879.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, San Diego, Calif., 1981).

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Figures (2)

Fig. 1
Fig. 1

The rms value f of the chromatic dispersion over the vacuum wavelength range (1.25 μm, 1.60 μm) as a function of the outer radius a in a W fiber. The cutoff vacuum wavelength is 1.25 μm. The relative refractive-index increases in the core and in the inner cladding are 1.02 and 0.99, respectively.

Fig. 2
Fig. 2

Chromatic dispersion for the optimal W fiber (N 1, N 2, b, a) = (1.02, 0.99, 1.91 (μm, 2.85 μm). The rms value of the chromatic dispersion over the vacuum wavelength range (1.25 μm, 1.60 μm) is equal to 0.9 ps/(km nm). The cutoff vacuum wavelength is 1.25 μm.

Tables (3)

Tables Icon

Table 1 Minimum rms Chromatic Dispersion (in Picoseconds per Kilometers Times Nanometers) in a W Fiber for Different Doping Levels in the Core and in the Inner Cladding a

Tables Icon

Table 2 Minimum rms Chromatic Dispersion (in Picoseconds per Kilometers Times Nanometers) in a W Fiber for Different Doping Levels in the Core and in the Inner Cladding a

Tables Icon

Table 3 Minimum rms Chromatic Dispersion (in picoseconds per kilometer times nanometers) in a Triangular-lndex Fiber with a Depressed Inner Cladding for Different Doping Levels in the Core Center and in the Inner Cladding a

Equations (6)

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n ( r , λ 0 ) = N ( r , λ 0 ) n s ( λ 0 ) ,
n ( r , λ 0 ) = N ( r ) n s ( λ 0 ) .
C = λ 0 c d 2 n e d λ 0 2 ,
f = ( 1 λ 2 λ 1 λ 1 λ 2 C 2 ( λ 0 ) d λ 0 ) 1 / 2 ,
N ( r ) = { N 1 0 r < b N 2 b r < a 1 r a ,
N ( r ) = { N 1 + ( 1 N 1 ) r b 0 r < b N 2 b r < a 1 r a .

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