Abstract

A three-parameter description of optical fiber material dispersion is proposed which fits the available data and reveals the key roles played by bond length, lattice structure, chemical valence, average energy gap, and atomic mass. Using broadly applicable trends in electronic and phonon oscillator strengths, simple expressions are deduced for material dispersion including the zero crossover wavelength λc. These results impose severe constraints on fiber design which essentially limit the possibilities for significantly improving on pure silica to sulfates (particularly Li2SO4) and to BeF2. The predicted value of λc for the latter material is 1.05 μm.

© 1979 Optical Society of America

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References

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  1. D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
    [CrossRef]
  2. M. DiDomenico, Appl. Opt. 11, 652 (1972).
    [CrossRef] [PubMed]
  3. S. H. Wemple, J. Gabbe, G. D. Boyd, J. Appl. Phys. 46, 3597 (1975).
    [CrossRef]
  4. M. S. Mangir, R. W. Hellwarth, Phys. Rev. B 16, 856 (1977).
    [CrossRef]
  5. S. H. Wemple, J. Chem. Phys. 67, 2151 (1977).
    [CrossRef]
  6. J. D. Axe, Phys. Rev. A 139, 1215 (1965).
  7. J. W. Fleming, J. Am. Ceram. Soc. 59, 503 (1976); J. W. Fleming, Electron. Lett. 14, 326 (1978).
    [CrossRef]
  8. C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978); L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
    [CrossRef] [PubMed]
  9. J. Biscol, B. E. Warren, J. Am. Ceram. Soc. 21, 287 (1938).
    [CrossRef]
  10. J. Krogh-Moe, Phys. Chem. Glasses 3, 101 (1962); S. Greenblatt, P. J. Bray, Phys. Chem. Glasses 8, 213 (1967); M. F. Milberg, J. G. O’Keefe, R. A. Verhelst, H. O. Hooper, Phys. Chem. Glasses 13, 79 (1972).
  11. C. R. Hammond, S. R. Norman, Opt. Quantum Electron. 9, 399 (1977).
    [CrossRef]
  12. See references to Table I.
  13. S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, L. G. Van Uitert, J. Appl. Phys. 44, 5432 (1973).
    [CrossRef]
  14. R. L. Mozzi, B. E. Warren, J. Appl. Crystallogr. 3, 251 (1970).
    [CrossRef]
  15. Assuming that Ed ≈ 16 eV in Li2SO4, based on observed oscillator strengths in LiKSO4 and K2SO4, and making use of the single available refractive index value of 1.465 at 0.589 μm, we estimate that Eo ≈ 14.3 eV in Li2SO4.
  16. R. C. Weast, Ed., Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, 1975), p. B-76.

1978 (1)

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978); L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

1977 (3)

C. R. Hammond, S. R. Norman, Opt. Quantum Electron. 9, 399 (1977).
[CrossRef]

M. S. Mangir, R. W. Hellwarth, Phys. Rev. B 16, 856 (1977).
[CrossRef]

S. H. Wemple, J. Chem. Phys. 67, 2151 (1977).
[CrossRef]

1976 (1)

J. W. Fleming, J. Am. Ceram. Soc. 59, 503 (1976); J. W. Fleming, Electron. Lett. 14, 326 (1978).
[CrossRef]

1975 (2)

S. H. Wemple, J. Gabbe, G. D. Boyd, J. Appl. Phys. 46, 3597 (1975).
[CrossRef]

D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

1973 (1)

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, L. G. Van Uitert, J. Appl. Phys. 44, 5432 (1973).
[CrossRef]

1972 (1)

1970 (1)

R. L. Mozzi, B. E. Warren, J. Appl. Crystallogr. 3, 251 (1970).
[CrossRef]

1965 (1)

J. D. Axe, Phys. Rev. A 139, 1215 (1965).

1962 (1)

J. Krogh-Moe, Phys. Chem. Glasses 3, 101 (1962); S. Greenblatt, P. J. Bray, Phys. Chem. Glasses 8, 213 (1967); M. F. Milberg, J. G. O’Keefe, R. A. Verhelst, H. O. Hooper, Phys. Chem. Glasses 13, 79 (1972).

1938 (1)

J. Biscol, B. E. Warren, J. Am. Ceram. Soc. 21, 287 (1938).
[CrossRef]

Axe, J. D.

J. D. Axe, Phys. Rev. A 139, 1215 (1965).

Biscol, J.

J. Biscol, B. E. Warren, J. Am. Ceram. Soc. 21, 287 (1938).
[CrossRef]

Boyd, G. D.

S. H. Wemple, J. Gabbe, G. D. Boyd, J. Appl. Phys. 46, 3597 (1975).
[CrossRef]

Cohen, L. G.

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978); L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

DiDomenico, M.

Fleming, J. W.

J. W. Fleming, J. Am. Ceram. Soc. 59, 503 (1976); 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); L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

French, W. G.

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978); L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

Gabbe, J.

S. H. Wemple, J. Gabbe, G. D. Boyd, J. Appl. Phys. 46, 3597 (1975).
[CrossRef]

Gambling, W. A.

D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

Hammond, C. R.

C. R. Hammond, S. R. Norman, Opt. Quantum Electron. 9, 399 (1977).
[CrossRef]

Hellwarth, R. W.

M. S. Mangir, R. W. Hellwarth, Phys. Rev. B 16, 856 (1977).
[CrossRef]

Jaeger, R. E.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, L. G. Van Uitert, J. Appl. Phys. 44, 5432 (1973).
[CrossRef]

Krogh-Moe, J.

J. Krogh-Moe, Phys. Chem. Glasses 3, 101 (1962); S. Greenblatt, P. J. Bray, Phys. Chem. Glasses 8, 213 (1967); M. F. Milberg, J. G. O’Keefe, R. A. Verhelst, H. O. Hooper, Phys. Chem. Glasses 13, 79 (1972).

Lin, C.

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978); L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

Mangir, M. S.

M. S. Mangir, R. W. Hellwarth, Phys. Rev. B 16, 856 (1977).
[CrossRef]

Mozzi, R. L.

R. L. Mozzi, B. E. Warren, J. Appl. Crystallogr. 3, 251 (1970).
[CrossRef]

Norman, S. R.

C. R. Hammond, S. R. Norman, Opt. Quantum Electron. 9, 399 (1977).
[CrossRef]

Payne, D. N.

D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

Pinnow, D. A.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, L. G. Van Uitert, J. Appl. Phys. 44, 5432 (1973).
[CrossRef]

Rich, T. C.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, L. G. Van Uitert, J. Appl. Phys. 44, 5432 (1973).
[CrossRef]

Van Uitert, L. G.

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, L. G. Van Uitert, J. Appl. Phys. 44, 5432 (1973).
[CrossRef]

Warren, B. E.

R. L. Mozzi, B. E. Warren, J. Appl. Crystallogr. 3, 251 (1970).
[CrossRef]

J. Biscol, B. E. Warren, J. Am. Ceram. Soc. 21, 287 (1938).
[CrossRef]

Wemple, S. H.

S. H. Wemple, J. Chem. Phys. 67, 2151 (1977).
[CrossRef]

S. H. Wemple, J. Gabbe, G. D. Boyd, J. Appl. Phys. 46, 3597 (1975).
[CrossRef]

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, L. G. Van Uitert, J. Appl. Phys. 44, 5432 (1973).
[CrossRef]

Appl. Opt. (1)

Electron. Lett. (2)

D. N. Payne, W. A. Gambling, Electron. Lett. 11, 176 (1975).
[CrossRef]

C. Lin, L. G. Cohen, W. G. French, V. A. Foertmeyer, Electron. Lett. 14, 170 (1978); L. G. Cohen, C. Lin, Appl. Opt. 16, 3136 (1977).
[CrossRef] [PubMed]

J. Am. Ceram. Soc. (2)

J. Biscol, B. E. Warren, J. Am. Ceram. Soc. 21, 287 (1938).
[CrossRef]

J. W. Fleming, J. Am. Ceram. Soc. 59, 503 (1976); J. W. Fleming, Electron. Lett. 14, 326 (1978).
[CrossRef]

J. Appl. Crystallogr. (1)

R. L. Mozzi, B. E. Warren, J. Appl. Crystallogr. 3, 251 (1970).
[CrossRef]

J. Appl. Phys. (2)

S. H. Wemple, D. A. Pinnow, T. C. Rich, R. E. Jaeger, L. G. Van Uitert, J. Appl. Phys. 44, 5432 (1973).
[CrossRef]

S. H. Wemple, J. Gabbe, G. D. Boyd, J. Appl. Phys. 46, 3597 (1975).
[CrossRef]

J. Chem. Phys. (1)

S. H. Wemple, J. Chem. Phys. 67, 2151 (1977).
[CrossRef]

Opt. Quantum Electron. (1)

C. R. Hammond, S. R. Norman, Opt. Quantum Electron. 9, 399 (1977).
[CrossRef]

Phys. Chem. Glasses (1)

J. Krogh-Moe, Phys. Chem. Glasses 3, 101 (1962); S. Greenblatt, P. J. Bray, Phys. Chem. Glasses 8, 213 (1967); M. F. Milberg, J. G. O’Keefe, R. A. Verhelst, H. O. Hooper, Phys. Chem. Glasses 13, 79 (1972).

Phys. Rev. A (1)

J. D. Axe, Phys. Rev. A 139, 1215 (1965).

Phys. Rev. B (1)

M. S. Mangir, R. W. Hellwarth, Phys. Rev. B 16, 856 (1977).
[CrossRef]

Other (3)

See references to Table I.

Assuming that Ed ≈ 16 eV in Li2SO4, based on observed oscillator strengths in LiKSO4 and K2SO4, and making use of the single available refractive index value of 1.465 at 0.589 μm, we estimate that Eo ≈ 14.3 eV in Li2SO4.

R. C. Weast, Ed., Handbook of Chemistry and Physics (Chemical Rubber Co., Cleveland, 1975), p. B-76.

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Figures (2)

Fig. 1
Fig. 1

Plot of lattice oscillator strength El against prediction of Eq. (7). The result for ZnSe was taken from Ref. 4.

Fig. 2
Fig. 2

Material dispersion results for several solids based on the three-parameter fit described in the text. The borosilicate is sample II of Table III, the germania glass is sample III, and the soda borosilicate is sample VI. The phosphosilicate (sample IV) falls on the SiO2(B2O3) line below 1 μm and on the SiO2 line above 1 μm (see text for a discussion of BeF2).

Tables (5)

Tables Icon

Table I Short Table of Structure Factors Partially Extracted from Ref. 5; (v-) = vitreous and (c-) = crystalline

Tables Icon

Table II Predicted Phonon Oscillator Strengths El Based on Eq. (7)

Tables Icon

Table III Dispersion Parameters for Several Silica Based Glasses

Tables Icon

Table IV Values of Average Bond Length d ¯, Structure Factor β, and f-Value for Several Glasses Listed in Table III: Values in Parentheses are Estimates (See Text)

Tables Icon

Table V Dispersion Parameters and Crossover Wavelength λc for Two First Row Fluorides; Estimated Parameters are Enclosed in Parentheses (See Text)

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

M = λ c d 2 n d λ 2 ,
n 2 - 1 = E d E o / ( E o 2 - ω 2 ) - E l 2 / ω 2 ,
M ( λ ) 1.54 × 10 4 ( E d / E o 3 ) / ( n λ 3 ) - 2.17 × 10 3 E l 2 λ / n psec / nm · km ,
λ c 1.63 ( E d / E o 3 E l 2 ) 1 / 4 μ m .
E d = f n e Z a ( N A d 3 ) ,
E l 2 = 4 π N A Z a 2 e 2 / μ ¯ ,
E l = 0.86 Z a ( N A / μ ) 1 / 2 eV ,
M ~ f β Z a / ( E o 3 λ 3 ) ,
λ c ~ [ f μ d 3 / ( E o 3 Z a ) ] 1 / 4 .
M ( λ ) = ( 10 4 α 2 / n λ 3 ) ( E d / E o 3 ) ( 1 - Γ 2 ) - 2 ( 1 + A ) - 10 4 ( α - 2 / c o ) ( λ / n ) E l 2 ( 1 + B ) ,

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