Abstract

A new model for analyzing optical properties of silicate glass materials including borosilicates has been developed. The model is based on computing refractive-index and density values of a given optical glass whose oxide composition is known in terms of weight fractions. The refractive-index variation with wavelength has also been used to predict the chromatic behavior of these glasses. The model has been compared with the existing chromatic model and was found to give more accurate values for borosilicates.

© 1994 Optical Society of America

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References

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  1. S. D. Fantone, “Refractive index and spectral models for gradient index materials,” Appl. Opt. 22, 432–440 (1983).
    [CrossRef] [PubMed]
  2. D. P. Ryan-Howard, D. T. Moore, “Model for the chromatic properties of gradient-index glass,” Appl. Opt. 24, 4356–4366 (1985).
    [CrossRef] [PubMed]
  3. M. L. Huggins, “The dispersion of silicate glasses as a function of composition,” J. Opt. Soc. Am. 30, 514–518 (1940).
    [CrossRef]
  4. M. L. Huggins, K. H. Sun, D. O. Davis, “The dispersion of silicate glasses as a function of composition. II,” J. Opt. Soc. Am. 32, 635–650 (1942).
    [CrossRef]
  5. M. L. Huggins, K. H. Sun, “Calculation of density and optical constants of a glass from its composition in weight percentage,” J. Opt. Soc. Am. 26, 4–11 (1936).
  6. M. L. Huggins, “The density of silicate glasses as a function of composition,” J. Opt. Soc. Am. 30, 420–430 (1940).
    [CrossRef]
  7. M. L. Huggins, “The refractive index of silicate glasses as a function of composition,” J. Opt. Soc. Am. 30, 495–504 (1940).
    [CrossRef]
  8. M. B. Volf, “Chemical approach to glass,” Glass Sci. Technol. 7, 118–127 (1984).

1985 (1)

1984 (1)

M. B. Volf, “Chemical approach to glass,” Glass Sci. Technol. 7, 118–127 (1984).

1983 (1)

1942 (1)

1940 (3)

1936 (1)

M. L. Huggins, K. H. Sun, “Calculation of density and optical constants of a glass from its composition in weight percentage,” J. Opt. Soc. Am. 26, 4–11 (1936).

Davis, D. O.

Fantone, S. D.

Huggins, M. L.

Moore, D. T.

Ryan-Howard, D. P.

Sun, K. H.

M. L. Huggins, K. H. Sun, D. O. Davis, “The dispersion of silicate glasses as a function of composition. II,” J. Opt. Soc. Am. 32, 635–650 (1942).
[CrossRef]

M. L. Huggins, K. H. Sun, “Calculation of density and optical constants of a glass from its composition in weight percentage,” J. Opt. Soc. Am. 26, 4–11 (1936).

Volf, M. B.

M. B. Volf, “Chemical approach to glass,” Glass Sci. Technol. 7, 118–127 (1984).

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Figures (8)

Fig. 1
Fig. 1

VSi versus NSi for all silicate glasses: ◯, nonborosilicates; *, borosilicates.

Fig. 2
Fig. 2

VSi versus NSi for nonborosilicates. We fitted the continuous curve by using the least-squares method.

Fig. 3
Fig. 3

Comparison between the modified HSD model (◯) and the present model (*) for the rofractive index and density of nonborosilicates.

Fig. 4
Fig. 4

VSi verus NSi for borosilicates using the modified HSD model.

Fig. 5
Fig. 5

VSi versus NSi for borosilicates as given by the present model when the following exist: (a) SiO2, B2O3, Na2O, and BaO (+, for NBa < 0.1; x for NBa ≥ 0.1); (b) SiO2, B2O3, and Na2O, (c). SiO2, B2O3, and BaO.

Fig. 6
Fig. 6

VB versus NB for borosilicates as given by the present model when the following exist: (a) VB′ versus NB′ for SiO2, B2O3, Na2O, and BaO; (b) VB′ versus NB′ for SiO2, B203, and Na2O; (c) VB′ versus NB′ for SiO2, B2O3, and BaO; (d) VB″ versus VB″ for all borosilicates.

Fig. 7
Fig. 7

VSi versus NSi for borosilicates in which the data points of Figs. 5(a)–5(c) are grouped together.

Fig. 8
Fig. 8

Comparison between the modified HSD model (◯) and the present model (*) for the refractive index and the density of borosilicates.

Tables (1)

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Table 1 Coefficients Used in Equation VM = C2NM2 + C1NM + C0

Equations (29)

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R = ( n 1 ) / ρ ,
R M O = ( m R M + n R O ) / W ,
n = 1 + d R i f i , i = 1 M ,
ρ = 1 / ( A V 0 ) ,
n = 1 + R i f i / A V 0 .
n λ = 1 + a M λ N M V 0 ,
a M λ = R M λ W M m M
N M = ( m M f M / W M ) A
V 0 = k + V 0 , i , i = 1 M ,
V 0 , M = b M + c M N M ,
a M λ = d M [ 1 ( g M 1 / λ 2 ) 0.000048 λ 2 ] ,
a M λ = d M ° [ 1 ( g M ° 1 / λ 2 ) 0.000048 λ 2 ] + d M [ 1 ( g M 1 / λ 2 ) ] N M ,
a M λ = d M ° [ 1 ( g M ° 1 / λ 2 ) 0.000048 λ 2 ] + d M [ 1 ( g M 1 / λ 2 ) ] N M 2 .
N B = N B + N B ,
N B = 2 4 N Si 3 N B , N B = 4 ( N Si + N B ) 2 if ( N Si + N B ) > 0.5 , N B = N B , N B = 0 if ( N Si + N B ) < 0.5.
N si B = N Si + N B for N B / N Si < 0.55 , N si B = N Si + 0.85 N B for N B / N Si 0.55.
V 0 = a i λ N i ( n λ 1 )
V 0 = 1 A ρ .
V 0 = k + V 0 , Si + V 0 , i
V 0 , Si = V 0 V 0 , i .
V Si = 21.1559 N Si 2 + 3.4304 N Si + 6.4492.
V Si = 15.0273 N Si + 3.7652 when N Ba < 0.1 ,
V Si = 12.7956 N Si + 4.6694 when N Ba 0.1.
V Si = 25.1407 N Si + 0.4106.
V Si = 12.4391 N Si + 4.6792.
V B = 23.3735 N B 2 1.8103 N B + 1.6995.
V B = 25.4742 N B 2 + 5.1784 N B + 0.6019.
V B = 5.3647 N B + 1.2728.
V B = 19.2887 N B + 0.1149.

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