Abstract

We thoroughly and critically review studies reporting the real (refractive index) and imaginary (absorption index) parts of the complex refractive index of silica glass over the spectral range from 30nm to 1000μm. The general features of the optical constants over the electromagnetic spectrum are relatively consistent throughout the literature. In particular, silica glass is effectively opaque for wavelengths shorter than 200nm and larger than 3.54.0μm. Strong absorption bands are observed (i) below 160nm due to the interaction with electrons, absorption by impurities, and the presence of OH groups and point defects; (ii) at 2.732.85, 3.5, and 4.3μm also caused by OH groups; and (iii) at 99.5, 12.5, and 2123μm due to Si―O―Si resonance modes of vibration. However, the actual values of the refractive and absorption indices can vary significantly due to the glass manufacturing process, crystallinity, wavelength, and temperature and to the presence of impurities, point defects, inclusions, and bubbles, as well as to the experimental uncertainties and approximations in the retrieval methods. Moreover, new formulas providing comprehensive approximations of the optical properties of silica glass are proposed between 7 and 50μm. These formulas are consistent with experimental data and substantially extend the spectral range of 0.217μm covered by existing formulas and can be used in various engineering applications.

© 2007 Optical Society of America

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2007 (1)

K. Kajihara, "Improvement of vacuum-ultraviolet transparency of silica glass by modification of point defects," J. Ceram. Soc. Jpn. 115, 85-91 (2007).
[CrossRef]

2006 (3)

A. M. Efimov and V. G. Pogareva, "IR absorption spectra of vitreous silica and silicate glasses: The nature of bands in the 1300 to 5000 cm−1 region," Chem. Geol. 229, 198-217 (2006).
[CrossRef]

D. D. S. Meneses, M. Malki, and P. Echegut, "Structure and lattice dynamics of binary lead silicate glasses investigated by infrared spectroscopy," J. Non-Crystal. Solids 352, 769-776 (2006).
[CrossRef]

T. Yamamuro, S. Sato, T. Zenno, N. Takeyama, H. Matsuhara, I. Maeda, and Y. Matsueda, "Measurement of refractive indices of 20 optical materials at low temperatures," Opt. Eng. 45, 083401 (2006).
[CrossRef]

2005 (1)

D. D. S. Meneses, G. Gruener, M. Malki, and P. Echegut, "Causal Voigt profile for modeling reflectivity spectra of glasses," J. Non-Cryst. Solids 351, 124-129 (2005).
[CrossRef]

2003 (1)

G.-L. Tan, M. F. Lemon, and R. H. French, "Optical properties and London dispersion forces of amorphous silica determined by vacuum ultraviolet spectroscopy and spectroscopic ellipsometry," J. Am. Ceram. Soc. 86, 1885-1892 (2003).
[CrossRef]

2001 (2)

C. Tan and J. Arndt, "Refractive index, optical dispersion, and group velocity of infrared wave in silica glass," J. Phys. Chem. Solids 62, 1087-1092 (2001).
[CrossRef]

M. Khashan and A. Nassif, "Dispersion of the optical constants of quartz and polymethyl methacrylate glasses in a wide spectral range: 0.2-3 μm," Opt. Commun. 188, 129-139 (2001).
[CrossRef]

2000 (5)

Y. Ikuta, S. Kikugawa, T. Kawahara, H. Mishiro, N. Shimodaira, and S. Yoshizawa, "New silica glass AQF for 157-nm lithography," Proc. SPIE 4000, 1510-1514 (2000).
[CrossRef]

N. Shimodaira, K. Saito, A. Ikushima, T. Kamihori, and S. Yoshizawa, "UV transmittance of fused silica glass influenced by thermal disorder," Proc. SPIE 4000, 1553-1559 (2000).
[CrossRef]

V. Plotnichenko, V. Sokolov, and E. Dianov, "Hydroxyl groups in high-purity silica glass," J. Non-Cryst. Solids 261, 186-194 (2000).
[CrossRef]

C. Tan and J. Arndt, "Temperature dependence of refractive index of glass SiO2 in the infrared wavelength range," J. Phys. Chem. Solids 61, 1315-1320 (2000).
[CrossRef]

Y. Ikuta, S. Kikugawa, T. Kawahara, H. Mishiro, K. Okada, K. Ochiai, K. Hino, T. Nakajima, M. Kawata, and S. Yoshizawa, "New modified silica glass for 157-nm lithography," Proc. SPIE 4066, 564-570 (2000).
[CrossRef]

1999 (3)

C. M. Smith and L. A. Moore, "Fused silica for 157-nm transmittance," Proc. SPIE 3676, 834-841 (1999).
[CrossRef]

P. J. Riu and C. Lapaz, "Practical limits of the Kramers-Krönig relationships applied to experimental bioimpedance data," Ann. N.Y. Acad. Sci. 873, 374-380 (1999).
[CrossRef]

C. Tan, "Optical interference and refractive index of silica glass in the infrared absorption region," J. Non-Cryst. Solids 249, 51-54 (1999).
[CrossRef]

1998 (1)

C. Tan, "Determination of refractive index of silica glass for infrared wavelengths by IR spectroscopy," J. Non-Cryst. Solids 223, 158-163 (1998).
[CrossRef]

1997 (1)

T. Henning and H. Mutschke, "Low-temperature infrared properties of cosmic dust analogues," Astron. Astrophys. 327, 743-754 (1997).

1996 (2)

K. M. Davis, A. Agarwal, M. Tomozawa, and K. Hirao, "Quantitative infrared spectroscopic measurement of hydroxyl concentrations in silica glass," J. Non-Cryst. Solids 203, 27-36 (1996).
[CrossRef]

L. Dombrovsky, "Quartz-fiber thermal insulation: infrared radiative properties and calculation of radiative-conductive heat transfer," J. Heat Transfer 118, 408-414 (1996).
[CrossRef]

1989 (1)

C. Koike, H. Hasegawa, N. Asada, and T. Komatuzaki, "Optical constants of fine particles for the infrared region," Mon. Not. R. Astron. Soc. 239, 127-137 (1989).

1987 (1)

A. P. Zhilinskii, A. P. Gorchakov, T. S. Egorova, and N. A. Miskinova, "Optical characteristics of fused quartz in the far IR range," Opt. Spectrosc. 62, 783-784 (1987).

1982 (3)

G. V. Saidov and E. B. Bernstein, "Optical constants of surface layer of fused quartz in the 900-1300 cm−1 range," Fiz. Khim. Stekla 8, 75-81 (1982).

R. K. Mamedov, G. M. Mansurov, and N. I. Dubovikov, "Optical constants of quartz glass in the IR range," Opt. Mekh. Prom. 4, 56 (1982) [Sov. J. Opt. Technol. 49, 256 (1982)].

G. M. Mansurov, R. K. Mamedov, S. Sudarushkin, V. K. Sidorin, K. K. Sidorin, V. I. Pshenitsyn, and V. M. Zolotarev, "Study of the nature of a polished quartz-glass surface by ellipsometric and spectroscopic methods," Opt. Spectrosc. 52, 852-857 (1982).

1979 (3)

E. Ellis, D. W. Johnson, A. Breeze, P. M. Magee, and P. G. Perkins, "The electronic structure and optical properties of oxide glasses I. SiO2, Na2O:SiO2 and Na2O:CaO:SiO2," Philos. Mag. B 40, 105-124 (1979).
[CrossRef]

H. Philipp, "The infrared optical properties of SiO2 and SiO2 layers on silicon," J. Appl. Phys. 50, 1053-1057 (1979).
[CrossRef]

A. V. Dvurechensky, V. Petrov, and V. Y. Reznik, "Spectral emissivity and absorption coefficient of silica glass at extremely high temperatures in the semitransparent region," Infrared Phys. 19, 465-469 (1979).
[CrossRef]

1978 (1)

T. J. Parker, J. E. Ford, and W. G. Chambers, "The optical constants of pure fused quartz in the far-infrared," Infrared Phys. 18, 215-219 (1978).
[CrossRef]

1977 (2)

P. Lamy, "Optical constants of crystalline and fused quartz in the far ultraviolet," Appl. Opt. 16, 2212-2214 (1977).
[CrossRef] [PubMed]

D. Griscom, "The electronic structure of SiO2: a review of recent spectroscopic and theoretical advances," J. Non-Cryst. Solids 24, 155-234 (1977).
[CrossRef]

1975 (1)

V. Petrov and S. Stepanov, "Radiation characteristics of quartz glasses spectral radiating power," Teplofiz. Vys. Temp. 13, 335-345 (1975).

1974 (2)

G. H. Sigel, "Ultraviolet spectra of silicate glasses: a review of some experimental evidence," J. Non-Cryst. Solids 13, 372-398 (1974).
[CrossRef]

T. Steyer, K. L. Day, and R. Huffman, "Infrared absorption by small amorphous quartz spheres," Appl. Opt. 13, 1586-1590 (1974).
[CrossRef] [PubMed]

1972 (1)

S. Popova, T. Tolstykh, and V. Vorobev, "Optical characteristics of amorphous quartz in the 1400-200 cm−1 region," Opt. Spectrosc. 33, 444-445 (1972).

1971 (2)

H. R. Philipp, "Optical properties of non-crystalline Si, SiO, SiOx and SiO2," J. Phys. Chem. Solids 32, 1935-1945 (1971).
[CrossRef]

E. Beder, C. Bass, and W. Shackleford, "Transmittivity and absorption of fused quartz between 0.2 and 3.5 μm from room temperature to 1500 °C," J. Am. Ceram. Soc. 10, 2263-2268 (1971).

1970 (4)

V. Zolotarev, "The optical constants of amorphous SiO2 and GeO2 in the valence band region," Opt. Spectrosc. 29, 34-37 (1970).

O. Girin, Y. Kondratev, and E. Raaben, "Optical constants and spectral microcharacteristics of NaO2-SiO2 glasses in the IR region of the spectrum," Opt. Spectrosc. 29, 397-403 (1970).

P. T. T. Wong and E. Whalley, "Infrared and Raman spectra of glasses. Part 2. Far infrared spectrum of vitreous silica in the range 100-15 cm−1," Discuss. Faraday Soc. 50, 94-102 (1970).
[CrossRef]

R. Bruckner, "Properties and structure of vitreous silica. I," J. Non-Cryst. Solids 5, 123-175 (1970).
[CrossRef]

1969 (1)

1968 (2)

W. Bagdade and R. Stolen, "Far infrared absorption in fused quartz and soft glass," J. Phys. Chem. Solids 29, 2001-2008 (1968).
[CrossRef]

M. Miler, "Infrared absorption of glassy silicon dioxide," Czech. J. Phys. 18, 354-362 (1968).
[CrossRef]

1967 (3)

1966 (3)

R. K. Bogens and A. G. Zhukov, "The optical constants of fused quartz in the far infrared," J. Appl. Spectrosc. 25, 54-55 (1966).
[CrossRef]

D. Heath and P. Sacher, "Effects of a simulated high-energy space environment on the ultraviolet transmittance of optical material between 1050 Å and 3000 Å," Appl. Opt. 5, 937-943 (1966).
[CrossRef] [PubMed]

H. R. Philipp, "Optical transitions in crystalline and fused quartz," Solid State Commun. 4, 73-75 (1966).
[CrossRef]

1965 (4)

D. Gillespie, A. Olsen, and L. Nichols, "Transmittance of optical materials at high temperatures in the 1-μ to 12-μ range," Appl. Opt. 4, 1488-1493 (1965).
[CrossRef]

A. F. Grenis and M. J. Matkovich, "Blackbody reference for temperature above 1200 K. Study for design requirements," AMRA TR 65, 1-18 (1965).

I. Malitson, "Interspecimen comparison of the refractive index of fused silica," J. Opt. Soc. Am. 55, 1205-1209 (1965).
[CrossRef]

G. Hetherington, K. H. Jack, and M. W. Ramsay, "The high-temperature electrolysis of vitreous silica, part I. Oxidation, ultra-violet induced fluorescence, and irradiation colour," Phys. Chem. Glasses 6, 6-15 (1965).

1964 (1)

L. Bogdan, "Measurement of radiative heat transfer with thin-film resistance thermometers," NASA CR 27, 1-39 (1964).

1962 (1)

M. Herzberger and C. Salzberg, "Refractive indices of infrared optical materials and color correction of infrared lenses," J. Opt. Am. 52, 420-427 (1962).
[CrossRef]

1961 (1)

L. E. Sutton and O. N. Stavroudis, "Fitting refractive index data by least squares," J. Opt. Soc. of Am. 51, 901-905 (1961).
[CrossRef]

1955 (1)

J. Reitzel, "Infrared spectra of SiO2 from 400 cm−1 to 600 cm−1," J. Chem. Phys. 23, 2407-2409 (1955).
[CrossRef]

1954 (1)

1953 (1)

I. Simon and H. McMahon, "Study of the structure of quartz, cristobalite, and vitreous silica by reflection in infrared," J. Chem. Phys. 21, 23-30 (1953).
[CrossRef]

1936 (2)

G. Calingaert, S. Heron, and R. Stair, "Sapphire and other new combustion-chamber window materials," SAE J. 39, 448-450 (1936).

D. G. Drummond, "The infra-red absorption spectra of quartz and fused silica from 1 to 7.5 μ II--experimental results," Proc. R. Soc. London Ser. A 153, 328-339 (1936).
[CrossRef]

1929 (1)

1927 (1)

G. Hart, "The nomenclature of silica," Am. Mineral. 12, 383-395 (1927).

Am. Mineral. (1)

G. Hart, "The nomenclature of silica," Am. Mineral. 12, 383-395 (1927).

AMRA TR (1)

A. F. Grenis and M. J. Matkovich, "Blackbody reference for temperature above 1200 K. Study for design requirements," AMRA TR 65, 1-18 (1965).

Ann. N.Y. Acad. Sci. (1)

P. J. Riu and C. Lapaz, "Practical limits of the Kramers-Krönig relationships applied to experimental bioimpedance data," Ann. N.Y. Acad. Sci. 873, 374-380 (1999).
[CrossRef]

Appl. Opt. (5)

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Figures (7)

Fig. 1
Fig. 1

Real n λ and imaginary k λ parts of the complex refractive index of silica glass reported in the literature and summarized in Table 1. The solid curve (present study) was obtained with Eqs. (21)–(24) by using coefficients listed in Table 2.

Fig. 2
Fig. 2

Real n λ and imaginary k λ parts of the complex refractive index of silica glass between 30 nm and 1 μ m as reported in the literature and summarized in Table 1.

Fig. 3
Fig. 3

Real n λ and imaginary k λ parts of the complex refractive index of silica glass between 1 and 15 μ m as reported in the literature and summarized in Table 1. The solid curve (present study) was obtained with Eqs. (21)–(24) by using coefficients listed in Table 2.

Fig. 4
Fig. 4

Real n λ and imaginary k λ parts of the complex refractive index of silica glass between 15 and 100 μ m as reported in the literature and summarized in Table 1. The solid curve (present study) was obtained with Eqs. (21)–(24) by using coefficients listed in Table 2.

Fig. 5
Fig. 5

Real n λ and imaginary k λ parts of the complex refractive index of silica glass between 100 and 1000 μ m as reported in the literature and summarized in Table 1.

Fig. 6
Fig. 6

Residuals between experimental [49] and predicted values of n λ and k λ . The predicted values are based on Eqs. (21)–(24) with coefficients listed in Table 2.

Fig. 7
Fig. 7

Residuals between the experimental data on the refractive index and absorption index and values predicted in this work by using Eqs. (21)–(24) along with coefficients listed in Table 2.

Tables (2)

Tables Icon

Table 1 Summary of the Experimental Data Reporting the Complex Index of Refraction of Silica Glass at Room Temperature

Tables Icon

Table 3 Parameters Used to Interpolate the Refractive Index n λ and Absorption Index k λ of Silica Glass by Using Eqs. (21)–(24) a , b

Equations (25)

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

m λ = n λ + i k λ ,
λ = c λ ν = 1 η ,
n λ = sin ( θ min + ϕ 2 ) sin ( ϕ 2 ) n air ,
n ν = 1 + 2 π P 0 ν k ν ν 2 ν 2 d ν ,
k ν = 2 ν π P 0 n ν ν 2 ν 2 d ν ,
Θ ( ν ) = 2 ν π P 0 d ln R ( ν ) ν 2 ν 2 d ν ,
R ( ν ) = | r | 2 = ( n ν 1 ) 2 + k ν 2 ( n ν + 1 ) 2 + k ν 2 .
r = 1 n ν i k ν 1 + n ν + i k ν = | r | e i Θ .
n ν = 1 R ( ν ) 1 + R ( ν ) 2 R ( ν ) cos Θ ,
k ν = 2 R ( ν ) sin Θ 1 + R ( ν ) 2 R ( ν ) cos Θ .
T 0 , λ ( L ) = ( 1 ρ λ ) 2 e κ λ L 1 ( ρ λ ) 2 e 2 κ λ L ,
ρ λ = ( n λ 1 ) 2 + k λ 2 ( n λ + 1 ) 2 + k λ 2 ,
κ λ = 4 π k λ λ .
k λ = ( λ 4 π L ) ln [ ( 1 ρ λ ) 4 + 4 ρ λ 2 T 0 , λ ( 1 ρ λ ) 2 ρ λ 2 T 0 , λ ] .
k λ = ( λ 4 π L ) ln [ 1 ρ λ ρ λ ϵ λ , 0 1 ρ λ ϵ λ , 0 ] .
ϵ ( λ ) = n λ 2 k λ 2 ,     ϵ ( λ ) = 2 n λ k λ .
ϵ ( ν ) = 1 + j ν p j 2 ν j 2 ν 2 i γ j ν = 1 + j ν p j 2 ( ν j 2 ν 2 ) + i γ j ν p j 2 ν ( ν j 2 ν 2 ) 2 + γ j 2 ν 2 ,
ϵ ( λ ) = ϵ ( λ ) = 1 + j A j 2 λ 2 ( λ 2 λ j 2 ) ,
ϵ ( λ ) = n λ 2 = 1 + j A j 2 λ 2 ( λ 2 λ j 2 ) .
n λ 2 = 1 + 0.6961663 λ 2 λ 2 ( 0.0684043 ) 2 + 0.4079426 λ 2 λ 2 ( 0.1162414 ) 2 + 0.8974794 λ 2 λ 2 ( 9.896161 ) 2 .
ϵ ( η ) = ϵ ( η ) + i ϵ ( η ) = ϵ + j [ g c j k k g ( η ) + i g c j ( η ) ] ,
g c j ( η ) = α j exp [ 4 ln 2 ( η η 0 j σ j ) 2 ] α j × exp [ 4 ln 2 ( η + η 0 j σ j ) 2 ] ,
g c j k k g ( η ) = 2 α j π [ D ( 2 ln 2 η + η 0 j σ j ) D ( 2 ln 2 η η 0 j σ j ) ] .
D ( x ) = e x 2 0 x e t 2 d t .
R ( η ) = | ϵ ( η ) 1 ϵ ( η ) + 1 | 2 ,

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