Abstract

A Fabry–Perot-type interferometer is described that permits the concurrent measurement of the coefficient of thermal expansion (α) and the thermooptic coefficient (dn/dT) of transparent materials. Measurements of the a and the dn/dT of vitreous silica and a heavy-metal fluoride glass show that the technique is accurate, reproducible, and easily performed. In addition, the technique is used to show that the dn/dT of heavy-metal fluoride glasses is negative and temperature dependent. The magnitude of dn/dT is found to increase with increasing temperature.

© 1991 Optical Society of America

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  1. M. Sparks, “Optical distortion by heated windows in high power laser systems” J. Appl. Phys. 42, 5029–5046 (1971).
    [CrossRef]
  2. B. Bendow, P. D. Gianino, “Thermal lensing of laser beams in optically transmitting materials, I. general formulation,” Appl. Phys. 2, 1–10 (1973).
    [CrossRef]
  3. J. R. Jaspere, P. D. Gianino, “Thermal lensing in infrared window materials” J. Appl. Phys. 43, 1686–1693 (1972).
    [CrossRef]
  4. R. J. Harris, G. T. Johnston, G. A. Kepple, P. C. Krok, H. Mukai, “Infrared thermooptic coefficient measurement of polycrystalline ZnSe, ZnS, CdTe, CaF2, and BaF2, single crystal KCL, and Tl-20 glass,” Appl. Opt. 16, 436–438 (1977).
    [CrossRef] [PubMed]
  5. R. J. Harris, M. E. Gangl, “Thermo-optic coefficient (dn/dT) of 1.3 μm laser window materials,” in Laser Induced Damage in Optical Materials: 1981, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newnam, eds., NBS-SP-638 (U.S. Government Printing Office, Washington, D.C., 1983), pp. 171–174.
    [CrossRef]
  6. W. J. Cho, T. S. Hahn, S. S. Choi, K. H. Chung, “Thermo-optic coefficients of ZrF4-based glasses,” Mater. Sci. Forum 32–33, 361–366 (1988).
    [CrossRef]
  7. P. Greason, J. Dietro, B. Bendow, D. J. Martin, “Temperature dependence of the refractive index of fluoro-zirconate Glass,” Mater. Sci. Forum 6, 607–610 (1985).
    [CrossRef]
  8. J. Dietro, UDRI, University of Dayton, Dayton, Ohio 45469 (personal communication).
  9. S. J. Bennett, “An absolute interferometric dilatometer,” J. Phys. E 10, 525–530 (1977).
    [CrossRef]
  10. S. F. Jacobs, S. C. Johnston, J. M. Sasian, M. Watson, J. D. Targrove, D. Bass, “Surface figure changes due to thermal cycling hysteresis,” Appl. Opt. 26, 4438–4442 (1987).
    [CrossRef] [PubMed]
  11. X. Pan, Y. Qi, “Relation between thermo-optic coefficient of glass and temperature and wavelength,” Collect. Pap. 14th Int. Cong. Glass 1, 201–207 (1986).
  12. R. Bruckner, “Properties and structure of vitreous silica, I.,” J. Non-Cryst. Solids 5, 123–175 (1970).
    [CrossRef]
  13. A. Winter, M. J. Cabannes, “On the structure of vitreous silica,” C. R. Acad. Sci. Paris 240, 2397–1400 (1955).
  14. T. Izumitani, T. Yamashita, M. Tokida, K. Miura, H. Tajima, “New fluoroaluminate glasses and their crystallization tendencies and physical properties,” Mater. Sci. Forum 19–20, 19–26 (1987).
    [CrossRef]
  15. R. M. Waxler, G. W. Cleek, “The effect of temperature and pressure on the refractive index of some oxide glasses,” J. Res. Nat. Bur. Stand. (USA) 77A, 755–763 (1973).
    [CrossRef]
  16. A. C. Clare, J. M. Parker, “Thermal mismatch stresses in fluoride glass fibres,” in Infrared Fiber Optics, J. A. Harrington, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1048, 64–71 (1989).
  17. R. C. Weast, M. J. Astle, Eds., CRC Handbook of Chemistry and Physics (CRC, Boca Raton, Fla.1981), p. E-393.

1988 (1)

W. J. Cho, T. S. Hahn, S. S. Choi, K. H. Chung, “Thermo-optic coefficients of ZrF4-based glasses,” Mater. Sci. Forum 32–33, 361–366 (1988).
[CrossRef]

1987 (2)

T. Izumitani, T. Yamashita, M. Tokida, K. Miura, H. Tajima, “New fluoroaluminate glasses and their crystallization tendencies and physical properties,” Mater. Sci. Forum 19–20, 19–26 (1987).
[CrossRef]

S. F. Jacobs, S. C. Johnston, J. M. Sasian, M. Watson, J. D. Targrove, D. Bass, “Surface figure changes due to thermal cycling hysteresis,” Appl. Opt. 26, 4438–4442 (1987).
[CrossRef] [PubMed]

1986 (1)

X. Pan, Y. Qi, “Relation between thermo-optic coefficient of glass and temperature and wavelength,” Collect. Pap. 14th Int. Cong. Glass 1, 201–207 (1986).

1985 (1)

P. Greason, J. Dietro, B. Bendow, D. J. Martin, “Temperature dependence of the refractive index of fluoro-zirconate Glass,” Mater. Sci. Forum 6, 607–610 (1985).
[CrossRef]

1977 (2)

1973 (2)

B. Bendow, P. D. Gianino, “Thermal lensing of laser beams in optically transmitting materials, I. general formulation,” Appl. Phys. 2, 1–10 (1973).
[CrossRef]

R. M. Waxler, G. W. Cleek, “The effect of temperature and pressure on the refractive index of some oxide glasses,” J. Res. Nat. Bur. Stand. (USA) 77A, 755–763 (1973).
[CrossRef]

1972 (1)

J. R. Jaspere, P. D. Gianino, “Thermal lensing in infrared window materials” J. Appl. Phys. 43, 1686–1693 (1972).
[CrossRef]

1971 (1)

M. Sparks, “Optical distortion by heated windows in high power laser systems” J. Appl. Phys. 42, 5029–5046 (1971).
[CrossRef]

1970 (1)

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

1955 (1)

A. Winter, M. J. Cabannes, “On the structure of vitreous silica,” C. R. Acad. Sci. Paris 240, 2397–1400 (1955).

Bass, D.

Bendow, B.

P. Greason, J. Dietro, B. Bendow, D. J. Martin, “Temperature dependence of the refractive index of fluoro-zirconate Glass,” Mater. Sci. Forum 6, 607–610 (1985).
[CrossRef]

B. Bendow, P. D. Gianino, “Thermal lensing of laser beams in optically transmitting materials, I. general formulation,” Appl. Phys. 2, 1–10 (1973).
[CrossRef]

Bennett, S. J.

S. J. Bennett, “An absolute interferometric dilatometer,” J. Phys. E 10, 525–530 (1977).
[CrossRef]

Bruckner, R.

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

Cabannes, M. J.

A. Winter, M. J. Cabannes, “On the structure of vitreous silica,” C. R. Acad. Sci. Paris 240, 2397–1400 (1955).

Cho, W. J.

W. J. Cho, T. S. Hahn, S. S. Choi, K. H. Chung, “Thermo-optic coefficients of ZrF4-based glasses,” Mater. Sci. Forum 32–33, 361–366 (1988).
[CrossRef]

Choi, S. S.

W. J. Cho, T. S. Hahn, S. S. Choi, K. H. Chung, “Thermo-optic coefficients of ZrF4-based glasses,” Mater. Sci. Forum 32–33, 361–366 (1988).
[CrossRef]

Chung, K. H.

W. J. Cho, T. S. Hahn, S. S. Choi, K. H. Chung, “Thermo-optic coefficients of ZrF4-based glasses,” Mater. Sci. Forum 32–33, 361–366 (1988).
[CrossRef]

Clare, A. C.

A. C. Clare, J. M. Parker, “Thermal mismatch stresses in fluoride glass fibres,” in Infrared Fiber Optics, J. A. Harrington, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1048, 64–71 (1989).

Cleek, G. W.

R. M. Waxler, G. W. Cleek, “The effect of temperature and pressure on the refractive index of some oxide glasses,” J. Res. Nat. Bur. Stand. (USA) 77A, 755–763 (1973).
[CrossRef]

Dietro, J.

P. Greason, J. Dietro, B. Bendow, D. J. Martin, “Temperature dependence of the refractive index of fluoro-zirconate Glass,” Mater. Sci. Forum 6, 607–610 (1985).
[CrossRef]

J. Dietro, UDRI, University of Dayton, Dayton, Ohio 45469 (personal communication).

Gangl, M. E.

R. J. Harris, M. E. Gangl, “Thermo-optic coefficient (dn/dT) of 1.3 μm laser window materials,” in Laser Induced Damage in Optical Materials: 1981, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newnam, eds., NBS-SP-638 (U.S. Government Printing Office, Washington, D.C., 1983), pp. 171–174.
[CrossRef]

Gianino, P. D.

B. Bendow, P. D. Gianino, “Thermal lensing of laser beams in optically transmitting materials, I. general formulation,” Appl. Phys. 2, 1–10 (1973).
[CrossRef]

J. R. Jaspere, P. D. Gianino, “Thermal lensing in infrared window materials” J. Appl. Phys. 43, 1686–1693 (1972).
[CrossRef]

Greason, P.

P. Greason, J. Dietro, B. Bendow, D. J. Martin, “Temperature dependence of the refractive index of fluoro-zirconate Glass,” Mater. Sci. Forum 6, 607–610 (1985).
[CrossRef]

Hahn, T. S.

W. J. Cho, T. S. Hahn, S. S. Choi, K. H. Chung, “Thermo-optic coefficients of ZrF4-based glasses,” Mater. Sci. Forum 32–33, 361–366 (1988).
[CrossRef]

Harris, R. J.

R. J. Harris, G. T. Johnston, G. A. Kepple, P. C. Krok, H. Mukai, “Infrared thermooptic coefficient measurement of polycrystalline ZnSe, ZnS, CdTe, CaF2, and BaF2, single crystal KCL, and Tl-20 glass,” Appl. Opt. 16, 436–438 (1977).
[CrossRef] [PubMed]

R. J. Harris, M. E. Gangl, “Thermo-optic coefficient (dn/dT) of 1.3 μm laser window materials,” in Laser Induced Damage in Optical Materials: 1981, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newnam, eds., NBS-SP-638 (U.S. Government Printing Office, Washington, D.C., 1983), pp. 171–174.
[CrossRef]

Izumitani, T.

T. Izumitani, T. Yamashita, M. Tokida, K. Miura, H. Tajima, “New fluoroaluminate glasses and their crystallization tendencies and physical properties,” Mater. Sci. Forum 19–20, 19–26 (1987).
[CrossRef]

Jacobs, S. F.

Jaspere, J. R.

J. R. Jaspere, P. D. Gianino, “Thermal lensing in infrared window materials” J. Appl. Phys. 43, 1686–1693 (1972).
[CrossRef]

Johnston, G. T.

Johnston, S. C.

Kepple, G. A.

Krok, P. C.

Martin, D. J.

P. Greason, J. Dietro, B. Bendow, D. J. Martin, “Temperature dependence of the refractive index of fluoro-zirconate Glass,” Mater. Sci. Forum 6, 607–610 (1985).
[CrossRef]

Miura, K.

T. Izumitani, T. Yamashita, M. Tokida, K. Miura, H. Tajima, “New fluoroaluminate glasses and their crystallization tendencies and physical properties,” Mater. Sci. Forum 19–20, 19–26 (1987).
[CrossRef]

Mukai, H.

Pan, X.

X. Pan, Y. Qi, “Relation between thermo-optic coefficient of glass and temperature and wavelength,” Collect. Pap. 14th Int. Cong. Glass 1, 201–207 (1986).

Parker, J. M.

A. C. Clare, J. M. Parker, “Thermal mismatch stresses in fluoride glass fibres,” in Infrared Fiber Optics, J. A. Harrington, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1048, 64–71 (1989).

Qi, Y.

X. Pan, Y. Qi, “Relation between thermo-optic coefficient of glass and temperature and wavelength,” Collect. Pap. 14th Int. Cong. Glass 1, 201–207 (1986).

Sasian, J. M.

Sparks, M.

M. Sparks, “Optical distortion by heated windows in high power laser systems” J. Appl. Phys. 42, 5029–5046 (1971).
[CrossRef]

Tajima, H.

T. Izumitani, T. Yamashita, M. Tokida, K. Miura, H. Tajima, “New fluoroaluminate glasses and their crystallization tendencies and physical properties,” Mater. Sci. Forum 19–20, 19–26 (1987).
[CrossRef]

Targrove, J. D.

Tokida, M.

T. Izumitani, T. Yamashita, M. Tokida, K. Miura, H. Tajima, “New fluoroaluminate glasses and their crystallization tendencies and physical properties,” Mater. Sci. Forum 19–20, 19–26 (1987).
[CrossRef]

Watson, M.

Waxler, R. M.

R. M. Waxler, G. W. Cleek, “The effect of temperature and pressure on the refractive index of some oxide glasses,” J. Res. Nat. Bur. Stand. (USA) 77A, 755–763 (1973).
[CrossRef]

Winter, A.

A. Winter, M. J. Cabannes, “On the structure of vitreous silica,” C. R. Acad. Sci. Paris 240, 2397–1400 (1955).

Yamashita, T.

T. Izumitani, T. Yamashita, M. Tokida, K. Miura, H. Tajima, “New fluoroaluminate glasses and their crystallization tendencies and physical properties,” Mater. Sci. Forum 19–20, 19–26 (1987).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. (1)

B. Bendow, P. D. Gianino, “Thermal lensing of laser beams in optically transmitting materials, I. general formulation,” Appl. Phys. 2, 1–10 (1973).
[CrossRef]

C. R. Acad. Sci. Paris (1)

A. Winter, M. J. Cabannes, “On the structure of vitreous silica,” C. R. Acad. Sci. Paris 240, 2397–1400 (1955).

Collect. Pap. 14th Int. Cong. Glass (1)

X. Pan, Y. Qi, “Relation between thermo-optic coefficient of glass and temperature and wavelength,” Collect. Pap. 14th Int. Cong. Glass 1, 201–207 (1986).

J. Appl. Phys. (2)

M. Sparks, “Optical distortion by heated windows in high power laser systems” J. Appl. Phys. 42, 5029–5046 (1971).
[CrossRef]

J. R. Jaspere, P. D. Gianino, “Thermal lensing in infrared window materials” J. Appl. Phys. 43, 1686–1693 (1972).
[CrossRef]

J. Non-Cryst. Solids (1)

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

J. Phys. E (1)

S. J. Bennett, “An absolute interferometric dilatometer,” J. Phys. E 10, 525–530 (1977).
[CrossRef]

J. Res. Nat. Bur. Stand. (USA) (1)

R. M. Waxler, G. W. Cleek, “The effect of temperature and pressure on the refractive index of some oxide glasses,” J. Res. Nat. Bur. Stand. (USA) 77A, 755–763 (1973).
[CrossRef]

Mater. Sci. Forum (3)

T. Izumitani, T. Yamashita, M. Tokida, K. Miura, H. Tajima, “New fluoroaluminate glasses and their crystallization tendencies and physical properties,” Mater. Sci. Forum 19–20, 19–26 (1987).
[CrossRef]

W. J. Cho, T. S. Hahn, S. S. Choi, K. H. Chung, “Thermo-optic coefficients of ZrF4-based glasses,” Mater. Sci. Forum 32–33, 361–366 (1988).
[CrossRef]

P. Greason, J. Dietro, B. Bendow, D. J. Martin, “Temperature dependence of the refractive index of fluoro-zirconate Glass,” Mater. Sci. Forum 6, 607–610 (1985).
[CrossRef]

Other (4)

J. Dietro, UDRI, University of Dayton, Dayton, Ohio 45469 (personal communication).

R. J. Harris, M. E. Gangl, “Thermo-optic coefficient (dn/dT) of 1.3 μm laser window materials,” in Laser Induced Damage in Optical Materials: 1981, H. E. Bennett, A. H. Guenther, D. Milam, B. E. Newnam, eds., NBS-SP-638 (U.S. Government Printing Office, Washington, D.C., 1983), pp. 171–174.
[CrossRef]

A. C. Clare, J. M. Parker, “Thermal mismatch stresses in fluoride glass fibres,” in Infrared Fiber Optics, J. A. Harrington, A. Katzir, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1048, 64–71 (1989).

R. C. Weast, M. J. Astle, Eds., CRC Handbook of Chemistry and Physics (CRC, Boca Raton, Fla.1981), p. E-393.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental apparatus for measurement of dn/dT and α.

Fig. 2
Fig. 2

Typical interference fringe patterns showing areas monitored by detectors.

Fig. 3
Fig. 3

Coefficient of thermal expansion for ZBLAN as determined by the interferometer and thermomechanical analyzer (TMA).

Fig. 4
Fig. 4

Effect of heating rate on the measurement of the dn/dT of ZBLAN glass.

Fig. 5
Fig. 5

dn/dT of ZBLAN glass measured on heating and cooling.

Tables (3)

Tables Icon

Table I Average dn/dT and α of Vitreous Silica from 25 to 150°C

Tables Icon

Table II Linear Regression Data (dn/dT = AT + B) for the Measurement of dn/dT of ZBLAN Glass at Various Heating Rates

Tables Icon

Table III Linear Regression Data (dn/dT = AT + B) for the Measurement of dn/dT of ZBLAN Glass On Thermal Cycling

Equations (5)

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

d n / d T + ( n 1 ) ( 1 + υ ) α = 0 ,
d n / d T = ( λ / 2 l Δ T ) n α ,
α = N λ / ( 2 l Δ T ) .
d n / d T = ( N g n N a ) λ / ( 2 l Δ T ) ,
d n / d T = A T + B ,

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