Abstract

The changes in optical path length and refractive index with temperature are measured at 633 nm in undoped YAG in the 85–285 K temperature range. At 100 K the change in optical path length with temperature is only ∼25% of its value at 300 K; the change of refractive index with temperature is also substantially reduced at low temperatures.

© 1998 Optical Society of America

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  1. D. C. Brown, “Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers,” IEEE J. Quantum Electron. 33, 861–873 (1997).
    [CrossRef]
  2. J. D. Foster, L. M. Osterink, “Index of refraction and expansion thermal coefficients of Nd:YAG,” Appl. Opt. 7, 2428–2429 (1968).
    [CrossRef] [PubMed]
  3. D. Taylor, “Thermal expansion data XI. Complex oxides, A2BO5, and the garnets,” Trans. J. Br. Ceram. Soc. 86, 1–6 (1987).
  4. W. J. Croft, “Low temperature thermal expansion of yttrium aluminum garnet,” Am. Mineral. 50, 1634–1636 (1965).
  5. P. H. Klein, W. J. Croft, “Thermal conductivity, diffusivity, and expansion of Y2O3, Y3Al5O12, and LaF3 in the range 77–300 K,” J. Appl. Phys. 38, 1603–1607 (1967).
    [CrossRef]
  6. Note that in Refs. 4 and 5 the tabulated thermal expansion coefficients at low temperature are much larger than that given by the equation in Ref. 3 [Eq. (4) of this study], because the tabulated values were not calculated correctly in Refs. 4 and 5. They appear to have been calculated by use of the equation α(TC) = [a(TC) - a(0)]/TC, where TC is the temperature in degrees Celcius and a(TC) is the temperature-dependent lattice constant. This actually gives an estimate for α(TC/2) not α(TC) and consequently the tabulated values for the thermal expansion coefficient are too large.
  7. T. K. Gupta, J. Valentich, “Thermal expansion of yttrium aluminum garnet,” J. Am. Ceram. Soc. 54, 355–356 (1971).
    [CrossRef]
  8. R. K. Kirby, “Thermal expansion,” in Concise Encyclopedia of Solid State Physics, R. G. Lerner, G. L. Trigg, eds. (Addison-Wesley, Reading, Mass., 1983), pp. 275–276.
  9. D. D. Young, K. C. Jungling, T. L. Williamson, E. R. Nichols, “Holographic interferometry measurement of the thermal refractive index coefficient and the thermal expansion coefficient of Nd:YAG and Nd:YALO,” IEEE J. Quantum Electron. QE-8, 720–721 (1972).
    [CrossRef]
  10. O. S. Shchavelev, V. A. Babkina, Z. S. Mal’tseva, “Thermo-optic properties, expansion coefficient, and refractive index of yttrium aluminum garnet,” Sov. J. Opt. Technol. 40, 623–624 (1973).
  11. V. V. Blazhko, M. M. Bubnov, E. M. Dianov, A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Sov. J. Quantum Electron. 6, 624–625 (1976).
    [CrossRef]
  12. L. G. DeShazer, S. C. Rand, B. A. Wechsler, “Laser crystals,” in CRC Handbook of Laser Science and Technology, Vol. 5, Pt. 3. Applications, Coatings, and Fabrication, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1987), pp. 281–338.
  13. E. V. Zharikov, Yu. S. Privis, P. A. Studenikin, V. A. Chikov, V. D. Shigorin, I. A. Shcherbakov, “Temperaturewise measurements of refractive indices of rare-earth garnets,” Sov. Phys. Crystallogr. 34, 712–714 (1989).
  14. W. F. Krupke, M. D. Shinn, J. E. Marion, J. A. Caird, S. E. Stokowski, “Spectroscopic, optical, and thermomechanical properties of neodymium- and chromium-doped gadolinium scandium gallium garnet,” J. Opt. Soc. Am. B 3, 102–113 (1986).
    [CrossRef]
  15. A. A. Kaminskii, Laser Crystals: Physics and Properties (Springer-Verlag, Berlin, 1981), p. 351.

1997 (1)

D. C. Brown, “Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers,” IEEE J. Quantum Electron. 33, 861–873 (1997).
[CrossRef]

1989 (1)

E. V. Zharikov, Yu. S. Privis, P. A. Studenikin, V. A. Chikov, V. D. Shigorin, I. A. Shcherbakov, “Temperaturewise measurements of refractive indices of rare-earth garnets,” Sov. Phys. Crystallogr. 34, 712–714 (1989).

1987 (1)

D. Taylor, “Thermal expansion data XI. Complex oxides, A2BO5, and the garnets,” Trans. J. Br. Ceram. Soc. 86, 1–6 (1987).

1986 (1)

1976 (1)

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Sov. J. Quantum Electron. 6, 624–625 (1976).
[CrossRef]

1973 (1)

O. S. Shchavelev, V. A. Babkina, Z. S. Mal’tseva, “Thermo-optic properties, expansion coefficient, and refractive index of yttrium aluminum garnet,” Sov. J. Opt. Technol. 40, 623–624 (1973).

1972 (1)

D. D. Young, K. C. Jungling, T. L. Williamson, E. R. Nichols, “Holographic interferometry measurement of the thermal refractive index coefficient and the thermal expansion coefficient of Nd:YAG and Nd:YALO,” IEEE J. Quantum Electron. QE-8, 720–721 (1972).
[CrossRef]

1971 (1)

T. K. Gupta, J. Valentich, “Thermal expansion of yttrium aluminum garnet,” J. Am. Ceram. Soc. 54, 355–356 (1971).
[CrossRef]

1968 (1)

1967 (1)

P. H. Klein, W. J. Croft, “Thermal conductivity, diffusivity, and expansion of Y2O3, Y3Al5O12, and LaF3 in the range 77–300 K,” J. Appl. Phys. 38, 1603–1607 (1967).
[CrossRef]

1965 (1)

W. J. Croft, “Low temperature thermal expansion of yttrium aluminum garnet,” Am. Mineral. 50, 1634–1636 (1965).

Babkina, V. A.

O. S. Shchavelev, V. A. Babkina, Z. S. Mal’tseva, “Thermo-optic properties, expansion coefficient, and refractive index of yttrium aluminum garnet,” Sov. J. Opt. Technol. 40, 623–624 (1973).

Blazhko, V. V.

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Sov. J. Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Brown, D. C.

D. C. Brown, “Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers,” IEEE J. Quantum Electron. 33, 861–873 (1997).
[CrossRef]

Bubnov, M. M.

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Sov. J. Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Caird, J. A.

Chikolini, A. V.

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Sov. J. Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Chikov, V. A.

E. V. Zharikov, Yu. S. Privis, P. A. Studenikin, V. A. Chikov, V. D. Shigorin, I. A. Shcherbakov, “Temperaturewise measurements of refractive indices of rare-earth garnets,” Sov. Phys. Crystallogr. 34, 712–714 (1989).

Croft, W. J.

P. H. Klein, W. J. Croft, “Thermal conductivity, diffusivity, and expansion of Y2O3, Y3Al5O12, and LaF3 in the range 77–300 K,” J. Appl. Phys. 38, 1603–1607 (1967).
[CrossRef]

W. J. Croft, “Low temperature thermal expansion of yttrium aluminum garnet,” Am. Mineral. 50, 1634–1636 (1965).

DeShazer, L. G.

L. G. DeShazer, S. C. Rand, B. A. Wechsler, “Laser crystals,” in CRC Handbook of Laser Science and Technology, Vol. 5, Pt. 3. Applications, Coatings, and Fabrication, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1987), pp. 281–338.

Dianov, E. M.

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Sov. J. Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Foster, J. D.

Gupta, T. K.

T. K. Gupta, J. Valentich, “Thermal expansion of yttrium aluminum garnet,” J. Am. Ceram. Soc. 54, 355–356 (1971).
[CrossRef]

Jungling, K. C.

D. D. Young, K. C. Jungling, T. L. Williamson, E. R. Nichols, “Holographic interferometry measurement of the thermal refractive index coefficient and the thermal expansion coefficient of Nd:YAG and Nd:YALO,” IEEE J. Quantum Electron. QE-8, 720–721 (1972).
[CrossRef]

Kaminskii, A. A.

A. A. Kaminskii, Laser Crystals: Physics and Properties (Springer-Verlag, Berlin, 1981), p. 351.

Kirby, R. K.

R. K. Kirby, “Thermal expansion,” in Concise Encyclopedia of Solid State Physics, R. G. Lerner, G. L. Trigg, eds. (Addison-Wesley, Reading, Mass., 1983), pp. 275–276.

Klein, P. H.

P. H. Klein, W. J. Croft, “Thermal conductivity, diffusivity, and expansion of Y2O3, Y3Al5O12, and LaF3 in the range 77–300 K,” J. Appl. Phys. 38, 1603–1607 (1967).
[CrossRef]

Krupke, W. F.

Mal’tseva, Z. S.

O. S. Shchavelev, V. A. Babkina, Z. S. Mal’tseva, “Thermo-optic properties, expansion coefficient, and refractive index of yttrium aluminum garnet,” Sov. J. Opt. Technol. 40, 623–624 (1973).

Marion, J. E.

Nichols, E. R.

D. D. Young, K. C. Jungling, T. L. Williamson, E. R. Nichols, “Holographic interferometry measurement of the thermal refractive index coefficient and the thermal expansion coefficient of Nd:YAG and Nd:YALO,” IEEE J. Quantum Electron. QE-8, 720–721 (1972).
[CrossRef]

Osterink, L. M.

Privis, Yu. S.

E. V. Zharikov, Yu. S. Privis, P. A. Studenikin, V. A. Chikov, V. D. Shigorin, I. A. Shcherbakov, “Temperaturewise measurements of refractive indices of rare-earth garnets,” Sov. Phys. Crystallogr. 34, 712–714 (1989).

Rand, S. C.

L. G. DeShazer, S. C. Rand, B. A. Wechsler, “Laser crystals,” in CRC Handbook of Laser Science and Technology, Vol. 5, Pt. 3. Applications, Coatings, and Fabrication, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1987), pp. 281–338.

Shchavelev, O. S.

O. S. Shchavelev, V. A. Babkina, Z. S. Mal’tseva, “Thermo-optic properties, expansion coefficient, and refractive index of yttrium aluminum garnet,” Sov. J. Opt. Technol. 40, 623–624 (1973).

Shcherbakov, I. A.

E. V. Zharikov, Yu. S. Privis, P. A. Studenikin, V. A. Chikov, V. D. Shigorin, I. A. Shcherbakov, “Temperaturewise measurements of refractive indices of rare-earth garnets,” Sov. Phys. Crystallogr. 34, 712–714 (1989).

Shigorin, V. D.

E. V. Zharikov, Yu. S. Privis, P. A. Studenikin, V. A. Chikov, V. D. Shigorin, I. A. Shcherbakov, “Temperaturewise measurements of refractive indices of rare-earth garnets,” Sov. Phys. Crystallogr. 34, 712–714 (1989).

Shinn, M. D.

Stokowski, S. E.

Studenikin, P. A.

E. V. Zharikov, Yu. S. Privis, P. A. Studenikin, V. A. Chikov, V. D. Shigorin, I. A. Shcherbakov, “Temperaturewise measurements of refractive indices of rare-earth garnets,” Sov. Phys. Crystallogr. 34, 712–714 (1989).

Taylor, D.

D. Taylor, “Thermal expansion data XI. Complex oxides, A2BO5, and the garnets,” Trans. J. Br. Ceram. Soc. 86, 1–6 (1987).

Valentich, J.

T. K. Gupta, J. Valentich, “Thermal expansion of yttrium aluminum garnet,” J. Am. Ceram. Soc. 54, 355–356 (1971).
[CrossRef]

Wechsler, B. A.

L. G. DeShazer, S. C. Rand, B. A. Wechsler, “Laser crystals,” in CRC Handbook of Laser Science and Technology, Vol. 5, Pt. 3. Applications, Coatings, and Fabrication, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1987), pp. 281–338.

Williamson, T. L.

D. D. Young, K. C. Jungling, T. L. Williamson, E. R. Nichols, “Holographic interferometry measurement of the thermal refractive index coefficient and the thermal expansion coefficient of Nd:YAG and Nd:YALO,” IEEE J. Quantum Electron. QE-8, 720–721 (1972).
[CrossRef]

Young, D. D.

D. D. Young, K. C. Jungling, T. L. Williamson, E. R. Nichols, “Holographic interferometry measurement of the thermal refractive index coefficient and the thermal expansion coefficient of Nd:YAG and Nd:YALO,” IEEE J. Quantum Electron. QE-8, 720–721 (1972).
[CrossRef]

Zharikov, E. V.

E. V. Zharikov, Yu. S. Privis, P. A. Studenikin, V. A. Chikov, V. D. Shigorin, I. A. Shcherbakov, “Temperaturewise measurements of refractive indices of rare-earth garnets,” Sov. Phys. Crystallogr. 34, 712–714 (1989).

Am. Mineral. (1)

W. J. Croft, “Low temperature thermal expansion of yttrium aluminum garnet,” Am. Mineral. 50, 1634–1636 (1965).

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

D. D. Young, K. C. Jungling, T. L. Williamson, E. R. Nichols, “Holographic interferometry measurement of the thermal refractive index coefficient and the thermal expansion coefficient of Nd:YAG and Nd:YALO,” IEEE J. Quantum Electron. QE-8, 720–721 (1972).
[CrossRef]

D. C. Brown, “Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers,” IEEE J. Quantum Electron. 33, 861–873 (1997).
[CrossRef]

J. Am. Ceram. Soc. (1)

T. K. Gupta, J. Valentich, “Thermal expansion of yttrium aluminum garnet,” J. Am. Ceram. Soc. 54, 355–356 (1971).
[CrossRef]

J. Appl. Phys. (1)

P. H. Klein, W. J. Croft, “Thermal conductivity, diffusivity, and expansion of Y2O3, Y3Al5O12, and LaF3 in the range 77–300 K,” J. Appl. Phys. 38, 1603–1607 (1967).
[CrossRef]

J. Opt. Soc. Am. B (1)

Sov. J. Opt. Technol. (1)

O. S. Shchavelev, V. A. Babkina, Z. S. Mal’tseva, “Thermo-optic properties, expansion coefficient, and refractive index of yttrium aluminum garnet,” Sov. J. Opt. Technol. 40, 623–624 (1973).

Sov. J. Quantum Electron. (1)

V. V. Blazhko, M. M. Bubnov, E. M. Dianov, A. V. Chikolini, “Determination of the temperature dependence of the linear expansion coefficient and of the temperature coefficient of the refractive index of laser glasses,” Sov. J. Quantum Electron. 6, 624–625 (1976).
[CrossRef]

Sov. Phys. Crystallogr. (1)

E. V. Zharikov, Yu. S. Privis, P. A. Studenikin, V. A. Chikov, V. D. Shigorin, I. A. Shcherbakov, “Temperaturewise measurements of refractive indices of rare-earth garnets,” Sov. Phys. Crystallogr. 34, 712–714 (1989).

Trans. J. Br. Ceram. Soc. (1)

D. Taylor, “Thermal expansion data XI. Complex oxides, A2BO5, and the garnets,” Trans. J. Br. Ceram. Soc. 86, 1–6 (1987).

Other (4)

Note that in Refs. 4 and 5 the tabulated thermal expansion coefficients at low temperature are much larger than that given by the equation in Ref. 3 [Eq. (4) of this study], because the tabulated values were not calculated correctly in Refs. 4 and 5. They appear to have been calculated by use of the equation α(TC) = [a(TC) - a(0)]/TC, where TC is the temperature in degrees Celcius and a(TC) is the temperature-dependent lattice constant. This actually gives an estimate for α(TC/2) not α(TC) and consequently the tabulated values for the thermal expansion coefficient are too large.

L. G. DeShazer, S. C. Rand, B. A. Wechsler, “Laser crystals,” in CRC Handbook of Laser Science and Technology, Vol. 5, Pt. 3. Applications, Coatings, and Fabrication, M. J. Weber, ed. (CRC Press, Boca Raton, Fla., 1987), pp. 281–338.

R. K. Kirby, “Thermal expansion,” in Concise Encyclopedia of Solid State Physics, R. G. Lerner, G. L. Trigg, eds. (Addison-Wesley, Reading, Mass., 1983), pp. 275–276.

A. A. Kaminskii, Laser Crystals: Physics and Properties (Springer-Verlag, Berlin, 1981), p. 351.

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Figures (3)

Fig. 1
Fig. 1

Diagram of the experimental apparatus. In this drawing, the angle between the incident and reflected beams from the sample is greatly exaggerated for clarity.

Fig. 2
Fig. 2

γ at 633 nm for YAG. Open circles are our measurements of γ in undoped YAG; the open square is for Nd:YAG from Ref. 2; the open triangle is for Nd:YAG from Ref. 9; the dashed line is for Nd:YAG from Ref. 11.

Fig. 3
Fig. 3

dn/dT at 633 nm for YAG. Filled circles are our measurements taken with Eq. (4) whereas the diamonds represent measurements taken with Eq. (5); the square is for Nd:YAG from Ref. 2; the triangle is for Nd:YAG from Ref. 9; the line is for Nd:YAG from Ref. 11; and the cross is for undoped YAG from Ref. 12.

Equations (5)

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

γ = 1 nL d nL d T .
γ = 1 n d n d T + α ,
α = 1 L d L d T .
α = - 1.78 × 10 - 6 + 3.3 × 10 - 8 T ,
α = 1.14 × 10 - 7 T 0.69 ,

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