Abstract

The thermal expansion coefficient and dn/dT are measured by interferometry techniques in undoped YAG below 300 K. The thermal expansion coefficient at 125 K is measured to be 2.70 × 10-6 K-1 and dn/dT at 633 nm is 2.5 × 10-6 K-1, compared with 7 × 10-6 K-1 and 9 × 10-6 K-1 for these quantities at 300 K.

© 1999 Optical Society of America

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References

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  1. T. Y. Fan, T. Crow, B. Hoden, “Cooled Yb:YAG for high-power solid state lasers,” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 200–205 (1998).
    [CrossRef]
  2. D. C. Brown, “Ultrahigh-average-power diode-pumped Nd:YAG and Yb:YAG lasers,” IEEE J. Quantum Electron. 33, 861–873 (1997).
    [CrossRef]
  3. D. C. Brown, “Nonlinear thermal distortion in YAG rod amplifiers,” IEEE J. Quantum Electron. 34, 2383–2392 (1998).
    [CrossRef]
  4. D. C. Brown, “Nonlinear thermal and stress effects and scaling behavior of YAG slab amplifiers,” IEEE J. Quantum Electron. 34, 2393–2402 (1998).
    [CrossRef]
  5. T. Y. Fan, J. L. Daneu, “Thermal coefficients of the optical path length and refractive index of YAG,” Appl. Opt. 37, 1635–1637 (1998).
    [CrossRef]
  6. W. J. Croft, “Low temperature thermal expansion of yttrium aluminum garnet,” Am. Mineral. 50, 1634–1636 (1965).
  7. 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]
  8. Note that in Refs. 6 and 7 the tabulated thermal expansion coefficients at low temperature are much larger than indicated by the tabulated lattice constants. This is so because the tabulated expansion coefficients were not calculated correctly in Refs. 6 and 7. They appear to have been calculated with the equation α(TC) = [a(TC) - a(0)]/TC, where TC is the temperature in degrees Celsius and a(TC) is the temperature-dependent lattice constant. This actually gives an estimate for α(TC/2) and not for α(TC), and consequently the tabulated values for thermal expansion coefficient are too large.
  9. D. Taylor, “Thermal expansion data. XI. Complex oxides, A2BO5, and the garnets,” Trans. J. Br. Ceram. Soc. 86, 1–6 (1987).
  10. J. D. Foster, L. M. Osterink, “Index of refraction and expansion thermal coefficients of Nd:YAG,” Appl. Opt. 7, 2428–2429 (1968).
    [CrossRef] [PubMed]
  11. 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.
  12. 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]
  13. K. E. Wilson, “Thermo-optics of nonlinear crystals and laser materials,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1980).
  14. 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).
  15. 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]
  16. K. L. Ovanesyan, A. G. Petrosyan, G. O. Shirinyan, A. A. Avetisyan, “Optical dispersion and thermal expansion of garnets Lu3Al5O12, Er3Al5O12, and Y3Al5O12,” Inorg. Mater. 17, 308–310 (1981).

1998

D. C. Brown, “Nonlinear thermal distortion in YAG rod amplifiers,” IEEE J. Quantum Electron. 34, 2383–2392 (1998).
[CrossRef]

D. C. Brown, “Nonlinear thermal and stress effects and scaling behavior of YAG slab amplifiers,” IEEE J. Quantum Electron. 34, 2393–2402 (1998).
[CrossRef]

T. Y. Fan, J. L. Daneu, “Thermal coefficients of the optical path length and refractive index of YAG,” Appl. Opt. 37, 1635–1637 (1998).
[CrossRef]

1997

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

1987

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

1981

K. L. Ovanesyan, A. G. Petrosyan, G. O. Shirinyan, A. A. Avetisyan, “Optical dispersion and thermal expansion of garnets Lu3Al5O12, Er3Al5O12, and Y3Al5O12,” Inorg. Mater. 17, 308–310 (1981).

1976

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

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

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]

1968

1967

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

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

Avetisyan, A. A.

K. L. Ovanesyan, A. G. Petrosyan, G. O. Shirinyan, A. A. Avetisyan, “Optical dispersion and thermal expansion of garnets Lu3Al5O12, Er3Al5O12, and Y3Al5O12,” Inorg. Mater. 17, 308–310 (1981).

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, “Nonlinear thermal distortion in YAG rod amplifiers,” IEEE J. Quantum Electron. 34, 2383–2392 (1998).
[CrossRef]

D. C. Brown, “Nonlinear thermal and stress effects and scaling behavior of YAG slab amplifiers,” IEEE J. Quantum Electron. 34, 2393–2402 (1998).
[CrossRef]

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]

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]

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).

Crow, T.

T. Y. Fan, T. Crow, B. Hoden, “Cooled Yb:YAG for high-power solid state lasers,” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 200–205 (1998).
[CrossRef]

Daneu, J. L.

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]

Fan, T. Y.

T. Y. Fan, J. L. Daneu, “Thermal coefficients of the optical path length and refractive index of YAG,” Appl. Opt. 37, 1635–1637 (1998).
[CrossRef]

T. Y. Fan, T. Crow, B. Hoden, “Cooled Yb:YAG for high-power solid state lasers,” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 200–205 (1998).
[CrossRef]

Foster, J. D.

Hoden, B.

T. Y. Fan, T. Crow, B. Hoden, “Cooled Yb:YAG for high-power solid state lasers,” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 200–205 (1998).
[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]

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]

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).

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.

Ovanesyan, K. L.

K. L. Ovanesyan, A. G. Petrosyan, G. O. Shirinyan, A. A. Avetisyan, “Optical dispersion and thermal expansion of garnets Lu3Al5O12, Er3Al5O12, and Y3Al5O12,” Inorg. Mater. 17, 308–310 (1981).

Petrosyan, A. G.

K. L. Ovanesyan, A. G. Petrosyan, G. O. Shirinyan, A. A. Avetisyan, “Optical dispersion and thermal expansion of garnets Lu3Al5O12, Er3Al5O12, and Y3Al5O12,” Inorg. Mater. 17, 308–310 (1981).

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).

Shirinyan, G. O.

K. L. Ovanesyan, A. G. Petrosyan, G. O. Shirinyan, A. A. Avetisyan, “Optical dispersion and thermal expansion of garnets Lu3Al5O12, Er3Al5O12, and Y3Al5O12,” Inorg. Mater. 17, 308–310 (1981).

Taylor, D.

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

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]

Wilson, K. E.

K. E. Wilson, “Thermo-optics of nonlinear crystals and laser materials,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1980).

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]

Am. Mineral.

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

Appl. Opt.

IEEE J. Quantum Electron.

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

D. C. Brown, “Nonlinear thermal distortion in YAG rod amplifiers,” IEEE J. Quantum Electron. 34, 2383–2392 (1998).
[CrossRef]

D. C. Brown, “Nonlinear thermal and stress effects and scaling behavior of YAG slab amplifiers,” IEEE J. Quantum Electron. 34, 2393–2402 (1998).
[CrossRef]

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]

Inorg. Mater.

K. L. Ovanesyan, A. G. Petrosyan, G. O. Shirinyan, A. A. Avetisyan, “Optical dispersion and thermal expansion of garnets Lu3Al5O12, Er3Al5O12, and Y3Al5O12,” Inorg. Mater. 17, 308–310 (1981).

J. Appl. Phys.

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]

Sov. J. Opt. Technol.

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.

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]

Trans. J. Br. Ceram. Soc.

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

Other

K. E. Wilson, “Thermo-optics of nonlinear crystals and laser materials,” Ph.D. dissertation (University of Southern California, Los Angeles, Calif., 1980).

Note that in Refs. 6 and 7 the tabulated thermal expansion coefficients at low temperature are much larger than indicated by the tabulated lattice constants. This is so because the tabulated expansion coefficients were not calculated correctly in Refs. 6 and 7. They appear to have been calculated with the equation α(TC) = [a(TC) - a(0)]/TC, where TC is the temperature in degrees Celsius and a(TC) is the temperature-dependent lattice constant. This actually gives an estimate for α(TC/2) and not for α(TC), and consequently the tabulated values for thermal expansion coefficient are too large.

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.

T. Y. Fan, T. Crow, B. Hoden, “Cooled Yb:YAG for high-power solid state lasers,” in Airborne Laser Advanced Technology, T. D. Steiner, P. H. Merritt, eds., Proc. SPIE3381, 200–205 (1998).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

α for YAG. Data from this study; the solid-line fit is that of Eq. (1). Other data at somewhat higher temperature from other reports are also shown.

Fig. 2
Fig. 2

dn/dT at 633 nm and the fit of α for YAG. The solid line is the fit for α from Eq. (1). The rest of the data are dn/dT, with open circles calculated from the experimental data from Ref. 5 of the optical path-length change with temperature at 633 nm and other measurements for T > 300 for reference.

Tables (1)

Tables Icon

Table 1 Measured Values for α(T)

Equations (2)

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αT=aT+bT2+cT3
1nLdnLdT=1ndndT+α.

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