Abstract

Temperature measurement is required for many applications but can be difficult in some cases. Laser heating or cooling studies demand accurate measurements of temperature changes. A Michelson interferometer configuration has been used to investigate laser heating in solids. An analytical formula was derived to estimate the temperature change from the fringe count by taking into account the temperature dependence of the sample length and refractive index. When 115mW of a focused Ar+ laser beam (488nm) passes through a Pr3+-doped YAG sample, its temperature increased by 11.7±1.0K along the beam path due to nonradiative relaxation. The power dependence of the fringe count/movement was recorded. The temperature change was estimated by the interferometric method and is in agreement with that measured by a thermocouple.

© 2011 Optical Society of America

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References

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2009

I. Kamma, P. Kommidi, and B. R. Reddy, “High temperature measurement using luminescence of Pr3+ doped YAG and Ho3+ doped CaF2,” Phys. Status Solidi C 6, S187–S190 (2009).
[CrossRef]

2008

1999

1998

1996

T. Sato and J. Suda, “Temperature dependence of the linewidth of the first order Raman spectra for aragonite crystal,” J. Phys. Soc. Jpn. 65, 482–488 (1996).
[CrossRef]

K. I. Kang, T. G. Chang, I. Glesk, and P. R. Prucnal, “Nonlinear-index-of-refraction measurement in a resonant region by the use of fiber Mach–Zehnder interferometer,” Appl. Opt. 35, 1485–1488 (1996).
[CrossRef] [PubMed]

1995

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995).
[CrossRef]

1994

X. Wu, W. M. Dennis, and W. M. Yen, “Temperature dependence of cross relaxation processes in Pr3+-doped yttrium aluminum garnet,” Phys. Rev. B 50, 6589–6595(1994).
[CrossRef]

M. Malinowski, M. F. Joubert, and B. Jacquier, “Dynamics of the IR-to-blue wavelength upconversion in Pr3+-doped yttrium aluminum garnet and LiYF4 crystals,” Phys. Rev. B 50, 12367–12374 (1994).
[CrossRef]

1983

G. C. Alessandretti and P. Violono, “Thermometry by CARS in an automobile engine,” J. Phys. D: Appl. Phys. 16, 1583–1594(1983).
[CrossRef]

1981

1976

1972

S. S. Sandhu and F. J. Weinberg, “A laser interferometer for combustion, aerodynamics and heat transfer studies,” J. Phys. E Sci. Instrum. 5, 1018–1020 (1972).
[CrossRef]

1968

Alessandretti, G. C.

G. C. Alessandretti and P. Violono, “Thermometry by CARS in an automobile engine,” J. Phys. D: Appl. Phys. 16, 1583–1594(1983).
[CrossRef]

Anderson, G.

Brewer, C.

Buchwald, M. I.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995).
[CrossRef]

Burky, M.

Chakravarty, A.

N. Cherroret, A. Chakravarty, and A. Kar, “Temperature dependent refractive index of semiconductors,” J. Mater. Sci. 43, 1795–1801 (2008).
[CrossRef]

Chang, T. G.

Cherroret, N.

N. Cherroret, A. Chakravarty, and A. Kar, “Temperature dependent refractive index of semiconductors,” J. Mater. Sci. 43, 1795–1801 (2008).
[CrossRef]

Cusso, F.

Daneu, J. L.

Dennis, W. M.

X. Wu, W. M. Dennis, and W. M. Yen, “Temperature dependence of cross relaxation processes in Pr3+-doped yttrium aluminum garnet,” Phys. Rev. B 50, 6589–6595(1994).
[CrossRef]

DesAutels, G. L.

Edwards, B. C.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995).
[CrossRef]

Epstein, R. I.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995).
[CrossRef]

Fan, T. Y.

Foster, J. D.

George, T. G.

Y. K. Kim, B. R. Reddy, T. G. George, and R. B. Lal, “Optical heterodyne interferometry technique for solution crystal growth rate measurement,” Opt. Eng. 37, 616–621 (1998).
[CrossRef]

Glesk, I.

Gosnell, T. R.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995).
[CrossRef]

Hariharan, P.

P. Hariharan, Optical Interferometry (Elsevier/Academic, 2003).

Hawkins, R. T.

Ishii, Y.

Jacquier, B.

M. Malinowski, M. F. Joubert, and B. Jacquier, “Dynamics of the IR-to-blue wavelength upconversion in Pr3+-doped yttrium aluminum garnet and LiYF4 crystals,” Phys. Rev. B 50, 12367–12374 (1994).
[CrossRef]

Joubert, M. F.

M. Malinowski, M. F. Joubert, and B. Jacquier, “Dynamics of the IR-to-blue wavelength upconversion in Pr3+-doped yttrium aluminum garnet and LiYF4 crystals,” Phys. Rev. B 50, 12367–12374 (1994).
[CrossRef]

Kamma, I.

I. Kamma, P. Kommidi, and B. R. Reddy, “High temperature measurement using luminescence of Pr3+ doped YAG and Ho3+ doped CaF2,” Phys. Status Solidi C 6, S187–S190 (2009).
[CrossRef]

Kang, K. I.

Kar, A.

N. Cherroret, A. Chakravarty, and A. Kar, “Temperature dependent refractive index of semiconductors,” J. Mater. Sci. 43, 1795–1801 (2008).
[CrossRef]

Kato, M.

Kim, Y. K.

Y. K. Kim, B. R. Reddy, T. G. George, and R. B. Lal, “Optical heterodyne interferometry technique for solution crystal growth rate measurement,” Opt. Eng. 37, 616–621 (1998).
[CrossRef]

Kommidi, P.

I. Kamma, P. Kommidi, and B. R. Reddy, “High temperature measurement using luminescence of Pr3+ doped YAG and Ho3+ doped CaF2,” Phys. Status Solidi C 6, S187–S190 (2009).
[CrossRef]

Kowalski, F. V.

Lal, R. B.

Y. K. Kim, B. R. Reddy, T. G. George, and R. B. Lal, “Optical heterodyne interferometry technique for solution crystal growth rate measurement,” Opt. Eng. 37, 616–621 (1998).
[CrossRef]

Malinowski, M.

M. Malinowski, M. F. Joubert, and B. Jacquier, “Dynamics of the IR-to-blue wavelength upconversion in Pr3+-doped yttrium aluminum garnet and LiYF4 crystals,” Phys. Rev. B 50, 12367–12374 (1994).
[CrossRef]

Mungan, C. E.

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995).
[CrossRef]

Munoz, J. A.

Osterink, L. M.

Peters, P.

Prucnal, P. R.

Reddy, B. R.

I. Kamma, P. Kommidi, and B. R. Reddy, “High temperature measurement using luminescence of Pr3+ doped YAG and Ho3+ doped CaF2,” Phys. Status Solidi C 6, S187–S190 (2009).
[CrossRef]

Y. K. Kim, B. R. Reddy, T. G. George, and R. B. Lal, “Optical heterodyne interferometry technique for solution crystal growth rate measurement,” Opt. Eng. 37, 616–621 (1998).
[CrossRef]

Sandhu, S. S.

S. S. Sandhu and F. J. Weinberg, “A laser interferometer for combustion, aerodynamics and heat transfer studies,” J. Phys. E Sci. Instrum. 5, 1018–1020 (1972).
[CrossRef]

Sato, T.

T. Sato and J. Suda, “Temperature dependence of the linewidth of the first order Raman spectra for aragonite crystal,” J. Phys. Soc. Jpn. 65, 482–488 (1996).
[CrossRef]

Schawlow, A. L.

Sommergen, G. E.

Suda, J.

T. Sato and J. Suda, “Temperature dependence of the linewidth of the first order Raman spectra for aragonite crystal,” J. Phys. Soc. Jpn. 65, 482–488 (1996).
[CrossRef]

Tocho, J. O.

Violono, P.

G. C. Alessandretti and P. Violono, “Thermometry by CARS in an automobile engine,” J. Phys. D: Appl. Phys. 16, 1583–1594(1983).
[CrossRef]

Wada, A.

Walker, M.

Weinberg, F. J.

S. S. Sandhu and F. J. Weinberg, “A laser interferometer for combustion, aerodynamics and heat transfer studies,” J. Phys. E Sci. Instrum. 5, 1018–1020 (1972).
[CrossRef]

Wu, X.

X. Wu, W. M. Dennis, and W. M. Yen, “Temperature dependence of cross relaxation processes in Pr3+-doped yttrium aluminum garnet,” Phys. Rev. B 50, 6589–6595(1994).
[CrossRef]

Wynne, R.

Yen, W. M.

X. Wu, W. M. Dennis, and W. M. Yen, “Temperature dependence of cross relaxation processes in Pr3+-doped yttrium aluminum garnet,” Phys. Rev. B 50, 6589–6595(1994).
[CrossRef]

Yoshizawa, T.

T. Yoshizawa, Handbook of Optical Metrology: Principles and Applications (CRC, 2009).
[CrossRef]

Appl. Opt.

J. Mater. Sci.

N. Cherroret, A. Chakravarty, and A. Kar, “Temperature dependent refractive index of semiconductors,” J. Mater. Sci. 43, 1795–1801 (2008).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. D: Appl. Phys.

G. C. Alessandretti and P. Violono, “Thermometry by CARS in an automobile engine,” J. Phys. D: Appl. Phys. 16, 1583–1594(1983).
[CrossRef]

J. Phys. E Sci. Instrum.

S. S. Sandhu and F. J. Weinberg, “A laser interferometer for combustion, aerodynamics and heat transfer studies,” J. Phys. E Sci. Instrum. 5, 1018–1020 (1972).
[CrossRef]

J. Phys. Soc. Jpn.

T. Sato and J. Suda, “Temperature dependence of the linewidth of the first order Raman spectra for aragonite crystal,” J. Phys. Soc. Jpn. 65, 482–488 (1996).
[CrossRef]

Nature

R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, and C. E. Mungan, “Observation of laser induced fluorescent cooling of a solid,” Nature 377, 500–503 (1995).
[CrossRef]

Opt. Eng.

Y. K. Kim, B. R. Reddy, T. G. George, and R. B. Lal, “Optical heterodyne interferometry technique for solution crystal growth rate measurement,” Opt. Eng. 37, 616–621 (1998).
[CrossRef]

Phys. Rev. B

X. Wu, W. M. Dennis, and W. M. Yen, “Temperature dependence of cross relaxation processes in Pr3+-doped yttrium aluminum garnet,” Phys. Rev. B 50, 6589–6595(1994).
[CrossRef]

M. Malinowski, M. F. Joubert, and B. Jacquier, “Dynamics of the IR-to-blue wavelength upconversion in Pr3+-doped yttrium aluminum garnet and LiYF4 crystals,” Phys. Rev. B 50, 12367–12374 (1994).
[CrossRef]

Phys. Status Solidi C

I. Kamma, P. Kommidi, and B. R. Reddy, “High temperature measurement using luminescence of Pr3+ doped YAG and Ho3+ doped CaF2,” Phys. Status Solidi C 6, S187–S190 (2009).
[CrossRef]

Other

YAG data sheet, VLOC, Fla. (www.vloc.com).

T. Yoshizawa, Handbook of Optical Metrology: Principles and Applications (CRC, 2009).
[CrossRef]

P. Hariharan, Optical Interferometry (Elsevier/Academic, 2003).

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Figures (7)

Fig. 1
Fig. 1

Partial energy level diagram of Pr 3 + -doped YAG crystal. Upward and downward arrows represent laser excitation and fluorescence transitions. The wavy arrows represent nonradiative relaxation.

Fig. 2
Fig. 2

Block diagram of the experimental setup: SA, sample; CF, color filter; BS, beam splitter; M, mirror; and D, detector.

Fig. 3
Fig. 3

Temporal variation of the detector output obtained when 115 mW of an Ar + laser beam was launched through the sample located at the focus. The Ar + laser was on from t = 0 to 600 s .

Fig. 4
Fig. 4

Temporal variation of the detector output during heating (the Ar + laser was on from t = 0 to 135 s ) and cooling (the Ar + was off from t = 135 to 300 s ) periods.

Fig. 5
Fig. 5

Temporal variation of the detector output from t = 0 to 400 s measured for different powers of an unfocused Ar + laser beam: (a)  50 mW (b)  100 mW , and (c)  140 mW . The Ar + laser was on from t = 0 to 400 s .

Fig. 6
Fig. 6

Sample mounting configuration for heating and cooling studies: 1, YAG sample; 2, aluminum block; 3, glass beaker; 4, water; 5, hot plate; and 6, thermocouple.

Fig. 7
Fig. 7

Temporal variation of the detector output measured when the sample holder was (a) heated in a water bath from 22.5 °C ( t = 0 s ) to 36.5 °C ( t = 853 s ), and (b) the water bath was naturally cooled in ambient air from 35 °C ( t = 0 s ) to 27.6 °C ( t = 2400 s ).

Equations (14)

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

D 1 = 2 η 1 ( L 1 L 2 ) + 2 η 2 L 2 ,
D 2 = 2 η 1 L 1 ,
OPD = D 1 D 2 = 2 η 1 ( L 1 L 2 ) + 2 η 2 L 2 2 η 1 L 1 = 2 L 2 ( η 2 η 1 ) = 2 L 2 ( η 2 1 ) = 2 L ( η 1 ) ,
η ( T ) = η 0 + d η d T Δ T ,
L ( T ) = L 0 + d L d T Δ T ,
Δ ( OPD ) = 2 [ Δ ( η L ) Δ L ] = 2 [ ( Δ η ) L + η Δ L Δ L ] ,
Δ ( OPD ) = 2 ( L d η d T Δ T + η d L d T Δ T d L d T Δ T ) ,
Δ ( OPD ) = 2 L η ( 1 η d η d T Δ T + 1 L d L d T Δ T 1 L η d L d T Δ T ) .
Δ ( OPD ) = 2 L η ( 1 η d η d T + α α η ) Δ T ,
α = 1 L d L d T .
λ N = 2 L η ( γ α η ) Δ T ,
γ = 1 η d η d T + α .
Δ T = λ N 2 L η ( γ α η ) .
Δ T u = ( T N ) 2 ( Δ N u ) 2 + ( T L ) 2 ( Δ L u ) 2 + ( T η ) 2 ( Δ η u ) 2 + ( T α ) 2 ( Δ α u ) 2 + ( T γ ) 2 ( Δ γ u ) 2 ,

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