Abstract

We present a comprehensive investigation of the temperature distribution in laser-cooled cylindrical solid-state samples doped with rare-earth ions. We consider Yb3+-doped fluorozirconate samples pumped at a wavelength of 1015 nm with Gaussian and “Top-Hat” pump beams. The influence of the parameters of a beam on the temperature distribution is investigated in detail for optimizing the sample design for the all-optical cryocooler.

© 2010 Optical Society of America

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  1. P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenz und temperature-strahlung,” Z. Phys. 57, 739–746 (1929).
    [CrossRef]
  2. 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]
  3. M. P. Hehlen, “Novel materials for laser refrigeration,”Proc. SPIE 7228, 72280E (2009).
    [CrossRef]
  4. D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
    [CrossRef]
  5. W. M. Patterson, M. Sheik-Bahae, R. I. Epstein, and M. P. Hehlen, “Model of laser-induced temperature changes in solid-state optical refrigerators,” J. Appl. Phys. 107, 063108 (2010).
    [CrossRef]
  6. R. Caspary, “Applied rare-earth spectroscopy for fiber laser optimization,” Ph.D. dissertation (Technischen Universität Carolo-Wilhelmina zu Braunschweig, 2002).
  7. A. E. Siegman, “New development in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
    [CrossRef]
  8. J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling tp 208 K by optical refrigeration,” Appl. Phys. Lett. 86, 154107 (2005).
    [CrossRef]
  9. T. R. Gosnell, “Laser cooling of a solid by 65 K starting from room temperature,” Opt. Lett. 24, 1041–1043 (1999).
    [CrossRef]
  10. X. Zhu and N. Peyghambarian, “High-power ZBLAN glass fiber lasers: review and prospect,” Adv. OptoElectron. 2010, 501956 (2010).

2010 (3)

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[CrossRef]

W. M. Patterson, M. Sheik-Bahae, R. I. Epstein, and M. P. Hehlen, “Model of laser-induced temperature changes in solid-state optical refrigerators,” J. Appl. Phys. 107, 063108 (2010).
[CrossRef]

X. Zhu and N. Peyghambarian, “High-power ZBLAN glass fiber lasers: review and prospect,” Adv. OptoElectron. 2010, 501956 (2010).

2009 (1)

M. P. Hehlen, “Novel materials for laser refrigeration,”Proc. SPIE 7228, 72280E (2009).
[CrossRef]

2005 (1)

J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling tp 208 K by optical refrigeration,” Appl. Phys. Lett. 86, 154107 (2005).
[CrossRef]

2002 (1)

R. Caspary, “Applied rare-earth spectroscopy for fiber laser optimization,” Ph.D. dissertation (Technischen Universität Carolo-Wilhelmina zu Braunschweig, 2002).

1999 (1)

1995 (1)

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]

1990 (1)

A. E. Siegman, “New development in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[CrossRef]

1929 (1)

P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenz und temperature-strahlung,” Z. Phys. 57, 739–746 (1929).
[CrossRef]

Bigotta, S.

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[CrossRef]

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]

Caspary, R.

R. Caspary, “Applied rare-earth spectroscopy for fiber laser optimization,” Ph.D. dissertation (Technischen Universität Carolo-Wilhelmina zu Braunschweig, 2002).

Distel, J.

J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling tp 208 K by optical refrigeration,” Appl. Phys. Lett. 86, 154107 (2005).
[CrossRef]

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.

W. M. Patterson, M. Sheik-Bahae, R. I. Epstein, and M. P. Hehlen, “Model of laser-induced temperature changes in solid-state optical refrigerators,” J. Appl. Phys. 107, 063108 (2010).
[CrossRef]

J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling tp 208 K by optical refrigeration,” Appl. Phys. Lett. 86, 154107 (2005).
[CrossRef]

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]

Gosnell, T. R.

T. R. Gosnell, “Laser cooling of a solid by 65 K starting from room temperature,” Opt. Lett. 24, 1041–1043 (1999).
[CrossRef]

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]

Greenfield, S. R.

J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling tp 208 K by optical refrigeration,” Appl. Phys. Lett. 86, 154107 (2005).
[CrossRef]

Hehlen, M. P.

W. M. Patterson, M. Sheik-Bahae, R. I. Epstein, and M. P. Hehlen, “Model of laser-induced temperature changes in solid-state optical refrigerators,” J. Appl. Phys. 107, 063108 (2010).
[CrossRef]

M. P. Hehlen, “Novel materials for laser refrigeration,”Proc. SPIE 7228, 72280E (2009).
[CrossRef]

Lieto, A. D.

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[CrossRef]

Melgaard, S. D.

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[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]

Patterson, W. M.

W. M. Patterson, M. Sheik-Bahae, R. I. Epstein, and M. P. Hehlen, “Model of laser-induced temperature changes in solid-state optical refrigerators,” J. Appl. Phys. 107, 063108 (2010).
[CrossRef]

Peyghambarian, N.

X. Zhu and N. Peyghambarian, “High-power ZBLAN glass fiber lasers: review and prospect,” Adv. OptoElectron. 2010, 501956 (2010).

Pringsheim, P.

P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenz und temperature-strahlung,” Z. Phys. 57, 739–746 (1929).
[CrossRef]

Seletskiy, D. V.

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[CrossRef]

Sheik-Bahae, M.

W. M. Patterson, M. Sheik-Bahae, R. I. Epstein, and M. P. Hehlen, “Model of laser-induced temperature changes in solid-state optical refrigerators,” J. Appl. Phys. 107, 063108 (2010).
[CrossRef]

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “New development in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[CrossRef]

Thiede, J.

J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling tp 208 K by optical refrigeration,” Appl. Phys. Lett. 86, 154107 (2005).
[CrossRef]

Tonelli, M.

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[CrossRef]

Zhu, X.

X. Zhu and N. Peyghambarian, “High-power ZBLAN glass fiber lasers: review and prospect,” Adv. OptoElectron. 2010, 501956 (2010).

Adv. OptoElectron. (1)

X. Zhu and N. Peyghambarian, “High-power ZBLAN glass fiber lasers: review and prospect,” Adv. OptoElectron. 2010, 501956 (2010).

Appl. Phys. Lett. (1)

J. Thiede, J. Distel, S. R. Greenfield, and R. I. Epstein, “Cooling tp 208 K by optical refrigeration,” Appl. Phys. Lett. 86, 154107 (2005).
[CrossRef]

J. Appl. Phys. (1)

W. M. Patterson, M. Sheik-Bahae, R. I. Epstein, and M. P. Hehlen, “Model of laser-induced temperature changes in solid-state optical refrigerators,” J. Appl. Phys. 107, 063108 (2010).
[CrossRef]

Nat. Photonics (1)

D. V. Seletskiy, S. D. Melgaard, S. Bigotta, A. D. Lieto, M. Tonelli, and M. Sheik-Bahae, “Laser cooling of solids to cryogenic temperatures,” Nat. Photonics 4, 161–164 (2010).
[CrossRef]

Nature (1)

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. Lett. (1)

Proc. SPIE (2)

M. P. Hehlen, “Novel materials for laser refrigeration,”Proc. SPIE 7228, 72280E (2009).
[CrossRef]

A. E. Siegman, “New development in laser resonators,” Proc. SPIE 1224, 2–14 (1990).
[CrossRef]

Z. Phys. (1)

P. Pringsheim, “Zwei bemerkungen über den unterschied von lumineszenz und temperature-strahlung,” Z. Phys. 57, 739–746 (1929).
[CrossRef]

Other (1)

R. Caspary, “Applied rare-earth spectroscopy for fiber laser optimization,” Ph.D. dissertation (Technischen Universität Carolo-Wilhelmina zu Braunschweig, 2002).

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Figures (5)

Fig. 1
Fig. 1

Temperature dependence of (a) mean fluorescence wavelength λ F , (b) laser-cooling efficiency η, and (c) absorption cross section б abs ( λ p ) at λ p = 1015   nm .

Fig. 2
Fig. 2

Temperature of the surface of the sample, T ( R ) , as a function of the length of the sample.

Fig. 3
Fig. 3

Distribution of the temperature difference Δ T in a sample for a Gaussian beam with (a) M 2 = 1 , (b) M 2 = 15 , and (c) M 2 = 30 .

Fig. 4
Fig. 4

Distribution of the temperature difference Δ T in a sample for a Top-Hat beam with (a) M 2 = 1 , (b) M 2 = 15 , and (c) M 2 = 30 .

Fig. 5
Fig. 5

Maximum of the absolute value of the temperature difference in the sample, max | Δ T ( r , z ) | = | Δ T ( 0 , 0 ) | , as a function of ω 0 . The upper curve corresponds to the Gaussian beam. The lower curve corresponds to the Top-Hat beam.

Equations (11)

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1 r r ( r T ( r ) r ) = Q κ ,
Q ( r , z ) = η z I ( r , z ) ,
I z = P abs p ( r , z ) α ( 1 e α L ) e α z ,
p ( r , z ) = 2 π ω p 2 ( z ) exp ( 2 r 2 ω p 2 ( z ) ) exp ( α z ) ,
n ( λ ) = A λ 4 + B λ 2 + C + D λ 2 + E λ 4 ,
Δ T ( r , z ) = η P abs 4 π κ α e α z ( 1 e α L ) [ ln ( R 2 r 2 ) + E 1 ( 2 R 2 ω p 2 ( z ) ) E 1 ( 2 r 2 ω p 2 ( z ) ) ] .
p ( r , z ) = 1 π ω p 2 ( z ) θ [ ω p 2 ( z ) r 2 ] exp ( α z ) ,
Δ T ( r , z ) = η P abs 4 π κ α e α z [ 1 e α L ] { ln ( R ω 0 ) 2 + 1 r 2 ω p 2 , r < ω p ln ( R r ) 2 , r ω p . }
A eff η I z = 2 π R ε σ B ( T r 4 T 4 ( R , z ) ) ,
λ F ( T ) = 1007.8 T / 24 ( nm ) .
σ abs ( T ) = σ abs ( T r ) + | σ abs T | T r ( T T r ) ,

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