Abstract

We analyze the random process of fluorescence reabsorption and trapping in solid-state optical materials in general and its influence on the efficiency of optical cooling of solids by anti-Stokes fluorescence in particular. Using the absorption and fluorescence spectra of Yb3+:ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN) as input data, we employ a random-walk model to test analytical approximations of the fluorescence escape efficiency and cooling efficiency, including reflections at the boundary.

© 2005 Optical Society of America

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  1. R. I. Epstein, M. I. Buchwald, B. C. Edwards, T. R. Gosnell, C. E. Mungan, “Observations of laser-induced fluorescent cooling of a solid,” Nature (London) 377, 500–503 (1995).
    [CrossRef]
  2. A. Rayner, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Condensed phase optical refrigeration,” J. Opt. Soc. Am. B. 20, 1037–1053 (2003).
    [CrossRef]
  3. C. E. Mungan, T. R. Gosnell, “Laser cooling of solids,” Adv. At. Mol. Opt. Phys. 40, 161–228 (1999).
    [CrossRef]
  4. M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).
  5. B. C. Edwards, M. I. Buchwald, R. I. Epstein, “Development of the Los Alamos solid-state optical refrigerator,” Rev. Sci. Instrum. 69, 2050–2055 (1998).
    [CrossRef]
  6. W. N. Carr, G. E. Pittman, “One-watt GaAs P-N junction infrared source,” Appl. Phys. Lett. 3, 173–175 (1963).
    [CrossRef]
  7. H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys. A 64, 143–147 (1997).
    [CrossRef]
  8. M. Sheik-Bahae, R. I. Epstein, “Can laser light cool semiconductors?,” Phys. Rev. Lett. 92, 247403 (2004).
    [CrossRef] [PubMed]
  9. E. Finkeissen, M. Potemski, P. Wyder, L. Viña, G. Weimann, “Cooling of a semiconductor by luminescence upconversion,” Appl. Phys. Lett. 75, 1258–1260 (1999).
    [CrossRef]
  10. R. Frey, F. Micheron, J. P. Pochollo, “Comparison of Peltier and anti-Stokes optical coolings,” J. Appl. Phys. 87, 4489–4498 (2000).
    [CrossRef]
  11. J. S. Batchelder, A. H. Zewail, T. Cole, “Luminescent solar concentrators. 1: Theory of operation and techniques for performance evaluation,” Appl. Opt. 18, 3090–3110 (1979).
    [CrossRef] [PubMed]
  12. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72, 899–907 (1982).
    [CrossRef]
  13. I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
    [CrossRef]
  14. B. Heeg, G. Rumbles, “Influence of radiative transfer on optical cooling in the condensed phase,” J. Appl. Phys. 93, 1966–1973 (2003).
    [CrossRef]
  15. S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
    [CrossRef]
  16. R. W. Olson, R. F. Loring, M. D. Fayer, “Luminescent solar concentrators and the reabsorption problem,” Appl. Opt. 20, 2934–2940 (1981).
    [CrossRef] [PubMed]
  17. B. Saleh, Fundamentals of Photonics (Wiley, New York, 1991).
    [CrossRef]
  18. M. P. Hehlen, “Reabsorption artifacts in measured excited-state lifetimes in solids,” J. Opt. Soc. Am. B 14, 1312–1318 (1997).
    [CrossRef]

2004 (1)

M. Sheik-Bahae, R. I. Epstein, “Can laser light cool semiconductors?,” Phys. Rev. Lett. 92, 247403 (2004).
[CrossRef] [PubMed]

2003 (2)

A. Rayner, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Condensed phase optical refrigeration,” J. Opt. Soc. Am. B. 20, 1037–1053 (2003).
[CrossRef]

B. Heeg, G. Rumbles, “Influence of radiative transfer on optical cooling in the condensed phase,” J. Appl. Phys. 93, 1966–1973 (2003).
[CrossRef]

2000 (1)

R. Frey, F. Micheron, J. P. Pochollo, “Comparison of Peltier and anti-Stokes optical coolings,” J. Appl. Phys. 87, 4489–4498 (2000).
[CrossRef]

1999 (2)

C. E. Mungan, T. R. Gosnell, “Laser cooling of solids,” Adv. At. Mol. Opt. Phys. 40, 161–228 (1999).
[CrossRef]

E. Finkeissen, M. Potemski, P. Wyder, L. Viña, G. Weimann, “Cooling of a semiconductor by luminescence upconversion,” Appl. Phys. Lett. 75, 1258–1260 (1999).
[CrossRef]

1998 (1)

B. C. Edwards, M. I. Buchwald, R. I. Epstein, “Development of the Los Alamos solid-state optical refrigerator,” Rev. Sci. Instrum. 69, 2050–2055 (1998).
[CrossRef]

1997 (2)

H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys. A 64, 143–147 (1997).
[CrossRef]

M. P. Hehlen, “Reabsorption artifacts in measured excited-state lifetimes in solids,” J. Opt. Soc. Am. B 14, 1312–1318 (1997).
[CrossRef]

1995 (1)

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

1993 (1)

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

1982 (1)

1981 (1)

1979 (1)

1963 (1)

W. N. Carr, G. E. Pittman, “One-watt GaAs P-N junction infrared source,” Appl. Phys. Lett. 3, 173–175 (1963).
[CrossRef]

1943 (1)

S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
[CrossRef]

Batchelder, J. S.

Bender, D.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Bertness, K. A.

H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys. A 64, 143–147 (1997).
[CrossRef]

Bigotta, S.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Buchwald, M. I.

B. C. Edwards, M. I. Buchwald, R. I. Epstein, “Development of the Los Alamos solid-state optical refrigerator,” Rev. Sci. Instrum. 69, 2050–2055 (1998).
[CrossRef]

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

Caneau, C.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

Carr, W. N.

W. N. Carr, G. E. Pittman, “One-watt GaAs P-N junction infrared source,” Appl. Phys. Lett. 3, 173–175 (1963).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
[CrossRef]

Cole, T.

Cornell, E. A.

H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys. A 64, 143–147 (1997).
[CrossRef]

Distel, J.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Edwards, B. C.

B. C. Edwards, M. I. Buchwald, R. I. Epstein, “Development of the Los Alamos solid-state optical refrigerator,” Rev. Sci. Instrum. 69, 2050–2055 (1998).
[CrossRef]

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

Epstein, R. I.

M. Sheik-Bahae, R. I. Epstein, “Can laser light cool semiconductors?,” Phys. Rev. Lett. 92, 247403 (2004).
[CrossRef] [PubMed]

B. C. Edwards, M. I. Buchwald, R. I. Epstein, “Development of the Los Alamos solid-state optical refrigerator,” Rev. Sci. Instrum. 69, 2050–2055 (1998).
[CrossRef]

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

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Fayer, M. D.

Finkeissen, E.

E. Finkeissen, M. Potemski, P. Wyder, L. Viña, G. Weimann, “Cooling of a semiconductor by luminescence upconversion,” Appl. Phys. Lett. 75, 1258–1260 (1999).
[CrossRef]

Frey, R.

R. Frey, F. Micheron, J. P. Pochollo, “Comparison of Peltier and anti-Stokes optical coolings,” J. Appl. Phys. 87, 4489–4498 (2000).
[CrossRef]

Gauck, H.

H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys. A 64, 143–147 (1997).
[CrossRef]

Gfroerer, T. H.

H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys. A 64, 143–147 (1997).
[CrossRef]

Gmitter, T. J.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

Gosnell, T. R.

C. E. Mungan, T. R. Gosnell, “Laser cooling of solids,” Adv. At. Mol. Opt. Phys. 40, 161–228 (1999).
[CrossRef]

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

Greenfield, S.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Hasselbeck, M. P.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Heckenberg, N. R.

A. Rayner, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Condensed phase optical refrigeration,” J. Opt. Soc. Am. B. 20, 1037–1053 (2003).
[CrossRef]

Heeg, B.

B. Heeg, G. Rumbles, “Influence of radiative transfer on optical cooling in the condensed phase,” J. Appl. Phys. 93, 1966–1973 (2003).
[CrossRef]

Hehlen, M. P.

M. P. Hehlen, “Reabsorption artifacts in measured excited-state lifetimes in solids,” J. Opt. Soc. Am. B 14, 1312–1318 (1997).
[CrossRef]

Imangholi, B.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Loring, R. F.

Micheron, F.

R. Frey, F. Micheron, J. P. Pochollo, “Comparison of Peltier and anti-Stokes optical coolings,” J. Appl. Phys. 87, 4489–4498 (2000).
[CrossRef]

Mungan, C. E.

C. E. Mungan, T. R. Gosnell, “Laser cooling of solids,” Adv. At. Mol. Opt. Phys. 40, 161–228 (1999).
[CrossRef]

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

Olson, R. W.

Patterson, W.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Pittman, G. E.

W. N. Carr, G. E. Pittman, “One-watt GaAs P-N junction infrared source,” Appl. Phys. Lett. 3, 173–175 (1963).
[CrossRef]

Pochollo, J. P.

R. Frey, F. Micheron, J. P. Pochollo, “Comparison of Peltier and anti-Stokes optical coolings,” J. Appl. Phys. 87, 4489–4498 (2000).
[CrossRef]

Potemski, M.

E. Finkeissen, M. Potemski, P. Wyder, L. Viña, G. Weimann, “Cooling of a semiconductor by luminescence upconversion,” Appl. Phys. Lett. 75, 1258–1260 (1999).
[CrossRef]

Rayner, A.

A. Rayner, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Condensed phase optical refrigeration,” J. Opt. Soc. Am. B. 20, 1037–1053 (2003).
[CrossRef]

Renn, M. J.

H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys. A 64, 143–147 (1997).
[CrossRef]

Rubinsztein-Dunlop, H.

A. Rayner, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Condensed phase optical refrigeration,” J. Opt. Soc. Am. B. 20, 1037–1053 (2003).
[CrossRef]

Rumbles, G.

B. Heeg, G. Rumbles, “Influence of radiative transfer on optical cooling in the condensed phase,” J. Appl. Phys. 93, 1966–1973 (2003).
[CrossRef]

Saleh, B.

B. Saleh, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Schnitzer, I.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

Seletskiy, D.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Sheik-Bahae, M.

M. Sheik-Bahae, R. I. Epstein, “Can laser light cool semiconductors?,” Phys. Rev. Lett. 92, 247403 (2004).
[CrossRef] [PubMed]

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Thiede, J.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Vadiee, N.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Vankipuram, V.

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

Viña, L.

E. Finkeissen, M. Potemski, P. Wyder, L. Viña, G. Weimann, “Cooling of a semiconductor by luminescence upconversion,” Appl. Phys. Lett. 75, 1258–1260 (1999).
[CrossRef]

Weimann, G.

E. Finkeissen, M. Potemski, P. Wyder, L. Viña, G. Weimann, “Cooling of a semiconductor by luminescence upconversion,” Appl. Phys. Lett. 75, 1258–1260 (1999).
[CrossRef]

Wyder, P.

E. Finkeissen, M. Potemski, P. Wyder, L. Viña, G. Weimann, “Cooling of a semiconductor by luminescence upconversion,” Appl. Phys. Lett. 75, 1258–1260 (1999).
[CrossRef]

Yablonovitch, E.

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72, 899–907 (1982).
[CrossRef]

Zewail, A. H.

Adv. At. Mol. Opt. Phys. (1)

C. E. Mungan, T. R. Gosnell, “Laser cooling of solids,” Adv. At. Mol. Opt. Phys. 40, 161–228 (1999).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

E. Finkeissen, M. Potemski, P. Wyder, L. Viña, G. Weimann, “Cooling of a semiconductor by luminescence upconversion,” Appl. Phys. Lett. 75, 1258–1260 (1999).
[CrossRef]

Appl. Phys. A (1)

H. Gauck, T. H. Gfroerer, M. J. Renn, E. A. Cornell, K. A. Bertness, “External radiative quantum efficiency of 96% from a GaAs/GaInP heterostructure,” Appl. Phys. A 64, 143–147 (1997).
[CrossRef]

Appl. Phys. Lett. (2)

W. N. Carr, G. E. Pittman, “One-watt GaAs P-N junction infrared source,” Appl. Phys. Lett. 3, 173–175 (1963).
[CrossRef]

I. Schnitzer, E. Yablonovitch, C. Caneau, T. J. Gmitter, “Ultrahigh spontaneous emission quantum efficiency, 99.7% internally and 72% externally, from AlGaAs/GaAs/AlGaAs double heterostructures,” Appl. Phys. Lett. 62, 131–133 (1993).
[CrossRef]

J. Appl. Phys. (1)

B. Heeg, G. Rumbles, “Influence of radiative transfer on optical cooling in the condensed phase,” J. Appl. Phys. 93, 1966–1973 (2003).
[CrossRef]

J. Appl. Phys. (1)

R. Frey, F. Micheron, J. P. Pochollo, “Comparison of Peltier and anti-Stokes optical coolings,” J. Appl. Phys. 87, 4489–4498 (2000).
[CrossRef]

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

M. P. Hehlen, “Reabsorption artifacts in measured excited-state lifetimes in solids,” J. Opt. Soc. Am. B 14, 1312–1318 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

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

A. Rayner, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Condensed phase optical refrigeration,” J. Opt. Soc. Am. B. 20, 1037–1053 (2003).
[CrossRef]

Nature (London) (1)

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

Phys. Rev. Lett. (1)

M. Sheik-Bahae, R. I. Epstein, “Can laser light cool semiconductors?,” Phys. Rev. Lett. 92, 247403 (2004).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

S. Chandrasekhar, “Stochastic problems in physics and astronomy,” Rev. Mod. Phys. 15, 1–89 (1943).
[CrossRef]

Rev. Sci. Instrum. (1)

B. C. Edwards, M. I. Buchwald, R. I. Epstein, “Development of the Los Alamos solid-state optical refrigerator,” Rev. Sci. Instrum. 69, 2050–2055 (1998).
[CrossRef]

Other (2)

M. P. Hasselbeck, M. Sheik-Bahae, J. Thiede, J. Distel, S. Greenfield, W. Patterson, S. Bigotta, B. Imangholi, D. Seletskiy, D. Bender, V. Vankipuram, N. Vadiee, R. I. Epstein, “Laser cooling of infrared sensors,” in Earth Observing Systems IX, W. Barnes, J. Butler, eds., Proc. SPIE5543, 31–40 (2004).

B. Saleh, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Geometry of cell used to estimate the photon escape efficiency.

Fig. 2
Fig. 2

Two-dimensional schematic of possible photon trajectories.

Fig. 3
Fig. 3

Absorption, normalized fluorescence, and spectral overlap for 2%-doped Yb3+:ZBLAN. The reabsorption coefficient is obtained by integrating the overlap region, resulting in a value of aR = 0.266. This value corresponds to an average step size ave = 11.3 mm.

Fig. 4
Fig. 4

Coefficient G as a function of the dimensionless step size ave/L comparing our current data obtained with a cubic geometry and an average step length ave = 11.3 mm and data obtained from Ref. 16.

Fig. 5
Fig. 5

Fluorescence escape efficiency ηe as a function of intrinsic quantum yield η0, including total internal reflections at the boundary, for several dimensions.

Fig. 6
Fig. 6

Total relative cooling efficiency ηcool for L = 5 mm, η0 = 0.99, obtained from Eq. (9) and from the random-walk model. For comparison, the values for ηc in the absence of reabsorption (i.e., η0 = 1) are included.

Fig. 7
Fig. 7

Escape efficiencies as a function of dimensionless step size based on Yb3+:ZBLAN for various values of relative background absorption. The parameter η0 is fixed at 0.99.

Fig. 8
Fig. 8

Relative cooling efficiencies as a function of dimensionless step size based on Yb3+:ZBLAN for various values of relative background absorption. The pump wavelength is fixed at 1010 nm and η0 is fixed at 0.99.

Tables (1)

Tables Icon

Table 1 Numerical Values of Relevant Parameters Used to Estimate the Escape Efficiency

Equations (11)

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

N = G ( L / ave ) 2
η 1 = ( η 0 ) N ,
η 0 = η 0 [ 1 α 0 ( α R + α 0 ) ] .
λ ¯ F , N = λ ¯ F 0 + Δ λ ( N ) = λ ¯ F 0 + ( N 1 ) δ λ .
λ R = α F 0 λ d λ / α F 0 d λ = α R 1 α F 0 λ d λ ,
λ ¯ F , N = λ F , N ¯ .
η e 1 = ( η 0 ) N [ F A + F C ( 1 A C ) ] .
η e 2 = ( η 0 ) N ( F B + F C A C ) η e 1 = ( η 0 ) N { ( 1 1 / n 2 ) 1 / 2 1 / n + [ 1 exp ( α R L / 2 ) / n } η e 1 = ( η 0 ) N [ ( 1 1 / n 2 ) 1 / 2 exp ( α R L / 2 ) / n ] η e 1 = B η e 1 .
η e = η e 1 + η e 2 + η e 3 + = η e 1 1 B = ( η 0 ) N ( { 1 [ 1 ( 1 / n ) 2 ] 1 / 2 } + exp ( α R L / 2 ) / n ) 1 [ ( 1 1 / n 2 ) 1 / 2 exp ( α R L / 2 ) / n ] ( η 0 ) N .
η c = ( λ ¯ F , N λ L ) / λ ¯ F , N ,
η cool = P cool P abs η c η e + ( 1 η e ) .

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