Abstract

A “generalized brightness theorem” is derived that describes the thermodynamic limitations of the fluorescent planar concentrator. The maximum brightness concentration ratio allowed by thermodynamics is exp (hΔν/kT) where Δν is the Stokes shift in fluorescence.

© 1980 Optical Society of America

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References

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  1. W. A. Shurcliff, “Radiance Amplification by Multi-Stage Fluorescence System,” J. Opt. Soc. Am. 41, 209 (1951);R. L. Garwin, “The Collection of Light from Scintillation Counters,” Rev. Sci. Instrum. 31, 1010–1011 (1960);W. H. Weber and J. Lambe, “Luminescent Greenhouse Collector for Solar Radiation,” Appl. Opt. 15, 2299–2300 (1976);A. Goetzberger and W. Greubel, “Solar Energy Conversion with Fluorescent Concentrators,” Appl. Phys. 14, 123–139 (1977).
    [CrossRef] [PubMed]
  2. L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, London, 1958).
  3. M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964).
  4. W. Shockley and H. J. Queisser, “Detailed Balance Limit of Efficiency of p-n Junction Solar Cells,” J. Appl. Phys. 32, 510–519 (1961).
    [CrossRef]
  5. E. H. Kennard “On the Thermodynamics of Fluorescence,” Phys. Rev. 11, 29–38 (1918).
    [CrossRef]
  6. W. von Roosbroeck and W. Shockley, “Photon-Radiative Recombination of Electrons and Holes in Germanium,” Phys. Rev. 94, 1558–1560 (1954).
    [CrossRef]
  7. R. T. Ross, “Some Thermodynamics of Photochemical Systems,” J. Chem. Phys. 46, 4590–4593 (1961).This reference also has a historical survey of the statistical model of the fluorescence spectrum.
    [CrossRef]

1961 (2)

W. Shockley and H. J. Queisser, “Detailed Balance Limit of Efficiency of p-n Junction Solar Cells,” J. Appl. Phys. 32, 510–519 (1961).
[CrossRef]

R. T. Ross, “Some Thermodynamics of Photochemical Systems,” J. Chem. Phys. 46, 4590–4593 (1961).This reference also has a historical survey of the statistical model of the fluorescence spectrum.
[CrossRef]

1954 (1)

W. von Roosbroeck and W. Shockley, “Photon-Radiative Recombination of Electrons and Holes in Germanium,” Phys. Rev. 94, 1558–1560 (1954).
[CrossRef]

1951 (1)

1918 (1)

E. H. Kennard “On the Thermodynamics of Fluorescence,” Phys. Rev. 11, 29–38 (1918).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964).

Kennard, E. H.

E. H. Kennard “On the Thermodynamics of Fluorescence,” Phys. Rev. 11, 29–38 (1918).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, London, 1958).

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, London, 1958).

Queisser, H. J.

W. Shockley and H. J. Queisser, “Detailed Balance Limit of Efficiency of p-n Junction Solar Cells,” J. Appl. Phys. 32, 510–519 (1961).
[CrossRef]

Ross, R. T.

R. T. Ross, “Some Thermodynamics of Photochemical Systems,” J. Chem. Phys. 46, 4590–4593 (1961).This reference also has a historical survey of the statistical model of the fluorescence spectrum.
[CrossRef]

Shockley, W.

W. Shockley and H. J. Queisser, “Detailed Balance Limit of Efficiency of p-n Junction Solar Cells,” J. Appl. Phys. 32, 510–519 (1961).
[CrossRef]

W. von Roosbroeck and W. Shockley, “Photon-Radiative Recombination of Electrons and Holes in Germanium,” Phys. Rev. 94, 1558–1560 (1954).
[CrossRef]

Shurcliff, W. A.

von Roosbroeck, W.

W. von Roosbroeck and W. Shockley, “Photon-Radiative Recombination of Electrons and Holes in Germanium,” Phys. Rev. 94, 1558–1560 (1954).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964).

J. Appl. Phys. (1)

W. Shockley and H. J. Queisser, “Detailed Balance Limit of Efficiency of p-n Junction Solar Cells,” J. Appl. Phys. 32, 510–519 (1961).
[CrossRef]

J. Chem. Phys. (1)

R. T. Ross, “Some Thermodynamics of Photochemical Systems,” J. Chem. Phys. 46, 4590–4593 (1961).This reference also has a historical survey of the statistical model of the fluorescence spectrum.
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. (2)

E. H. Kennard “On the Thermodynamics of Fluorescence,” Phys. Rev. 11, 29–38 (1918).
[CrossRef]

W. von Roosbroeck and W. Shockley, “Photon-Radiative Recombination of Electrons and Holes in Germanium,” Phys. Rev. 94, 1558–1560 (1954).
[CrossRef]

Other (2)

L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, London, 1958).

M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964).

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Figures (1)

FIG. 1
FIG. 1

Geometry of the fluorescent planar concentrator. Ω1 and Ω2 are the solid angles of the escape cone and the totally internally reflected ray, respectively.

Equations (13)

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Δ S 1 = K log ( 1 + 8 π n 2 ν 1 2 c 2 B 1 ) ,
Δ S 2 = K log ( 1 + 8 π n 2 ν 2 2 c 2 B 2 ) + h ( ν 1 ν 2 ) T
K log ( 1 + 8 π n 2 ν 1 2 c 2 B 1 ) / ( 1 + 8 π n 2 ν 2 2 c 2 B 2 ) h ( ν 1 ν 2 ) T .
C B 2 B 1 ν 2 2 ν 1 2 exp ( h ( ν 1 ν 2 ) K T ) .
μ Δ F = h ν T Δ S ,
K log ( 1 + 8 π n 2 ν 2 c 2 B ) = h ν μ T .
B ( ν , μ , T ) = 8 π n 2 ν 2 c 2 ( e ( h ν μ ) / K T 1 ) 1 .
F ( ν , μ , T ) = σ ( ν , μ , T ) B ( ν , μ , T ) ,
I ( ν ) B ( ν ) d Ω 4 π .
σ ( ν ) I 1 ( ν ) d ν + σ ( ν ) I 2 ( ν ) d ν = 1 Q σ ( ν ) e ( h ν μ ) / K T 1 8 π n 2 ν 2 c 2 d ν ( Ω 1 4 π + Ω 2 4 π ) .
d I 2 ( ν , x ) d x = N σ ( ν ) I 2 + N σ ( ν ) e ( h ν μ ) / K T 1 8 π n 2 ν 2 c 2 Ω 2 4 π ,
I 2 ( ν , x ) = 8 π n 2 ν 2 2 c 2 e ( μ h ν ) / K T Ω 2 4 π ( 1 e N σ ( ν ) x ) ,
I 2 ( ν , x ) = ( 8 π n 2 ν 2 2 c 2 e ( μ h ν ) / K T Ω 2 4 π N σ ( ν ) x ) × [ 1 e N σ ( ν ) x N σ ( ν ) x ] .