Abstract

Published works have predicted that the radiative transfer from a heated metal to a lossless dielectric a short distance away is many orders of magnitude times the free-space Planck density. It is shown analytically that the radiative transfer from a heated metal to a lossless dielectric of index n3 is n32e13 times the free-space Planck density, where e13 is the emissivity of the metal radiating into the lossless dielectric. This radiative transfer is never larger than n32 (approximately one order of magnitude for semiconductors in the infrared) times the free=space Planck density. The expressions presented show that the maximum radiative transfer from a lossy metallic heat source with a dielectric function of imaginary part I must be proportional to n33/I, of which a factor of n32 arises from the power density within a dielectric and a factor of n3/I arises from the emissivity of a metal radiating directly into a dielectric.

© 2000 Optical Society of America

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References

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  1. E. G. Cravalho, C. L. Tien, and R. P. Caren, J. Heat Transfer 89, 351 (1967).
    [CrossRef]
  2. R. S. DiMatteo, “Enhanced semiconductor carrier generation via microscale radiative transfer; MPC–an electrical power finance instrument policy; interrelated innovations in emerging energy technologies,” M. S. Thesis (Department of Electrical Engineering and Computer Science, and Technology and Policy Program, Massachusetts Institute of Technology, Cambridge, Mass., 1996).
  3. M. D. Whale, “A fluctuational electrodynamic analysis of microscale radiative transfer and the design of microscale thermophotovoltaic devices,” Ph.D. dissertation (Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1997).
  4. G. A. Domoto, R. F. Boehm, and C. L. Tien, J. Heat Transfer 92, 412 (1970).
    [CrossRef]
  5. C. M. Hargreaves, Phys. Lett. 30, 491 (1969).
    [CrossRef]
  6. J. J. Loomis and H. J. Maris, Phys. Rev. B 50, 18517 (1994), and conclusions therein.
    [CrossRef]
  7. J. L. Pan, H. K. H. Choy, and C. G. Fonstad, “Very large radiative transfer over small distances from a black body for thermophotovoltaic applications,” IEEE Trans. Electron Devices (to be published).
  8. J. E. Raynolds, in 5th National Renewable Energy Laboratory Conference on the Thermophotovoltaic Generation of Electricity, AIP Conf. Proc. (American Institute of Physics, Woodbury, N.Y., 1998).
  9. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media [translated from Russian by J. B. Sykes and J. S. Bell] (Pergamon, New York, 1960).
  10. E. Yablonovitch and G. Cody, IEEE Trans. Electron. Devices ED-29, 305 (1982).
  11. M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964).
  12. J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Optical Properties of Metals, Vols. I and II of Physics Data, Nr. 18-1 and 18-2 (Fachinformationzentrum, Karlsruhe, Germany, 1980).

1994

J. J. Loomis and H. J. Maris, Phys. Rev. B 50, 18517 (1994), and conclusions therein.
[CrossRef]

1982

E. Yablonovitch and G. Cody, IEEE Trans. Electron. Devices ED-29, 305 (1982).

1970

G. A. Domoto, R. F. Boehm, and C. L. Tien, J. Heat Transfer 92, 412 (1970).
[CrossRef]

1969

C. M. Hargreaves, Phys. Lett. 30, 491 (1969).
[CrossRef]

1967

E. G. Cravalho, C. L. Tien, and R. P. Caren, J. Heat Transfer 89, 351 (1967).
[CrossRef]

Boehm, R. F.

G. A. Domoto, R. F. Boehm, and C. L. Tien, J. Heat Transfer 92, 412 (1970).
[CrossRef]

Born, M.

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

Caren, R. P.

E. G. Cravalho, C. L. Tien, and R. P. Caren, J. Heat Transfer 89, 351 (1967).
[CrossRef]

Choy, H. K. H.

J. L. Pan, H. K. H. Choy, and C. G. Fonstad, “Very large radiative transfer over small distances from a black body for thermophotovoltaic applications,” IEEE Trans. Electron Devices (to be published).

Cody, G.

E. Yablonovitch and G. Cody, IEEE Trans. Electron. Devices ED-29, 305 (1982).

Cravalho, E. G.

E. G. Cravalho, C. L. Tien, and R. P. Caren, J. Heat Transfer 89, 351 (1967).
[CrossRef]

DiMatteo, R. S.

R. S. DiMatteo, “Enhanced semiconductor carrier generation via microscale radiative transfer; MPC–an electrical power finance instrument policy; interrelated innovations in emerging energy technologies,” M. S. Thesis (Department of Electrical Engineering and Computer Science, and Technology and Policy Program, Massachusetts Institute of Technology, Cambridge, Mass., 1996).

Domoto, G. A.

G. A. Domoto, R. F. Boehm, and C. L. Tien, J. Heat Transfer 92, 412 (1970).
[CrossRef]

Fonstad, C. G.

J. L. Pan, H. K. H. Choy, and C. G. Fonstad, “Very large radiative transfer over small distances from a black body for thermophotovoltaic applications,” IEEE Trans. Electron Devices (to be published).

Hargreaves, C. M.

C. M. Hargreaves, Phys. Lett. 30, 491 (1969).
[CrossRef]

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Optical Properties of Metals, Vols. I and II of Physics Data, Nr. 18-1 and 18-2 (Fachinformationzentrum, Karlsruhe, Germany, 1980).

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Optical Properties of Metals, Vols. I and II of Physics Data, Nr. 18-1 and 18-2 (Fachinformationzentrum, Karlsruhe, Germany, 1980).

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media [translated from Russian by J. B. Sykes and J. S. Bell] (Pergamon, New York, 1960).

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media [translated from Russian by J. B. Sykes and J. S. Bell] (Pergamon, New York, 1960).

Loomis, J. J.

J. J. Loomis and H. J. Maris, Phys. Rev. B 50, 18517 (1994), and conclusions therein.
[CrossRef]

Lynch, D. W.

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Optical Properties of Metals, Vols. I and II of Physics Data, Nr. 18-1 and 18-2 (Fachinformationzentrum, Karlsruhe, Germany, 1980).

Maris, H. J.

J. J. Loomis and H. J. Maris, Phys. Rev. B 50, 18517 (1994), and conclusions therein.
[CrossRef]

Pan, J. L.

J. L. Pan, H. K. H. Choy, and C. G. Fonstad, “Very large radiative transfer over small distances from a black body for thermophotovoltaic applications,” IEEE Trans. Electron Devices (to be published).

Raynolds, J. E.

J. E. Raynolds, in 5th National Renewable Energy Laboratory Conference on the Thermophotovoltaic Generation of Electricity, AIP Conf. Proc. (American Institute of Physics, Woodbury, N.Y., 1998).

Tien, C. L.

G. A. Domoto, R. F. Boehm, and C. L. Tien, J. Heat Transfer 92, 412 (1970).
[CrossRef]

E. G. Cravalho, C. L. Tien, and R. P. Caren, J. Heat Transfer 89, 351 (1967).
[CrossRef]

Weaver, J. H.

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Optical Properties of Metals, Vols. I and II of Physics Data, Nr. 18-1 and 18-2 (Fachinformationzentrum, Karlsruhe, Germany, 1980).

Whale, M. D.

M. D. Whale, “A fluctuational electrodynamic analysis of microscale radiative transfer and the design of microscale thermophotovoltaic devices,” Ph.D. dissertation (Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1997).

Wolf, E.

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

Yablonovitch, E.

E. Yablonovitch and G. Cody, IEEE Trans. Electron. Devices ED-29, 305 (1982).

IEEE Trans. Electron. Devices

E. Yablonovitch and G. Cody, IEEE Trans. Electron. Devices ED-29, 305 (1982).

J. Heat Transfer

E. G. Cravalho, C. L. Tien, and R. P. Caren, J. Heat Transfer 89, 351 (1967).
[CrossRef]

G. A. Domoto, R. F. Boehm, and C. L. Tien, J. Heat Transfer 92, 412 (1970).
[CrossRef]

Phys. Lett.

C. M. Hargreaves, Phys. Lett. 30, 491 (1969).
[CrossRef]

Phys. Rev. B

J. J. Loomis and H. J. Maris, Phys. Rev. B 50, 18517 (1994), and conclusions therein.
[CrossRef]

Other

J. L. Pan, H. K. H. Choy, and C. G. Fonstad, “Very large radiative transfer over small distances from a black body for thermophotovoltaic applications,” IEEE Trans. Electron Devices (to be published).

J. E. Raynolds, in 5th National Renewable Energy Laboratory Conference on the Thermophotovoltaic Generation of Electricity, AIP Conf. Proc. (American Institute of Physics, Woodbury, N.Y., 1998).

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media [translated from Russian by J. B. Sykes and J. S. Bell] (Pergamon, New York, 1960).

R. S. DiMatteo, “Enhanced semiconductor carrier generation via microscale radiative transfer; MPC–an electrical power finance instrument policy; interrelated innovations in emerging energy technologies,” M. S. Thesis (Department of Electrical Engineering and Computer Science, and Technology and Policy Program, Massachusetts Institute of Technology, Cambridge, Mass., 1996).

M. D. Whale, “A fluctuational electrodynamic analysis of microscale radiative transfer and the design of microscale thermophotovoltaic devices,” Ph.D. dissertation (Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1997).

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

J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Optical Properties of Metals, Vols. I and II of Physics Data, Nr. 18-1 and 18-2 (Fachinformationzentrum, Karlsruhe, Germany, 1980).

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Figures (2)

Fig. 1
Fig. 1

The problem studied here is to find the radiative density that originates from within the heated metal (medium 1), traverses a gap (medium 2) of width L, and then carries power into the semiconductor (medium 3) in the +zˆ direction.

Fig. 2
Fig. 2

Evaluation of Eq. (3) for the power density I13ω/2π radiated by a heated metal into a semiconductor a distance L away. The dielectric functions are for gold and GaAs at λfs=6.2 µm: I=1746, R=178, and n3=3.3.

Equations (6)

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

Wfsωdω=ωexpω/kBTBB-1ω2dω2π3c2.
Wsolidω=n32Wfsω.
I13ω=I31ω=2πn32Wfsωe13,
e13=p=TE,TM0π/2dθ3 sin θ3 cos θ3T31pθ3,
e13=82/3n3/I,
I13ω=2πn32Wfsω82/3n3/I

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