Abstract

Some previous works showed that radiative transfer between two closely spaced, lossy media diverges as 1/L2, where L is the spacing between the two media. This divergent power transfer clearly violates energy conservation. The explanation for this unphysical result is that too many optical modes were counted in those previous works, and many of those modes are physically unattainable. Moreover, many physically significant optical modes were not counted in the previous works.

© 2001 Optical Society of America

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References

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  1. A. A. Maradudin, Opt. Lett. 26, 479 (2001).
    [CrossRef]
  2. M. L. Levin, V. G. Polevoi, and S. M. Rytov, Sov. Phys. JETP 52, 1054 (1980).
  3. J. J. Loomis and H. J. Maris, Phys. Rev. B 50, 18517 (1994).
    [CrossRef]
  4. J. E. Raynolds, in Fourth NREL Conference on the Thermophotovoltaic Generation of Electricity, AIP Conf. Proc. 460 (American Institute of Physics, College Park, Maryland, 1998), pp. 49–57.
  5. D. Polder and M. Van Hove, Phys. Rev. B 4, 3303 (1971).
    [CrossRef]
  6. J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, Opt. Lett. 26, 480 (2001).
    [CrossRef]
  7. S. M. Rytov, “Theory of electric fluctuations and thermal radiation,” (Air Force Cambridge Research Center, Bedford, Mass., 1959).
  8. These power transmission coefficients are obtained from the standard Parratt (transmission line) equations.
  9. M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964), Chap.  13.
  10. J. L. Pan, Opt. Lett. 25, 369 (2000).
    [CrossRef]
  11. J. L. Pan, H. K. H. Choy, and C. G. Fonstad, IEEE Trans. Electron Devices 41, 241 (2000).
    [CrossRef]
  12. E. Yablonovitch and G. Cody, IEEE Trans. Electron Devices ED-29, 300 (1982).
    [CrossRef]

2001 (2)

2000 (2)

J. L. Pan, Opt. Lett. 25, 369 (2000).
[CrossRef]

J. L. Pan, H. K. H. Choy, and C. G. Fonstad, IEEE Trans. Electron Devices 41, 241 (2000).
[CrossRef]

1994 (1)

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

1982 (1)

E. Yablonovitch and G. Cody, IEEE Trans. Electron Devices ED-29, 300 (1982).
[CrossRef]

1980 (1)

M. L. Levin, V. G. Polevoi, and S. M. Rytov, Sov. Phys. JETP 52, 1054 (1980).

1971 (1)

D. Polder and M. Van Hove, Phys. Rev. B 4, 3303 (1971).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964), Chap.  13.

Carminati, R.

Choy, H. K. H.

J. L. Pan, H. K. H. Choy, and C. G. Fonstad, IEEE Trans. Electron Devices 41, 241 (2000).
[CrossRef]

Cody, G.

E. Yablonovitch and G. Cody, IEEE Trans. Electron Devices ED-29, 300 (1982).
[CrossRef]

Fonstad, C. G.

J. L. Pan, H. K. H. Choy, and C. G. Fonstad, IEEE Trans. Electron Devices 41, 241 (2000).
[CrossRef]

Greffet, J.-J.

Joulain, K.

Levin, M. L.

M. L. Levin, V. G. Polevoi, and S. M. Rytov, Sov. Phys. JETP 52, 1054 (1980).

Loomis, J. J.

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

Maradudin, A. A.

Maris, H. J.

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

Mulet, J.-P.

Pan, J. L.

J. L. Pan, Opt. Lett. 25, 369 (2000).
[CrossRef]

J. L. Pan, H. K. H. Choy, and C. G. Fonstad, IEEE Trans. Electron Devices 41, 241 (2000).
[CrossRef]

Polder, D.

D. Polder and M. Van Hove, Phys. Rev. B 4, 3303 (1971).
[CrossRef]

Polevoi, V. G.

M. L. Levin, V. G. Polevoi, and S. M. Rytov, Sov. Phys. JETP 52, 1054 (1980).

Raynolds, J. E.

J. E. Raynolds, in Fourth NREL Conference on the Thermophotovoltaic Generation of Electricity, AIP Conf. Proc. 460 (American Institute of Physics, College Park, Maryland, 1998), pp. 49–57.

Rytov, S. M.

M. L. Levin, V. G. Polevoi, and S. M. Rytov, Sov. Phys. JETP 52, 1054 (1980).

S. M. Rytov, “Theory of electric fluctuations and thermal radiation,” (Air Force Cambridge Research Center, Bedford, Mass., 1959).

Van Hove, M.

D. Polder and M. Van Hove, Phys. Rev. B 4, 3303 (1971).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964), Chap.  13.

Yablonovitch, E.

E. Yablonovitch and G. Cody, IEEE Trans. Electron Devices ED-29, 300 (1982).
[CrossRef]

IEEE Trans. Electron Devices (2)

J. L. Pan, H. K. H. Choy, and C. G. Fonstad, IEEE Trans. Electron Devices 41, 241 (2000).
[CrossRef]

E. Yablonovitch and G. Cody, IEEE Trans. Electron Devices ED-29, 300 (1982).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. B (2)

D. Polder and M. Van Hove, Phys. Rev. B 4, 3303 (1971).
[CrossRef]

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

Sov. Phys. JETP (1)

M. L. Levin, V. G. Polevoi, and S. M. Rytov, Sov. Phys. JETP 52, 1054 (1980).

Other (4)

J. E. Raynolds, in Fourth NREL Conference on the Thermophotovoltaic Generation of Electricity, AIP Conf. Proc. 460 (American Institute of Physics, College Park, Maryland, 1998), pp. 49–57.

S. M. Rytov, “Theory of electric fluctuations and thermal radiation,” (Air Force Cambridge Research Center, Bedford, Mass., 1959).

These power transmission coefficients are obtained from the standard Parratt (transmission line) equations.

M. Born and E. Wolf, Principles of Optics (Macmillan, New York, 1964), Chap.  13.

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Figures (1)

Fig. 1
Fig. 1

The problem discussed here is to find the radiative density that originates from within Material  1, traverses a gap (Material  2) of width L, and then carriers power into Material  3 in the +z^ direction. Materials  1 and 3 are explicitly assumed2-6 to be isotropic, lossy, and nonmagnetic. Material  2 is a vacuum.

Equations (13)

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P=1π2MW,
W=ωexpω/kBT-1,
MC-2L2for small L.
M=0kxdkxT13TE+T13TM,
expikxx+ik1zz,
kx=real,0kx,
k1z=k12-kx21/2=complex,
k1=ωμ0ϵ11/2k1R+ik1I,
expik1sinθ1x+ik1cosθ1zexpikxx+ik1zz,
kx=k1R+ik1Isinθ1,0kx2ω2μ0ϵ1,
k1z=k1R+ik1Icosθ1.
NTrans.Modes=θ1π/2dΩcosθ1T13TEθ1+T13TMθ1,=2π0π/2dθ1sinθ1cosθ1T13TEθ1+T13TMθ1,
NTrans.Modes2π,

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