Abstract

I show that under proper conditions, thin-film structures behave as thermal sources that are able to emit radiation in well-defined directions over a broad spectral band for both p- and s-polarization states of light. This effect results from the quantization of modes inside the structure as in a Fabry–Perot resonator. A theoretical demonstration of this effect is given by using the matrix transfer method. This result is similar to the most efficient reported results with gratings but with use of a completely different physical principle [Nature 416, 61 (2002)].

© 2004 Optical Society of America

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References

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  1. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
    [CrossRef] [PubMed]
  2. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
    [CrossRef] [PubMed]
  3. W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, 1429–1450 (1964).
    [CrossRef]
  4. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
  5. G. Chen, “Wave effects on radiative transfer in absorbing and emitting thin-film media,” Micro. Thermo. Eng. 1, 215–224 (1997).
  6. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Taylor & Francis, Washington, D.C., 1992).
  7. E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1998).

2002 (2)

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

1997 (1)

G. Chen, “Wave effects on radiative transfer in absorbing and emitting thin-film media,” Micro. Thermo. Eng. 1, 215–224 (1997).

1964 (1)

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, 1429–1450 (1964).
[CrossRef]

Carminati, R.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Chen, G.

G. Chen, “Wave effects on radiative transfer in absorbing and emitting thin-film media,” Micro. Thermo. Eng. 1, 215–224 (1997).

Chen, Y.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Greffet, J. J.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Guérin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Taylor & Francis, Washington, D.C., 1992).

Joulain, K.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Lamb, W. E.

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, 1429–1450 (1964).
[CrossRef]

Mainguy, S.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).

Mulet, J. P.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1998).

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Taylor & Francis, Washington, D.C., 1992).

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).

Micro. Thermo. Eng. (1)

G. Chen, “Wave effects on radiative transfer in absorbing and emitting thin-film media,” Micro. Thermo. Eng. 1, 215–224 (1997).

Nature (1)

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, Y. Chen, “Coherent emission of light by thermal sources,” Nature 416, 61–64 (2002).
[CrossRef] [PubMed]

Phys. Rev. A (1)

W. E. Lamb, “Theory of an optical maser,” Phys. Rev. A 134, 1429–1450 (1964).
[CrossRef]

Phys. Rev. Lett. (1)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Other (3)

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Taylor & Francis, Washington, D.C., 1992).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, San Diego, Calif., 1998).

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Figures (3)

Fig. 1
Fig. 1

Geometrical configuration of the system.

Fig. 2
Fig. 2

Spectral emissivity of a SiO2 film of thickness d=10 μm embedded in a germanium matrix for s polarization. Comparison between the directions of emissivity peaks (the thin fringes on the spectrum) calculated from Kirchhoff’s law and the direction of quantified metastable states obtained with Eq. (20) shows that propagative waves coming from the surrounding make the quantified modes within the film resonant. The spectral emissivity for p polarization (not shown here) is similar to this spectrum. Inset: emissivity curve versus the angle (in degree) for s polarization at λ=6.6 μm. The peaks are due to fundamental and secondary modes.

Fig. 3
Fig. 3

Spectral emission of a thin film (thickness, 7 μm; surrounding; germanium) designed to radiate as an infrared antenna. The optical properties of medium are given by expression (18) with 2(ω0)=0.8+0.06i (the p-polarization contribution has not been plotted). Inset: emissivity curves versus the angle (in degrees) for s polarization at 7 μm (solid line), 8 μm (dotted line), and 9 μm (dashed line).

Equations (25)

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EinEout-=T12T2propT21EoutEin+,
Tij=1tij1rijrij1,
Tjprop=exp(iϕj)00exp(-iϕj),
E-in=E+in=0.
det1 -r210 0 (I)  (T2) 0 0r21 -1=0.
1-r122exp(-2ik2xd)=0.
K2x=πmd,
K1x=0,
K2x2=2ω¯m2c2-K2,
K1x2=1ω¯m2c2-K2.
K=1ω¯mc,
ω¯m=cπdm2-1.
tE+outE-inE+in=0=t12t21exp(-ik2xd)1-r122exp(-2ik2xd),
rE-outE-inE+in=0=r12(exp(-2ik2xd)-1)1-r122exp(-2ik2xd).
(ω, k)=1-T-R,
k=ωc1sin θ1m=ωc22-k2x21/2.
k2=ωc 2-πmd2.
sin2 θ1m=112-πmcdω2.
N=E2ndλ,
dθ1mdω=0.
2(ω)=A1(ω)+πcmd21ω2,
A=11(ω0)2(ω0)-πcmd21ω02,
2(ω)=2(ω0)+πcmd21ω2-1ω02.
λ02n(λ0)d<λ0n(λ0).
θ1=arcsin1n1n2(λ0)-λ024d21/2.

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