Abstract

A thermal antenna is an electromagnetic source that emits in its surrounding a spatially coherent field in the infrared frequency range. Usually, its emission pattern changes with the wavelength so that the heat flux it radiates is weakly directive. Here, we show that a class of hyperbolic materials of type II possess a Brewster angle, which is weakly dependent on the wavelength, so that they can radiate like a true thermal antenna with a highly directional and p-polarized heat flux. The realization of these sources could open a new avenue in the field of thermal management in far-field regime.

© 2017 Optical Society of America

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References

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  1. M. Planck, “Law of energy distribution in normal spectra,” Ann. Phys. 4(3), 553–563 (1901).
    [Crossref]
  2. G. Kirchhoff, “Monatsberichte der Akademie der Wissenschaften zu Berlin,” sessions of Dec., 783 (1859).
  3. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
    [Crossref]
  4. P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. 2. doped silicon - Angular variation,” Phys. Rev. B 37(18), 10803 (1988).
    [Crossref]
  5. M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168(1–4), 117–122 (1999).
    [Crossref]
  6. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
    [Crossref] [PubMed]
  7. O. G. Kollyukh, A.I. Liptuga, V. Morozhenko, and V. I. Pipa, “Thermal radiation of plane-parallel semitransparent layers,” Opt. Commun. 225(4–6), 349–352 (2003).
    [Crossref]
  8. P. Ben-Abdallah, “Thermal antenna behavior for thin-film structures,” J. Opt. Soc. Am. A 21(7), 1368–1371 (2004).
    [Crossref]
  9. I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72(7), 075127 (2005).
    [Crossref]
  10. B. J. Lee, C. J. Fu, and Z. M. Zhang, “Coherent thermal emission from one-dimensional photonic crystals,” Appl. Phys. Lett. 87(7), 071904 (2005).
    [Crossref]
  11. J. Drevillon and P. Ben-Abdallah, “Ab initio design of coherent thermal sources,” J. Appl. Phys. 102(11), 114305 (2007).
    [Crossref]
  12. A. Battula and S. C. Chen, “Monochromatic polarized coherent emitter enhanced by surface plasmons and a cavity resonance,” Phys. Rev. B 74(24), 245407 (2006).
    [Crossref]
  13. K. Joulain and A. Loizeau, “Coherent thermal emission by microstructured waveguides,” J. Quant. Spectro. Rad. Trans 104(2), 208–216 (2007).
    [Crossref]
  14. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
    [Crossref] [PubMed]
  15. F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75(1), 016604 (2007).
    [Crossref]
  16. S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics 3 (Springer-Verlag, 1989).
  17. P. Ben-Abdallah and K. Joulain, “Fundamental limits for non contact transfers between two bodies,” Phys. Rev. B 82(12), 121419 (2010).
    [Crossref]
  18. S.-A. Biehs, E. Rousseau, and J.-J. Greffet, “Mesoscopic description of radiative heat transfer at the nanoscale,” Phys. Rev. Lett. 105(23), 234301 (2010).
    [Crossref]
  19. S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-Planckian thermal emission in the far-field regime,” Phys. Rev. B 93(16), 165405 (2016).
    [Crossref]
  20. L. Hu and S. T. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66(8), 085108 (2002).
    [Crossref]
  21. L. Sun and K. W. Yu, “Strategy for designing broadband epsilon-near-zero metamaterials,” J. Opt. Soc. Am. B 29, 5 (2012).
    [Crossref]
  22. L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103, 201109 (2013).
    [Crossref]
  23. P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, New Jersey, 2005).
  24. M. Tschikin, S. A. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15(10), 105101 (2013).
    [Crossref]
  25. J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
    [Crossref]

2016 (2)

S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-Planckian thermal emission in the far-field regime,” Phys. Rev. B 93(16), 165405 (2016).
[Crossref]

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

2013 (2)

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103, 201109 (2013).
[Crossref]

M. Tschikin, S. A. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15(10), 105101 (2013).
[Crossref]

2012 (1)

L. Sun and K. W. Yu, “Strategy for designing broadband epsilon-near-zero metamaterials,” J. Opt. Soc. Am. B 29, 5 (2012).
[Crossref]

2010 (2)

P. Ben-Abdallah and K. Joulain, “Fundamental limits for non contact transfers between two bodies,” Phys. Rev. B 82(12), 121419 (2010).
[Crossref]

S.-A. Biehs, E. Rousseau, and J.-J. Greffet, “Mesoscopic description of radiative heat transfer at the nanoscale,” Phys. Rev. Lett. 105(23), 234301 (2010).
[Crossref]

2007 (3)

K. Joulain and A. Loizeau, “Coherent thermal emission by microstructured waveguides,” J. Quant. Spectro. Rad. Trans 104(2), 208–216 (2007).
[Crossref]

J. Drevillon and P. Ben-Abdallah, “Ab initio design of coherent thermal sources,” J. Appl. Phys. 102(11), 114305 (2007).
[Crossref]

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75(1), 016604 (2007).
[Crossref]

2006 (1)

A. Battula and S. C. Chen, “Monochromatic polarized coherent emitter enhanced by surface plasmons and a cavity resonance,” Phys. Rev. B 74(24), 245407 (2006).
[Crossref]

2005 (3)

I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72(7), 075127 (2005).
[Crossref]

B. J. Lee, C. J. Fu, and Z. M. Zhang, “Coherent thermal emission from one-dimensional photonic crystals,” Appl. Phys. Lett. 87(7), 071904 (2005).
[Crossref]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

O. G. Kollyukh, A.I. Liptuga, V. Morozhenko, and V. I. Pipa, “Thermal radiation of plane-parallel semitransparent layers,” Opt. Commun. 225(4–6), 349–352 (2003).
[Crossref]

2002 (2)

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

L. Hu and S. T. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66(8), 085108 (2002).
[Crossref]

1999 (1)

M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168(1–4), 117–122 (1999).
[Crossref]

1988 (1)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. 2. doped silicon - Angular variation,” Phys. Rev. B 37(18), 10803 (1988).
[Crossref]

1986 (1)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

1901 (1)

M. Planck, “Law of energy distribution in normal spectra,” Ann. Phys. 4(3), 553–563 (1901).
[Crossref]

Baldassarre, L.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Ballabio, A.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Battula, A.

A. Battula and S. C. Chen, “Monochromatic polarized coherent emitter enhanced by surface plasmons and a cavity resonance,” Phys. Rev. B 74(24), 245407 (2006).
[Crossref]

Ben-Abdallah, P.

S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-Planckian thermal emission in the far-field regime,” Phys. Rev. B 93(16), 165405 (2016).
[Crossref]

M. Tschikin, S. A. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15(10), 105101 (2013).
[Crossref]

P. Ben-Abdallah and K. Joulain, “Fundamental limits for non contact transfers between two bodies,” Phys. Rev. B 82(12), 121419 (2010).
[Crossref]

J. Drevillon and P. Ben-Abdallah, “Ab initio design of coherent thermal sources,” J. Appl. Phys. 102(11), 114305 (2007).
[Crossref]

P. Ben-Abdallah, “Thermal antenna behavior for thin-film structures,” J. Opt. Soc. Am. A 21(7), 1368–1371 (2004).
[Crossref]

Biagioni, P.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Biehs, S. A.

M. Tschikin, S. A. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15(10), 105101 (2013).
[Crossref]

Biehs, S.-A.

S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-Planckian thermal emission in the far-field regime,” Phys. Rev. B 93(16), 165405 (2016).
[Crossref]

S.-A. Biehs, E. Rousseau, and J.-J. Greffet, “Mesoscopic description of radiative heat transfer at the nanoscale,” Phys. Rev. Lett. 105(23), 234301 (2010).
[Crossref]

Bollani, M.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Brida, D.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Calvani, P.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Carminati, R.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Celanovic, I.

I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72(7), 075127 (2005).
[Crossref]

Chen, S. C.

A. Battula and S. C. Chen, “Monochromatic polarized coherent emitter enhanced by surface plasmons and a cavity resonance,” Phys. Rev. B 74(24), 245407 (2006).
[Crossref]

Chen, Y.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Chui, S. T.

L. Hu and S. T. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66(8), 085108 (2002).
[Crossref]

Dong, Z. G.

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75(1), 016604 (2007).
[Crossref]

Drevillon, J.

J. Drevillon and P. Ben-Abdallah, “Ab initio design of coherent thermal sources,” J. Appl. Phys. 102(11), 114305 (2007).
[Crossref]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Fischer, M. P.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Frigerio, J.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Fu, C. J.

B. J. Lee, C. J. Fu, and Z. M. Zhang, “Coherent thermal emission from one-dimensional photonic crystals,” Appl. Phys. Lett. 87(7), 071904 (2005).
[Crossref]

Gallacher, K.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Gao, J.

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103, 201109 (2013).
[Crossref]

Gebhart, B.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. 2. doped silicon - Angular variation,” Phys. Rev. B 37(18), 10803 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

Giliberti, V.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Greffet, J. J.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Greffet, J.-J.

S.-A. Biehs, E. Rousseau, and J.-J. Greffet, “Mesoscopic description of radiative heat transfer at the nanoscale,” Phys. Rev. Lett. 105(23), 234301 (2010).
[Crossref]

Grupp, A.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Herminghaus, S.

M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168(1–4), 117–122 (1999).
[Crossref]

Hesketh, P. J.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. 2. doped silicon - Angular variation,” Phys. Rev. B 37(18), 10803 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

Hu, L.

L. Hu and S. T. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66(8), 085108 (2002).
[Crossref]

Isella, G.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Joulain, K.

P. Ben-Abdallah and K. Joulain, “Fundamental limits for non contact transfers between two bodies,” Phys. Rev. B 82(12), 121419 (2010).
[Crossref]

K. Joulain and A. Loizeau, “Coherent thermal emission by microstructured waveguides,” J. Quant. Spectro. Rad. Trans 104(2), 208–216 (2007).
[Crossref]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Kassakian, J.

I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72(7), 075127 (2005).
[Crossref]

Kirchhoff, G.

G. Kirchhoff, “Monatsberichte der Akademie der Wissenschaften zu Berlin,” sessions of Dec., 783 (1859).

Knoll, W.

M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168(1–4), 117–122 (1999).
[Crossref]

Kollyukh, O. G.

O. G. Kollyukh, A.I. Liptuga, V. Morozhenko, and V. I. Pipa, “Thermal radiation of plane-parallel semitransparent layers,” Opt. Commun. 225(4–6), 349–352 (2003).
[Crossref]

Kravtsov, Y. A.

S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics 3 (Springer-Verlag, 1989).

Kreiter, M.

M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168(1–4), 117–122 (1999).
[Crossref]

Lee, B. J.

B. J. Lee, C. J. Fu, and Z. M. Zhang, “Coherent thermal emission from one-dimensional photonic crystals,” Appl. Phys. Lett. 87(7), 071904 (2005).
[Crossref]

Li, T.

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75(1), 016604 (2007).
[Crossref]

Liptuga, A.I.

O. G. Kollyukh, A.I. Liptuga, V. Morozhenko, and V. I. Pipa, “Thermal radiation of plane-parallel semitransparent layers,” Opt. Commun. 225(4–6), 349–352 (2003).
[Crossref]

Liu, H.

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75(1), 016604 (2007).
[Crossref]

Loizeau, A.

K. Joulain and A. Loizeau, “Coherent thermal emission by microstructured waveguides,” J. Quant. Spectro. Rad. Trans 104(2), 208–216 (2007).
[Crossref]

Mainguy, S.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Manganelli, C.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Messina, R.

M. Tschikin, S. A. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15(10), 105101 (2013).
[Crossref]

Mittler-Neher, S.

M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168(1–4), 117–122 (1999).
[Crossref]

Morozhenko, V.

O. G. Kollyukh, A.I. Liptuga, V. Morozhenko, and V. I. Pipa, “Thermal radiation of plane-parallel semitransparent layers,” Opt. Commun. 225(4–6), 349–352 (2003).
[Crossref]

Mulet, J. P.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

Napolitani, E.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Nucara, A.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Ortolani, M.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Oster, J.

M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168(1–4), 117–122 (1999).
[Crossref]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Paul, D. J.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Perreault, D.

I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72(7), 075127 (2005).
[Crossref]

Pipa, V. I.

O. G. Kollyukh, A.I. Liptuga, V. Morozhenko, and V. I. Pipa, “Thermal radiation of plane-parallel semitransparent layers,” Opt. Commun. 225(4–6), 349–352 (2003).
[Crossref]

Planck, M.

M. Planck, “Law of energy distribution in normal spectra,” Ann. Phys. 4(3), 553–563 (1901).
[Crossref]

Rousseau, E.

S.-A. Biehs, E. Rousseau, and J.-J. Greffet, “Mesoscopic description of radiative heat transfer at the nanoscale,” Phys. Rev. Lett. 105(23), 234301 (2010).
[Crossref]

Rytov, S. M.

S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics 3 (Springer-Verlag, 1989).

Sakat, E.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Sambles, R.

M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168(1–4), 117–122 (1999).
[Crossref]

Sun, L.

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103, 201109 (2013).
[Crossref]

L. Sun and K. W. Yu, “Strategy for designing broadband epsilon-near-zero metamaterials,” J. Opt. Soc. Am. B 29, 5 (2012).
[Crossref]

Tatarskii, V. I.

S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics 3 (Springer-Verlag, 1989).

Tschikin, M.

M. Tschikin, S. A. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15(10), 105101 (2013).
[Crossref]

Virgilio, M.

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Wang, F. M.

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75(1), 016604 (2007).
[Crossref]

Yang, X.

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103, 201109 (2013).
[Crossref]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, New Jersey, 2005).

Yu, K. W.

L. Sun and K. W. Yu, “Strategy for designing broadband epsilon-near-zero metamaterials,” J. Opt. Soc. Am. B 29, 5 (2012).
[Crossref]

Zemel, J. N.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. 2. doped silicon - Angular variation,” Phys. Rev. B 37(18), 10803 (1988).
[Crossref]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

Zhang, S.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Zhang, X.

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75(1), 016604 (2007).
[Crossref]

Zhang, Z. M.

B. J. Lee, C. J. Fu, and Z. M. Zhang, “Coherent thermal emission from one-dimensional photonic crystals,” Appl. Phys. Lett. 87(7), 071904 (2005).
[Crossref]

Zhu, S. N.

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75(1), 016604 (2007).
[Crossref]

Ann. Phys. (1)

M. Planck, “Law of energy distribution in normal spectra,” Ann. Phys. 4(3), 553–563 (1901).
[Crossref]

Appl. Phys. Lett. (2)

B. J. Lee, C. J. Fu, and Z. M. Zhang, “Coherent thermal emission from one-dimensional photonic crystals,” Appl. Phys. Lett. 87(7), 071904 (2005).
[Crossref]

L. Sun, X. Yang, and J. Gao, “Loss-compensated broadband epsilon-near-zero metamaterials with gain media,” Appl. Phys. Lett. 103, 201109 (2013).
[Crossref]

J. Appl. Phys. (1)

J. Drevillon and P. Ben-Abdallah, “Ab initio design of coherent thermal sources,” J. Appl. Phys. 102(11), 114305 (2007).
[Crossref]

J. Opt. (1)

M. Tschikin, S. A. Biehs, R. Messina, and P. Ben-Abdallah, “On the limits of the effective description of hyperbolic materials in the presence of surface waves,” J. Opt. 15(10), 105101 (2013).
[Crossref]

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

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

L. Sun and K. W. Yu, “Strategy for designing broadband epsilon-near-zero metamaterials,” J. Opt. Soc. Am. B 29, 5 (2012).
[Crossref]

J. Quant. Spectro. Rad. Trans (1)

K. Joulain and A. Loizeau, “Coherent thermal emission by microstructured waveguides,” J. Quant. Spectro. Rad. Trans 104(2), 208–216 (2007).
[Crossref]

Nature (2)

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, “Coherent emission of light by thermal sources,” Nature 416(6876), 61–64 (2002).
[Crossref] [PubMed]

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Organ pipe radiant modes of periodic micromachined silicon surfaces,” Nature 324(6097), 549–551 (1986).
[Crossref]

Opt. Commun. (2)

O. G. Kollyukh, A.I. Liptuga, V. Morozhenko, and V. I. Pipa, “Thermal radiation of plane-parallel semitransparent layers,” Opt. Commun. 225(4–6), 349–352 (2003).
[Crossref]

M. Kreiter, J. Oster, R. Sambles, S. Herminghaus, S. Mittler-Neher, and W. Knoll, “Thermally induced emission of light from a metallic diffraction grating, mediated by surface plasmons,” Opt. Commun. 168(1–4), 117–122 (1999).
[Crossref]

Phys. Rev. B (7)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, “Polarized spectral emittance from periodic micromachined surfaces. 2. doped silicon - Angular variation,” Phys. Rev. B 37(18), 10803 (1988).
[Crossref]

A. Battula and S. C. Chen, “Monochromatic polarized coherent emitter enhanced by surface plasmons and a cavity resonance,” Phys. Rev. B 74(24), 245407 (2006).
[Crossref]

P. Ben-Abdallah and K. Joulain, “Fundamental limits for non contact transfers between two bodies,” Phys. Rev. B 82(12), 121419 (2010).
[Crossref]

I. Celanovic, D. Perreault, and J. Kassakian, “Resonant-cavity enhanced thermal emission,” Phys. Rev. B 72(7), 075127 (2005).
[Crossref]

S.-A. Biehs and P. Ben-Abdallah, “Revisiting super-Planckian thermal emission in the far-field regime,” Phys. Rev. B 93(16), 165405 (2016).
[Crossref]

L. Hu and S. T. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66(8), 085108 (2002).
[Crossref]

J. Frigerio, A. Ballabio, G. Isella, E. Sakat, P. Biagioni, M. Bollani, E. Napolitani, C. Manganelli, M. Virgilio, A. Grupp, M. P. Fischer, D. Brida, K. Gallacher, D. J. Paul, L. Baldassarre, P. Calvani, V. Giliberti, A. Nucara, and M. Ortolani, “Tunability and Losses of Mid-infrared Plasmonics in Heavily Doped Germanium Thin Films,” Phys. Rev. B 94, 085202 (2016).
[Crossref]

Phys. Rev. E (1)

F. M. Wang, H. Liu, T. Li, Z. G. Dong, S. N. Zhu, and X. Zhang, “Metamaterial of rod pairs standing on gold plate and its negative refraction property in the far-infrared frequency regime,” Phys. Rev. E 75(1), 016604 (2007).
[Crossref]

Phys. Rev. Lett. (2)

S.-A. Biehs, E. Rousseau, and J.-J. Greffet, “Mesoscopic description of radiative heat transfer at the nanoscale,” Phys. Rev. Lett. 105(23), 234301 (2010).
[Crossref]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[Crossref] [PubMed]

Other (3)

S. M. Rytov, Y. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics 3 (Springer-Verlag, 1989).

P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, New Jersey, 2005).

G. Kirchhoff, “Monatsberichte der Akademie der Wissenschaften zu Berlin,” sessions of Dec., 783 (1859).

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Figures (5)

Fig. 1
Fig. 1

Brewster angle (in degree) in the (ε, ε) plane for transparent uniaxial media. The black zones correspond to media which have no Brewster angle. The insets show the iso-frequency surfaces of different uniaxial crystals.

Fig. 2
Fig. 2

Reflection in s-polarization of HM for the type I (ε > 0) and type II (ε< 0). The light zone corresponds to the region where the reflection is close to 1.

Fig. 3
Fig. 3

Reflection in p-polarization of HM for type I (ε > 0) and type II (ε < 0) when (a) (| ε |= 0.5) and (b) (| ε |= 5).

Fig. 4
Fig. 4

Dielectric properties of materials given by an alternating layered medium as sketched in the inset and satisfying the inequalities (13) and (14). The set of solutions of this system is shown in grey.

Fig. 5
Fig. 5

Angular heat flux emitted by a dielectric-metal layered structure at T = 300 K for different filling factors f in dielectric of permittivity (a) ε1 = 0.9+i0.01, (b) ε1 = 0.5+i0.01, (c) ε1 = 0.1 + i0.01 and (d) ε1 = 1.1 + i0.01. The metallic layers are made with heavily doped germanium of permittivity ε2 = εGe [25]. The flux is normalized by the flux radiated by a blackbody at temperature T.

Equations (15)

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d Φ ( u ) = 2 0 d ω 2 π Θ ( ω , T ) T ( ω , κ ) d 2 κ ( 2 π ) 2 ,
T ( ω , κ , d ) : = 1 2 Tr[ ( 𝟙 ) ] .
: = ( r s s r s p r p s r p p ) .
ϵ ( ω , u ) : = T ( ω , κ ) = 1 2 { 2 | r s s | 2 | r p p | 2 | r s p | 2 | r p s | 2 } ,
d Φ ( u ) = 0 d ω c 2 ω 2 ϵ ( ω , u ) I ω 0 ( T ) d 2 κ π .
d Φ ( θ ) = 2 cos θ sin θ d θ ( 0 d ω ϵ ( ω , θ ) I ω 0 ( T ) ) .
r s s = γ 0 γ s γ 0 + γ s ,
r p p = ϵ γ 0 γ p ϵ γ 0 + γ p ,
r p s = r s p = 0
θ B = arcsin ϵ ( ϵ 1 ) ϵ ϵ 1 .
ϵ = f ϵ 1 + ( 1 f ) ϵ 2 ,
ϵ = ϵ 1 ϵ 2 f ϵ 2 + ( 1 f ) ϵ 1 ,
f ϵ 1 + ( 1 f ) ϵ 2 < 0 ,
( ϵ 1 f ) ( 1 f ) ϵ 1 < 1 ϵ 2 ,
ϵ G e = ϵ ( 1 ω p 2 ω ( ω + i γ ) ) ,

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