Abstract

The present paper theoretically demonstrates coherent thermal emission in the infrared region by exciting magnetic polaritons between metallic gratings and an opaque metallic film, separated by a dielectric spacer. The coupling of the metallic strips and the film induces a magnetic response that is characterized by a negative permeability and positive permittivity. On the other hand, the metallic film intrinsically exhibits a negative permittivity and positive permeability in the near infrared. This artificial structure is equivalent to a pair of single-negative materials. By exciting surface magnetic polaritons, large emissivity peaks can be achieved at the resonance frequencies and are almost independent of the emission angle. The resonance frequency of the magnetic response can be predicted by an analogy to an inductor and capacitor circuit. The proposed structure can be easily constructed using micro/nanofabrication.

© 2008 Optical Society of America

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References

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  1. Z. M. Zhang, Nano/Microscale Heat Transfer (McGraw-Hill, 2007).
  2. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  3. J.-J.  Greffet, R.  Carminati, K.  Joulain, J.-P.  Mulet, S.  Mainguy, and Y.  Chen, "Coherent emission of light by thermal sources," Nature  416, 61-64 (2002).
    [CrossRef] [PubMed]
  4. B. J. Lee, C. J. Fu, and Z. M. Zhang, "Coherent thermal emission from one-dimensional photonic crystals," Appl. Phys. Lett. 87, 071904 (2005).
    [CrossRef]
  5. B. J. Lee, Y. -B. Chen, and Z. M. Zhang, "Surface waves between metallic films and truncated photonic crystals observed with reflectance spectroscopy," Opt. Lett. 33, 204-206 (2008).
    [CrossRef] [PubMed]
  6. M.  Laroche, R.  Carminati, and J.-J.  Greffet, "Coherent thermal antenna using a photonic crystal slab," Phys. Rev. Lett.  96, 123903 (2006).
    [CrossRef] [PubMed]
  7. C. J. Fu, Z. M. Zhang, and D. B. Tanner, "Planar heterogeneous structures for coherent emission of radiation," Opt. Lett. 30, 1873-1875 (2005).
    [CrossRef] [PubMed]
  8. V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
    [CrossRef]
  9. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
    [CrossRef] [PubMed]
  10. L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411 (2002).
    [CrossRef]
  11. G.  Dolling, C.  Enkrich, M.  Wegener, J. F.  Zhou, C. M.  Soukoulis, and S.  Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett.  30, 3198-3200 (2005).
    [CrossRef] [PubMed]
  12. U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, "Negative index metamaterial combining magnetic resonators with metal films," Opt. Express 14, 7872-7877 (2006).
    [CrossRef] [PubMed]
  13. G.  Shvets and Y.  Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A  8, S122-S130 (2006).
    [CrossRef]
  14. J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
    [CrossRef] [PubMed]
  15. T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
    [CrossRef]
  16. B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theo. Nanosci. 5, 201-213 (2008).
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
  18. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economon, J. B. Pendry, C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005).
    [CrossRef] [PubMed]
  19. V. D. Lam, J. B. Kim, N. S. J. Lee, Y. P. Lee, and J. Y. Rhee, "Dependence of the magnetic-resonance frequency on the cut-wire width of cut-wire pair medium," Opt. Express 15, 16651-16656 (2008).
    [CrossRef]
  20. J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).
    [CrossRef]

2008 (4)

T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
[CrossRef]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theo. Nanosci. 5, 201-213 (2008).

V. D. Lam, J. B. Kim, N. S. J. Lee, Y. P. Lee, and J. Y. Rhee, "Dependence of the magnetic-resonance frequency on the cut-wire width of cut-wire pair medium," Opt. Express 15, 16651-16656 (2008).
[CrossRef]

B. J. Lee, Y. -B. Chen, and Z. M. Zhang, "Surface waves between metallic films and truncated photonic crystals observed with reflectance spectroscopy," Opt. Lett. 33, 204-206 (2008).
[CrossRef] [PubMed]

2007 (1)

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

2006 (5)

M.  Laroche, R.  Carminati, and J.-J.  Greffet, "Coherent thermal antenna using a photonic crystal slab," Phys. Rev. Lett.  96, 123903 (2006).
[CrossRef] [PubMed]

U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, "Negative index metamaterial combining magnetic resonators with metal films," Opt. Express 14, 7872-7877 (2006).
[CrossRef] [PubMed]

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
[CrossRef] [PubMed]

G.  Shvets and Y.  Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A  8, S122-S130 (2006).
[CrossRef]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).
[CrossRef]

2005 (4)

C. J. Fu, Z. M. Zhang, and D. B. Tanner, "Planar heterogeneous structures for coherent emission of radiation," Opt. Lett. 30, 1873-1875 (2005).
[CrossRef] [PubMed]

G.  Dolling, C.  Enkrich, M.  Wegener, J. F.  Zhou, C. M.  Soukoulis, and S.  Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett.  30, 3198-3200 (2005).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economon, J. B. Pendry, C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

B. J. Lee, C. J. Fu, and Z. M. Zhang, "Coherent thermal emission from one-dimensional photonic crystals," Appl. Phys. Lett. 87, 071904 (2005).
[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, 61-64 (2002).
[CrossRef] [PubMed]

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Carminati, R.

M.  Laroche, R.  Carminati, and J.-J.  Greffet, "Coherent thermal antenna using a photonic crystal slab," Phys. Rev. Lett.  96, 123903 (2006).
[CrossRef] [PubMed]

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

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, 61-64 (2002).
[CrossRef] [PubMed]

Chen, Y. -B.

Chen, Y.-B.

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theo. Nanosci. 5, 201-213 (2008).

Chettiar, U. K.

Dolling, G.

Economon, E. N.

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economon, J. B. Pendry, C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Enkrich, C.

Fu, C. J.

C. J. Fu, Z. M. Zhang, and D. B. Tanner, "Planar heterogeneous structures for coherent emission of radiation," Opt. Lett. 30, 1873-1875 (2005).
[CrossRef] [PubMed]

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

Greffet, J.-J.

M.  Laroche, R.  Carminati, and J.-J.  Greffet, "Coherent thermal antenna using a photonic crystal slab," Phys. Rev. Lett.  96, 123903 (2006).
[CrossRef] [PubMed]

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

Grigorenko, A. N.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411 (2002).
[CrossRef]

Joulain, K.

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

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economon, J. B. Pendry, C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Kildishev, A. V.

Kim, J. B.

Klar, T. A.

Koschny, T.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).
[CrossRef]

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economon, J. B. Pendry, C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Lam, V. D.

Laroche, M.

M.  Laroche, R.  Carminati, and J.-J.  Greffet, "Coherent thermal antenna using a photonic crystal slab," Phys. Rev. Lett.  96, 123903 (2006).
[CrossRef] [PubMed]

Lee, B. J.

B. J. Lee, Y. -B. Chen, and Z. M. Zhang, "Surface waves between metallic films and truncated photonic crystals observed with reflectance spectroscopy," Opt. Lett. 33, 204-206 (2008).
[CrossRef] [PubMed]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theo. Nanosci. 5, 201-213 (2008).

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

Lee, N. S. J.

Lee, Y. P.

Li, J. Q.

T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
[CrossRef]

Li, T.

T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
[CrossRef]

Linden, S.

Liu, H.

T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
[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, 61-64 (2002).
[CrossRef] [PubMed]

Makhnovskiy, D. P.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411 (2002).
[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, 61-64 (2002).
[CrossRef] [PubMed]

Panina, L. V.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411 (2002).
[CrossRef]

Pendry, J. B.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economon, J. B. Pendry, C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Rhee, J. Y.

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Shalaev, V. M.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Shvets, G.

G.  Shvets and Y.  Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A  8, S122-S130 (2006).
[CrossRef]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).
[CrossRef]

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
[CrossRef] [PubMed]

G.  Dolling, C.  Enkrich, M.  Wegener, J. F.  Zhou, C. M.  Soukoulis, and S.  Linden, "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials," Opt. Lett.  30, 3198-3200 (2005).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economon, J. B. Pendry, C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Tanner, D. B.

Tuttle, G.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).
[CrossRef]

Urzhumov, Y.

G.  Shvets and Y.  Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A  8, S122-S130 (2006).
[CrossRef]

Wang, F. M.

T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
[CrossRef]

Wang, S. M.

T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
[CrossRef]

Wegener, M.

Zhang, L.

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).
[CrossRef]

Zhang, X.

T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
[CrossRef]

Zhang, Z. M.

B. J. Lee, Y. -B. Chen, and Z. M. Zhang, "Surface waves between metallic films and truncated photonic crystals observed with reflectance spectroscopy," Opt. Lett. 33, 204-206 (2008).
[CrossRef] [PubMed]

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theo. Nanosci. 5, 201-213 (2008).

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

C. J. Fu, Z. M. Zhang, and D. B. Tanner, "Planar heterogeneous structures for coherent emission of radiation," Opt. Lett. 30, 1873-1875 (2005).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, "Unifying approach to left-handed material design," Opt. Lett. 31, 3620-3622 (2006).
[CrossRef] [PubMed]

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economon, J. B. Pendry, C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Zhou, J. F.

Zhu, S. N.

T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

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

J. Appl. Phys. (1)

T. Li, S. M. Wang, H. Liu, J. Q. Li, F. M. Wang, S. N. Zhu, and X. Zhang, "Dispersion of magnetic plasmon polaritons in perforated trilayer metamaterials," J. Appl. Phys. 103, 023104 (2008).
[CrossRef]

J. Comput. Theo. Nanosci. (1)

B. J. Lee, Y.-B. Chen, and Z. M. Zhang, "Transmission enhancement through nanoscale metallic slit arrays from the visible to mid-infrared," J. Comput. Theo. Nanosci. 5, 201-213 (2008).

J. Opt. A (1)

G.  Shvets and Y.  Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A  8, S122-S130 (2006).
[CrossRef]

Nat. Photonics (1)

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Nature (1)

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

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. B (2)

J. Zhou, L. Zhang, G. Tuttle, T. Koschny, and C. M. Soukoulis, "Negative index materials using simple short wire pairs," Phys. Rev. B 73, 041101 (2006).
[CrossRef]

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

M.  Laroche, R.  Carminati, and J.-J.  Greffet, "Coherent thermal antenna using a photonic crystal slab," Phys. Rev. Lett.  96, 123903 (2006).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economon, J. B. Pendry, C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef] [PubMed]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Other (3)

Z. M. Zhang, Nano/Microscale Heat Transfer (McGraw-Hill, 2007).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).

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Figures (5)

Fig. 1.
Fig. 1.

(a). Schematic of the proposed metamaterial structure with coherent thermal emission characteristics. Here, Λ is the grating period, w is the width of the metallic strip, and h is the thickness of the metal strip or grating. The thickness of the dielectric spacer is d. The coordinates system is also shown for a TM-polarized plane wave with a wavevector k incident at the angle θ. (b) Reflectance of the proposed structure for the TM wave at θ = 25°. The geometric parameters are Λ = 500 nm, w = 250 nm, and h = d = 20 nm. The dotted line shows the structure without the dielectric spacer (d = 0).

Fig. 2.
Fig. 2.

Contour plot of the spectral-directional emissivity of (a) the simple grating and (b) the Ag grating and Ag film separated by a SiO2 spacer. The geometric parameters are the same as those in Fig. 1. At θ = 25°, surface plasmon resonance is labeled as SP, while the magnetic polaritons are labeled as MP1, MP2, and MP3 for the fundamental, second, and third harmonic modes, respectively.

Fig. 3.
Fig. 3.

Contour shows the square of the magnitude of complex magnetic field in logarithmic scale and the arrows indicate the electric fields when the magnetic polariton is excited for conditions corresponding to MP1, MP2, and MP3 shown in Fig. 2(b). (a) MP1, ν = 5,670 cm-1; (b) MP2, ν = 11,490 cm-1; (c) MP3, ν = 16,095 cm-1.

Fig. 4.
Fig. 4.

Schematic of the equivalent inductor and capacitor circuit for the one period of the structure shown in Fig. 1(a).

Fig. 5.
Fig. 5.

Comparison of the predicted resonance condition with that obtained from the RCWA: (a) for different w values at Λ = 500 nm; (b) for different Λ values at w = 250 nm.

Equations (2)

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Z tot = ( L m + L e ) 1 ω 2 C e ( L m + L e ) 2 i ω C m + ( L m + L e )
ω R = ( C m + C e C m 2 + C e 2 ( L m + L e ) C m C e ) 1 2

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