Abstract

We studied angular distributions and spectra of thermal radiation of lamellar metal/dielectric metamaterials with hyperbolic dispersion and compared them with the corresponding characteristics of simple metallic films and pairs of metallic and dielectric layers. The spectra of thermal radiation, in the mid-infrared part of the spectrum, were nearly flat and featureless, in a good agreement with the model predictions. The angular distributions of thermal emission deviated from the predictions of the Kirchoff’s law and closely followed the Lambert’s law, ∝cosθ. The thermal radiation properties of hyperbolic metamaterials were not much different from those of simpler metallic structures.

© 2015 Optical Society of America

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References

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2014 (2)

L. Gu, T. U. Tumkur, G. Zhu, and M. A. Noginov, “Blue shift of spontaneous emission in hyperbolic metamaterial,” Sci Rep 4, 4969 (2014).
[Crossref] [PubMed]

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

2013 (4)

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Review 7(2), 265–271 (2013).
[Crossref]

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3, 041004 (2013).

C. Simovski, S. Maslovski, I. Nefedov, and S. Tretyakov, “Optimization of radiative heat transfer in hyperbolic metamaterials for thermophotovoltaic applications,” Opt. Express 21(12), 14988–15013 (2013).
[Crossref] [PubMed]

Y. Guo and Z. Jacob, “Thermal hyperbolic metamaterials,” Opt. Express 21(12), 15014–15019 (2013).
[Crossref] [PubMed]

2012 (3)

J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express 20(7), 8100–8116 (2012).
[Crossref] [PubMed]

Z. Jacob, I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012).
[Crossref]

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14(2), 024005 (2012).
[Crossref]

2011 (2)

J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a mid-infrared metamaterial,” Appl. Phys. Lett. 98(24), 241105 (2011).
[Crossref]

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

2010 (2)

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[Crossref] [PubMed]

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10(3), 916–922 (2010).
[Crossref] [PubMed]

2009 (3)

2007 (2)

2006 (2)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

2005 (1)

2003 (3)

P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

S. Y. Lin, J. Moreno, and J. G. Fleming, “Three-dimensional photonic-crystal emitter for thermal photovoltaic generation,” Appl. Phys. Lett. 83(2), 380–382 (2003).
[Crossref]

1998 (1)

1993 (1)

N. Kaiser, A. Zuber, and U. Kaiser, “Evaluation of thin MgF2 films by spectroscopic ellipsometry,” Thin Solid Films 232(1), 16–17 (1993).
[Crossref]

1965 (1)

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

1901 (1)

O. Lummer and F. Kurlbaum, “Der elektrisch geglühte “schwarze” Körper,” Annalen der Physik 5(8), 829–836 (1901).
[Crossref]

1900 (1)

H. Rubens and F. Kurlbaum, “Über die Emission langer Wellen durch den schwarzen Körper,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 181 (1900).

1898 (1)

O. Lummer and F. Kurlbaum, “Der electrisch geglühte “absolut schwarze” Körper und seine Temperaturmessung,” Verhandlungen der Deutschen Physikalischen Gesellschaft 17, 106–111 (1898).

1865 (1)

J. Tyndall, “Über leuchtende und dunkle Strahlung,” Annalen der Physik und Chemie 200(1), 36–53 (1865).
[Crossref]

1860 (1)

G. Kirchhoff, ““Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme and Licht,” Annalen der Physik und Chemie 109 (2), 275–301 (1860). “On the relation between the radiating and absorbing powers of different bodies for light and heat,” Philosophical Magazine and Journal of Science, Series 4, Vol 20, 1–21 (1860).

1791 (1)

P. Prevost, “Mémoire sur l'equilibre du feu,” J. Phys. 38, 314–322 (1791).

Alekseyev, L. V.

Barnakov, Y. A.

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[Crossref] [PubMed]

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[Crossref]

Belov, P. A.

P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Blanchard, R.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3, 041004 (2013).

Boltasseva, A.

Bonner, C. E.

Borneman, J. D.

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10(3), 916–922 (2010).
[Crossref] [PubMed]

Cai, W.

Capasso, F.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3, 041004 (2013).

Chang, Y.-C.

Chang, Y.-T.

Chen, C.-Y.

Chen, K.-P.

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10(3), 916–922 (2010).
[Crossref] [PubMed]

Chettiar, U. K.

Cortes, C. L.

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

Drachev, V. P.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Review 7(2), 265–271 (2013).
[Crossref]

J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express 20(7), 8100–8116 (2012).
[Crossref] [PubMed]

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10(3), 916–922 (2010).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[Crossref] [PubMed]

Dryden, D.

Engheta, N.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

Fan, S.

Fleming, J. G.

S. Y. Lin, J. Moreno, and J. G. Fleming, “Three-dimensional photonic-crystal emitter for thermal photovoltaic generation,” Appl. Phys. Lett. 83(2), 380–382 (2003).
[Crossref]

Genevet, P.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3, 041004 (2013).

Gu, L.

L. Gu, T. U. Tumkur, G. Zhu, and M. A. Noginov, “Blue shift of spontaneous emission in hyperbolic metamaterial,” Sci Rep 4, 4969 (2014).
[Crossref] [PubMed]

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

Guo, Y.

Hu, H.

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

Ishii, S.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Review 7(2), 265–271 (2013).
[Crossref]

Jacob, Z.

Jiang, Y.-W.

John, J.

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14(2), 024005 (2012).
[Crossref]

Jokerst, N. M.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Kaiser, N.

N. Kaiser, A. Zuber, and U. Kaiser, “Evaluation of thin MgF2 films by spectroscopic ellipsometry,” Thin Solid Films 232(1), 16–17 (1993).
[Crossref]

Kaiser, U.

N. Kaiser, A. Zuber, and U. Kaiser, “Evaluation of thin MgF2 films by spectroscopic ellipsometry,” Thin Solid Films 232(1), 16–17 (1993).
[Crossref]

Kats, M. A.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3, 041004 (2013).

Kildishev, A. V.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Review 7(2), 265–271 (2013).
[Crossref]

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10(3), 916–922 (2010).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[Crossref] [PubMed]

Kim, J.

Kirchhoff, G.

G. Kirchhoff, ““Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme and Licht,” Annalen der Physik und Chemie 109 (2), 275–301 (1860). “On the relation between the radiating and absorbing powers of different bodies for light and heat,” Philosophical Magazine and Journal of Science, Series 4, Vol 20, 1–21 (1860).

Ko, C.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3, 041004 (2013).

Kurlbaum, F.

O. Lummer and F. Kurlbaum, “Der elektrisch geglühte “schwarze” Körper,” Annalen der Physik 5(8), 829–836 (1901).
[Crossref]

H. Rubens and F. Kurlbaum, “Über die Emission langer Wellen durch den schwarzen Körper,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 181 (1900).

O. Lummer and F. Kurlbaum, “Der electrisch geglühte “absolut schwarze” Körper und seine Temperaturmessung,” Verhandlungen der Deutschen Physikalischen Gesellschaft 17, 106–111 (1898).

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Lee, S.-C.

Li, H.

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[Crossref] [PubMed]

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[Crossref]

Li, X.

Lin, S. Y.

S. Y. Lin, J. Moreno, and J. G. Fleming, “Three-dimensional photonic-crystal emitter for thermal photovoltaic generation,” Appl. Phys. Lett. 83(2), 380–382 (2003).
[Crossref]

Liu, X.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Livenere, J. E.

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

Lummer, O.

O. Lummer and F. Kurlbaum, “Der elektrisch geglühte “schwarze” Körper,” Annalen der Physik 5(8), 829–836 (1901).
[Crossref]

O. Lummer and F. Kurlbaum, “Der electrisch geglühte “absolut schwarze” Körper und seine Temperaturmessung,” Verhandlungen der Deutschen Physikalischen Gesellschaft 17, 106–111 (1898).

Marqués, R.

P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Maslovski, S.

Maslovski, S. I.

P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Mason, J. A.

J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a mid-infrared metamaterial,” Appl. Phys. Lett. 98(24), 241105 (2011).
[Crossref]

Mayy, M.

Milder, A.

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14(2), 024005 (2012).
[Crossref]

Moreno, J.

S. Y. Lin, J. Moreno, and J. G. Fleming, “Three-dimensional photonic-crystal emitter for thermal photovoltaic generation,” Appl. Phys. Lett. 83(2), 380–382 (2003).
[Crossref]

Naik, G. V.

Narimanov, E.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Review 7(2), 265–271 (2013).
[Crossref]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

Narimanov, E. E.

J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express 20(7), 8100–8116 (2012).
[Crossref] [PubMed]

Z. Jacob, I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012).
[Crossref]

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[Crossref] [PubMed]

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[Crossref]

Nataraj, G.

Nefedov, I.

Nefedov, I. S.

P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Neuner, B.

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14(2), 024005 (2012).
[Crossref]

Nicodemus, F. E.

Noginov, M. A.

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

L. Gu, T. U. Tumkur, G. Zhu, and M. A. Noginov, “Blue shift of spontaneous emission in hyperbolic metamaterial,” Sci Rep 4, 4969 (2014).
[Crossref] [PubMed]

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[Crossref] [PubMed]

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[Crossref]

Padilla, W. J.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Podolskiy, V. A.

Prevost, P.

P. Prevost, “Mémoire sur l'equilibre du feu,” J. Phys. 38, 314–322 (1791).

Prokes, S. M.

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

Ramanathan, S.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3, 041004 (2013).

Rephaeli, E.

Rubens, H.

H. Rubens and F. Kurlbaum, “Über die Emission langer Wellen durch den schwarzen Körper,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 181 (1900).

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Salandrino, A.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

Sarychev, A. K.

Savoy, S.

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14(2), 024005 (2012).
[Crossref]

Schurig, D.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Shalaev, V. M.

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Review 7(2), 265–271 (2013).
[Crossref]

J. Kim, V. P. Drachev, Z. Jacob, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Improving the radiative decay rate for dye molecules with hyperbolic metamaterials,” Opt. Express 20(7), 8100–8116 (2012).
[Crossref] [PubMed]

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10(3), 916–922 (2010).
[Crossref] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30(24), 3356–3358 (2005).
[Crossref] [PubMed]

Shvets, G.

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14(2), 024005 (2012).
[Crossref]

Silveirinha, M.

P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Simovski, C.

Simovski, C. R.

P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Smith, D. R.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

Smith, S.

J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a mid-infrared metamaterial,” Appl. Phys. Lett. 98(24), 241105 (2011).
[Crossref]

Smolyaninov, I.

Z. Jacob, I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012).
[Crossref]

Snyder, W. C.

Starr, A. F.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Starr, T.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Thongrattanasiri, S.

Tretyakov, S.

Tretyakov, S. A.

P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Tsai, D. P.

Tsai, M.-W.

Tumkur, T.

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[Crossref]

Tumkur, T. U.

L. Gu, T. U. Tumkur, G. Zhu, and M. A. Noginov, “Blue shift of spontaneous emission in hyperbolic metamaterial,” Sci Rep 4, 4969 (2014).
[Crossref] [PubMed]

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

Tyler, T.

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Tyndall, J.

J. Tyndall, “Über leuchtende und dunkle Strahlung,” Annalen der Physik und Chemie 200(1), 36–53 (1865).
[Crossref]

Wan, Z.

Wang, C.-M.

Wasserman, D.

J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a mid-infrared metamaterial,” Appl. Phys. Lett. 98(24), 241105 (2011).
[Crossref]

Wu, C.

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14(2), 024005 (2012).
[Crossref]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Ye, Y.-H.

Yuan, H.-K.

Zhang, S.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3, 041004 (2013).

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Zhu, G.

L. Gu, T. U. Tumkur, G. Zhu, and M. A. Noginov, “Blue shift of spontaneous emission in hyperbolic metamaterial,” Sci Rep 4, 4969 (2014).
[Crossref] [PubMed]

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

M. A. Noginov, H. Li, Y. A. Barnakov, D. Dryden, G. Nataraj, G. Zhu, C. E. Bonner, M. Mayy, Z. Jacob, and E. E. Narimanov, “Controlling spontaneous emission with metamaterials,” Opt. Lett. 35(11), 1863–1865 (2010).
[Crossref] [PubMed]

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[Crossref]

Zollars, B.

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14(2), 024005 (2012).
[Crossref]

Zuber, A.

N. Kaiser, A. Zuber, and U. Kaiser, “Evaluation of thin MgF2 films by spectroscopic ellipsometry,” Thin Solid Films 232(1), 16–17 (1993).
[Crossref]

Annalen der Physik (1)

O. Lummer and F. Kurlbaum, “Der elektrisch geglühte “schwarze” Körper,” Annalen der Physik 5(8), 829–836 (1901).
[Crossref]

Annalen der Physik und Chemie (1)

J. Tyndall, “Über leuchtende und dunkle Strahlung,” Annalen der Physik und Chemie 200(1), 36–53 (1865).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[Crossref]

S. Y. Lin, J. Moreno, and J. G. Fleming, “Three-dimensional photonic-crystal emitter for thermal photovoltaic generation,” Appl. Phys. Lett. 83(2), 380–382 (2003).
[Crossref]

J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a mid-infrared metamaterial,” Appl. Phys. Lett. 98(24), 241105 (2011).
[Crossref]

Z. Jacob, I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect: Radiative decay engineering with metamaterials,” Appl. Phys. Lett. 100(18), 181105 (2012).
[Crossref]

J. Opt. (1)

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14(2), 024005 (2012).
[Crossref]

J. Phys. (1)

P. Prevost, “Mémoire sur l'equilibre du feu,” J. Phys. 38, 314–322 (1791).

Laser Photonics Review (1)

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser Photonics Review 7(2), 265–271 (2013).
[Crossref]

Nano Lett. (1)

K.-P. Chen, V. P. Drachev, J. D. Borneman, A. V. Kildishev, and V. M. Shalaev, “Drude relaxation rate in grained gold nanoantennas,” Nano Lett. 10(3), 916–922 (2010).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (3)

Philosophical Magazine and Journal of Science, Series 4, Vol (1)

G. Kirchhoff, ““Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme and Licht,” Annalen der Physik und Chemie 109 (2), 275–301 (1860). “On the relation between the radiating and absorbing powers of different bodies for light and heat,” Philosophical Magazine and Journal of Science, Series 4, Vol 20, 1–21 (1860).

Phys. Rev. B (2)

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B 74(7), 075103 (2006).
[Crossref]

P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B 67(11), 113103 (2003).
[Crossref]

Phys. Rev. Lett. (2)

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref] [PubMed]

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107(4), 045901 (2011).
[Crossref] [PubMed]

Phys. Rev. X (1)

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium dioxide as a natural disordered metamaterial: perfect thermal emission and large broadband negative differential thermal emittance,” Phys. Rev. X 3, 041004 (2013).

Sci Rep (2)

L. Gu, T. U. Tumkur, G. Zhu, and M. A. Noginov, “Blue shift of spontaneous emission in hyperbolic metamaterial,” Sci Rep 4, 4969 (2014).
[Crossref] [PubMed]

L. Gu, J. E. Livenere, G. Zhu, T. U. Tumkur, H. Hu, C. L. Cortes, Z. Jacob, S. M. Prokes, and M. A. Noginov, “Angular distribution of emission from hyperbolic metamaterials,” Sci Rep 4, 7327 (2014).
[Crossref] [PubMed]

Science (1)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Thin Solid Films (1)

N. Kaiser, A. Zuber, and U. Kaiser, “Evaluation of thin MgF2 films by spectroscopic ellipsometry,” Thin Solid Films 232(1), 16–17 (1993).
[Crossref]

Verhandlungen der Deutschen Physikalischen Gesellschaft (2)

O. Lummer and F. Kurlbaum, “Der electrisch geglühte “absolut schwarze” Körper und seine Temperaturmessung,” Verhandlungen der Deutschen Physikalischen Gesellschaft 17, 106–111 (1898).

H. Rubens and F. Kurlbaum, “Über die Emission langer Wellen durch den schwarzen Körper,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 181 (1900).

Other (28)

M. Planck, “Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum,” Verhandlungen der Deutschen Physikalischen Gesellschaft 2, 237 (1900). Translated in D. ter Haar, “On the Theory of the Energy Distribution Law of the Normal Spectrum” in The Old Quantum Theory, 82. (Pergamon Press, 1967).

A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”. Annalen der Physik 17(6), 132–148 (1905). Translated in D. ter Haar, “On an heuristic point of view about the creation and conversion of light”, The Old Quantum Theory, 91–107 (Pergamon Press, 1967).

F. Paschen, “Über Gesetzmäßigkeiten in den Spectren fester Körper und über ein neue Bestimmung der Sonnentemperatur,” in Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen (Mathematisch-Physikalische Klasse) 294–304 (1895).

M. Planck “Über eine Verbesserung der Wienschen Spektralgleichung”. Deutsche Physikalische Gesellschaft. Verhandlungen 2, 202–204 (1900). Translated in D. ter Haar, “On an Improvement of Wien's Equation for the Spectrum”, The Old Quantum Theory, 79–81 (Pergamon Press, 1967).

J. Tyndall, Heat considered as a Mode of Motion (D. Appleton & Company, 1869).

Crova, A.P.P, (1880). “Étude des radiations émises par les corps incandescents. Mesure optique des hautes temperatures,” Annales de chimie et de physique, Série 5, vol. 19, 472–550 (1880).

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S. Chandrasekhar, S., Radiative Transfer (Dover Publications, 1960).

E. A. Milne, “Thermodynamics of the stars,” in Handbuch der Astrophysik (Springer, 1930), 65–255 .

G. B. Rybicki and A. P. Lightman, Radiative Processes in Astrophysics (John Wiley & Sons, 1979).

D. Mihalas and B. Weibel-Mihalas, Foundations of Radiation Hydrodynamics (Oxford University Press, 1984).

R. M. Goody and Y. L. Yung, Atmospheric Radiation: Theoretical Basis, 2nd edition (Oxford University Press, 1989).

H. Kangro, Early History of Planck's Radiation Law (Taylor & Francis, 1976).

P. Prevost, (1791) “Memoir on the Equilibrium of Heat” in The Laws of Radiation and Absorption: Memoirs by Prévost, Stewart, Kirchhoff, and Kirchhoff and Bunsen, translated and edited by D. B. Brace (American Book Company, 1901).

B. Stewart, “An account of some experiments on radiant heat, involving an extension of the Prevot’s theory of exchanges,” Transactions of the Royal Society of Edinburgh, Vol. XXII, part I (1858); reprinted in The Laws of Radiation and Absorption: Memoirs by Prévost, Stewart, Kirchhoff, and Kirchhoff and Bunsen, translated and edited by D. B. Brace (American Book Company, 1901).

H. von Helmholtz, Handbuch der physiologischen Optik, Allgemeinen Encyclopädie der Physik (Leopold Voss, 1857), Volume 9.

G. G. Stokes, “On the perfect blackness of the central spot in Newton's rings, and on the verification of Fresnel's formulae for the intensities of reflected and refracted rays,” Cambridge and Dublin Mathematical Journal, Vol. IV, 1–14 (1849); reprinted in Physical and Mathematical Papers, Vol. II, G. G. Stokes, ed., (Cambridge University Press, 1983).

G. R. Kirchhoff, “Über die Fraunhofer'schen Linien,” 662–665 (1859) in Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (Buchdruckerei der Königlichen Academie der Wissenschaften, 1875).

G. R. Kirchhoff, “Über den Zusammenhang zwischen Emission und Absorption von Licht und Wärme,” 783–787 (1859) in Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (Buchdruckerei der Königlichen Academie der Wissenschaften, 1875).

S. Fan, S. Sandhu, Z. Yu, A. P. Raman, L. Zhu, and M. Anoma, “Thermal radiation control: enhancement of solar sell performance and daytime radiative cooling,” presented at the SPIE Optics + Photonics, paper 9160–34, San Diego, CA, USA, 17–21 August 2014.

M. A. Noginov and V. A. Podolskiy, eds., Tutorials in Metamaterials (Taylor & Francis, 2011).

A. Kuznetsov, I. Melnikova, D. Pozdnyakov, O. Seroukhova, and A. Vasilyev, Remote Sensing of the Environment and Radiation Transfer: An Introductory Survey (Springer, 2012).

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E. E. Narimanov and I. I. Smolyaninov, “Beyond Stefan-Boltzmann Law: Thermal Hyper-Conductivity”, arXiv:1109.5444v1 [physics.optics] 26 Sept. 2011.

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Figures (7)

Fig. 1
Fig. 1 (a) Schematics of angular emission measurements. (b) Schematics of spectral emission measurements. (c) Spectral sensitivity of the InSb (1) and HgTe (2) photo-detectors. Adopted from the manufacturer’s (Hamamatsu) specification. (3) The product of the detector sensitivity spectrum and the blackbody radiation spectrum at T = 268 °C .
Fig. 2
Fig. 2 Ratio of the p-polarized reflectance and s-polarized reflectance, R(θ)p/R(θ)s, measured in the 300 nm thick gold film. Red circles: experiment at λ = 2μm; blue squares: experiment at λ = 1.2 μm. Corresponding solid lines – theoretical fits, as explained in Section 4.1.
Fig. 3
Fig. 3 Dependence of the temperature reading of the thermal camera plotted versus actual sample’s temperature measured with the thermocouple for 150 nm thick Au film (purple circles), ~400 nm thick Au/MgF2 lamellar metamaterial (red triangles), 270 nm MgF2 film deposited on top of Cu (green squares), and Cu (black crosses). The temperature scan was 26 min long. Inset: Thermal image of the Au-coated flat end of the solder iron before (left) and after (right) thermal degradation.
Fig. 4
Fig. 4 (a) Trace 1 (red squares) – thermal emission of Cu sample and background (recorded without cover). Trace 2 (green triangles) – thermal emission of background (primarily radiation shield, recorded with cover). Blue diamonds – corrected thermal emission of Cu sample (Trace 3 = Trace 1 – Trace 2). (b) Angular distribution of thermal radiation of a black soot (at T = 225 °C) normalized to unity in the maximum. Solid line: Lambertian distribution, ∝cos(θ). (c) Angular distribution of thermal radiation of Au coated surfaces normalized to unity at θ = 0. Four independent measurements have been done at Au film thickness 100 nm, T = 315 °C (purple crosses, brown squares, and green triangles) and film thickness 130 nm, T = 223 °C (red diamonds). Solid black circles: average over the four measurements. The error bars are shown for the averaged data as well as for one particular data set with the largest error bars. Black line: cos(θ). Red line: sample absorbance calculated at λ = 3.0 μm from the p and s polarized reflectance spectra as A = [(2-Rs-Rp)/2]cos(θ). Blue line: same as above at λ = 2.0 μm. (d) Angular distribution of thermal radiation of Au/MgF2 metamaterial (thickness ~400 nm, T = 222 °C, red circles), Au with MgF2 on top (film thickness 80nm/80nm, T = 225 °C, blue squares), and Cu (T = 230 °C, green triangles). All signals are normalized to unity at the maximum. Black line: cos(θ). Red line: absorbance of the Au/MgF2 metamaterial calculated at λ = 3.0 μm from the p and s polarized reflectance spectra as A = [(2-Rs-Rp)/3]cos(θ). Blue line: same as above at λ = 2.0 μm.
Fig. 5
Fig. 5 Spectra of thermal emissivity of Au coated surface (film thickness 150 nm, T = 280 °C, trace 1a, red) and lamellar Au/MgF2 metamaterial (thicknesses ~400 nm, T = 295 °C, trace 2a, black). Spectra of 1-ρ calculated for Au (1b) and lamellar Au/MgF2 metamaterial (2b). The characteristic error bar is shown in the upper right corner.
Fig. 6
Fig. 6 Spectra of dielectric permittivity of Au (ε’- trace 1, ε”- trace 2), and lamellar metal/dielectric metamaterial (ε’|| - trace 3, ε”|| - trace 4, ε’ - trace 5, and ε” - trace 6) in the directions parallel || and perpendicular ⊥ to the layers. Upper inset: schematic of a lamellar hyperbolic metamaterial. Lower inset: Zoomed spectra of dielectric permittivities plotted in the main frame.
Fig. 7
Fig. 7 (a) Calculated angular reflectance spectra of Au at λ = 1.2 μm (1, 2), λ = 2.0 μm (3, 4), and λ = 3.0 μm (5, 6) in p polarization (1, 3, 5) and s polarization (2, 4, 6). (b) Same for lamellar Au/MgF2 metamaterial.

Equations (5)

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I S ( λ ) I B ( λ ) = S( λ )B( λ, T S ) ε S ( λ ) S( λ )B( λ, T B ) ε B ( λ )        ε S ( λ )= I S ( λ )B( λ, T B ) I B ( λ )B( λ, T S ) ε B ( λ )
B( λ,T )= 2h c 2 λ 5 1 exp( hc/λ k B T )1       B( ν,T )= 2h ν 3 c 2 1 exp( hν/ k B T )1
ε( ω )= ε b ω p 2 ω 2 +iωγ
ε || =f ε m +( 1f ) ε d 1 ε = f ε m + ( 1f ) ε d
ρ( λ )= | r | 2 ={ | sin( θ θ t ) sin( θ+ θ t ) | 2       ,     θ t =arcsin( sinθ ε ll ) ,                      polarization.       | ε ll tan θ t tanθ ε ll tan θ t +tanθ | 2 ,    θ t =arctan ε sin 2 θ ε ll ε ε ll sin 2 θ  ,        polarization.     }

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