Abstract

We experimentally investigate the near-infrared emission from simple-to-fabricate, continuous-film Fabry-Perot-type resonators, consisting only of unstructured dielectric and metallic films. We show that the proposed configuration is suitable for realization of narrowband emitters, tunable in ranges from mid- to near-infrared, and demonstrate emission centered at the wavelength of 1.7 μm, which corresponds to the band gap energy of GaSb-based photodetectors. The emission is measured at 748 K and follows well the emissivity as predicted from reflection measurements and Kirchhoff’s reciprocity. The considered emitter configuration is spectrally highly tunable and, consisting of only few unstructured layers, is amenable to wafer-scale fabrication at low cost by use of standard deposition procedures.

© 2015 Optical Society of America

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    [Crossref]
  30. M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
    [Crossref]
  31. G. Allen, R. Bayles, W. Gile, and W. Jesser, “Small particle melting of pure metals,” Thin Solid Films 144, 297 (1986).
    [Crossref]
  32. Y. G. Chushak and L. S. Bartell, “Melting and Freezing of Gold Nanoclusters,” J. Phys. Chem. B 105, 11605 (2001).
    [Crossref]
  33. U. Guler, A. Boltasseva, and V. M. Shalaev, “Refractory plasmonics,” Science 344(6181), 263 (2014).
    [Crossref] [PubMed]
  34. C. Jeppesen, N. A. Mortensen, and A. Kristensen, “The effect of Ti and ITO adhesion layers on gold split-ring resonators,” Appl. Phys. Lett. 97, 263103 (2010).
    [Crossref]
  35. B. Lahiri, R. Dylewicz, R. M. De La Rue, and N. P. Johnson, “Impact of titanium adhesion layers on the response of arrays of metallic split-ring resonators (SRRs),” Opt. Express 18, 11202 (2010).
    [Crossref] [PubMed]

2014 (5)

Y. Shuai, H. Tan, and Y. Liang, “Polariton-enhanced emittance of metallic–dielectric multilayer structures for selective thermal emitters,” J. Quant. Spectrosc. Radiat. Transfer 135, 50 (2014).
[Crossref]

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

Y.-J. Chen, M.-C. Lee, and C.-M. Wang, “Dielectric function dependence on temperature for Au and Ag,” Jpn. J. Appl. Phys. 53, 08MG02 (2014).
[Crossref]

U. Guler, A. Boltasseva, and V. M. Shalaev, “Refractory plasmonics,” Science 344(6181), 263 (2014).
[Crossref] [PubMed]

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljačić, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126 (2014).
[Crossref] [PubMed]

2013 (4)

S. Molesky, C.J. Dewalt, and Z. Jacob, “High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics,” Opt. Express 21, A96 (2013).
[Crossref] [PubMed]

S. Tripura Sundari, K. Srinivasu, S. Dash, and A.K. Tyagi, “Temperature evolution of optical constants and their tuning in silver,” Solid State Commun. 167, 36 (2013).
[Crossref]

B. Zhao, L. Wang, Y. Shuai, and Z.M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637 (2013).
[Crossref]

M. Yan, “Metal–insulator–metal light absorber: a continuous structure,” J. Opt. 15, 025006 (2013).
[Crossref]

2012 (2)

L. Wang, S. Basu, and Z. Zhang, “Direct measurement of thermal emission from a Fabry–Perot Cavity resonator,” J. Heat Transfer 134, 072701 (2012).
[Crossref]

A.S. Gawarikar, R.P. Shea, and J.J. Talghader, “Radiation efficiency of narrowband coherent thermal emitters,” AIP Adv. 2, 032113 (2012).
[Crossref]

2011 (1)

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, 045901 (2011).
[Crossref] [PubMed]

2010 (2)

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “The effect of Ti and ITO adhesion layers on gold split-ring resonators,” Appl. Phys. Lett. 97, 263103 (2010).
[Crossref]

B. Lahiri, R. Dylewicz, R. M. De La Rue, and N. P. Johnson, “Impact of titanium adhesion layers on the response of arrays of metallic split-ring resonators (SRRs),” Opt. Express 18, 11202 (2010).
[Crossref] [PubMed]

2008 (2)

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008).
[Crossref]

2007 (2)

2005 (3)

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]

P. Ben-Abdallah and B. Ni, “Single-defect Bragg stacks for high-power narrow-band thermal emission,” J. Appl. Phys. 97, 104910 (2005).
[Crossref]

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

2004 (1)

F. Marquier, K. Joulain, J.-P. Mulet, R. Carminati, J.-J. Greffet, and Y. Chen, “Coherent spontaneous emission of light by thermal sources,” Phys. Rev. B 69, 155412 (2004).
[Crossref]

2003 (2)

S.-Y. Lin, J.G. Flemming, and I. El-Kady, “Experimental observation of photonic-crystal emission near a photonic band edge,” Appl. Phys. Lett. 83, 593 (2003).
[Crossref]

W. Turner, S. Spector, N. Gardiner, M. Fladeland, E. Sterling, and M. Steininger, “Remote sensing for biodiversity science and conservation,” Trends Ecol. Evol. 18(6), 306–314 (2003).
[Crossref]

2002 (1)

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

2001 (1)

Y. G. Chushak and L. S. Bartell, “Melting and Freezing of Gold Nanoclusters,” J. Phys. Chem. B 105, 11605 (2001).
[Crossref]

2000 (1)

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[Crossref]

1998 (1)

1996 (1)

1991 (1)

M. Brückner, J.H. Schäfer, C. Schiffer, and J. Uhlenbusch, “Measurements of the optical constants of solid and molten gold and tin at λ = 10.6μm,” J. Appl. Phys. 70, 1642 (1991).
[Crossref]

1986 (1)

G. Allen, R. Bayles, W. Gile, and W. Jesser, “Small particle melting of pure metals,” Thin Solid Films 144, 297 (1986).
[Crossref]

1972 (1)

K. Ujihara, “Reflectivity of metals at high temperatures,” J. Appl. Phys. 43, 2376 (1972).
[Crossref]

1965 (1)

1901 (1)

M. Planck, “Ueber das Gesetz der Energieverteilung im Normalspectrum,” Ann. Phys. 309, 553 (1901).
[Crossref]

Allen, G.

G. Allen, R. Bayles, W. Gile, and W. Jesser, “Small particle melting of pure metals,” Thin Solid Films 144, 297 (1986).
[Crossref]

Allen, L. H.

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[Crossref]

Bartell, L. S.

Y. G. Chushak and L. S. Bartell, “Melting and Freezing of Gold Nanoclusters,” J. Phys. Chem. B 105, 11605 (2001).
[Crossref]

Basu, S.

L. Wang, S. Basu, and Z. Zhang, “Direct measurement of thermal emission from a Fabry–Perot Cavity resonator,” J. Heat Transfer 134, 072701 (2012).
[Crossref]

Bayles, R.

G. Allen, R. Bayles, W. Gile, and W. Jesser, “Small particle melting of pure metals,” Thin Solid Films 144, 297 (1986).
[Crossref]

Ben-Abdallah, P.

P. Ben-Abdallah and B. Ni, “Single-defect Bragg stacks for high-power narrow-band thermal emission,” J. Appl. Phys. 97, 104910 (2005).
[Crossref]

Bierman, D. M.

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljačić, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126 (2014).
[Crossref] [PubMed]

Boltasseva, A.

U. Guler, A. Boltasseva, and V. M. Shalaev, “Refractory plasmonics,” Science 344(6181), 263 (2014).
[Crossref] [PubMed]

Boyce, B.

Brückner, M.

M. Brückner, J.H. Schäfer, C. Schiffer, and J. Uhlenbusch, “Measurements of the optical constants of solid and molten gold and tin at λ = 10.6μm,” J. Appl. Phys. 70, 1642 (1991).
[Crossref]

Busch, K.

M. Florescu, K. Busch, and J. P. Dowling, “Thermal radiation in photonic crystals,” Phys. Rev. B 75, 201101 (2007).
[Crossref]

Carminati, R.

F. Marquier, K. Joulain, J.-P. Mulet, R. Carminati, J.-J. Greffet, and Y. Chen, “Coherent spontaneous emission of light by thermal sources,” Phys. Rev. B 69, 155412 (2004).
[Crossref]

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

Celanovic, I.

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljačić, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126 (2014).
[Crossref] [PubMed]

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008).
[Crossref]

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

Chan, W. R.

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljačić, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126 (2014).
[Crossref] [PubMed]

Chang, Y.-C.

Chang, Y.-T.

Chen, C.-Y.

Chen, X.

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

Chen, Y.

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

F. Marquier, K. Joulain, J.-P. Mulet, R. Carminati, J.-J. Greffet, and Y. Chen, “Coherent spontaneous emission of light by thermal sources,” Phys. Rev. B 69, 155412 (2004).
[Crossref]

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

Chen, Y.-J.

Y.-J. Chen, M.-C. Lee, and C.-M. Wang, “Dielectric function dependence on temperature for Au and Ag,” Jpn. J. Appl. Phys. 53, 08MG02 (2014).
[Crossref]

Chushak, Y. G.

Y. G. Chushak and L. S. Bartell, “Melting and Freezing of Gold Nanoclusters,” J. Phys. Chem. B 105, 11605 (2001).
[Crossref]

Dash, S.

S. Tripura Sundari, K. Srinivasu, S. Dash, and A.K. Tyagi, “Temperature evolution of optical constants and their tuning in silver,” Solid State Commun. 167, 36 (2013).
[Crossref]

De La Rue, R. M.

Dewalt, C.J.

Dowling, J. P.

M. Florescu, K. Busch, and J. P. Dowling, “Thermal radiation in photonic crystals,” Phys. Rev. B 75, 201101 (2007).
[Crossref]

Dylewicz, R.

Efremov, M.Y.

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[Crossref]

El-Kady, I.

S.-Y. Lin, J.G. Flemming, and I. El-Kady, “Experimental observation of photonic-crystal emission near a photonic band edge,” Appl. Phys. Lett. 83, 593 (2003).
[Crossref]

Fladeland, M.

W. Turner, S. Spector, N. Gardiner, M. Fladeland, E. Sterling, and M. Steininger, “Remote sensing for biodiversity science and conservation,” Trends Ecol. Evol. 18(6), 306–314 (2003).
[Crossref]

Flemming, J.G.

S.-Y. Lin, J.G. Flemming, and I. El-Kady, “Experimental observation of photonic-crystal emission near a photonic band edge,” Appl. Phys. Lett. 83, 593 (2003).
[Crossref]

Florescu, M.

M. Florescu, K. Busch, and J. P. Dowling, “Thermal radiation in photonic crystals,” Phys. Rev. B 75, 201101 (2007).
[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, 071904 (2005).
[Crossref]

Fujimura, K.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Gardiner, N.

W. Turner, S. Spector, N. Gardiner, M. Fladeland, E. Sterling, and M. Steininger, “Remote sensing for biodiversity science and conservation,” Trends Ecol. Evol. 18(6), 306–314 (2003).
[Crossref]

Gawarikar, A.S.

A.S. Gawarikar, R.P. Shea, and J.J. Talghader, “Radiation efficiency of narrowband coherent thermal emitters,” AIP Adv. 2, 032113 (2012).
[Crossref]

Gile, W.

G. Allen, R. Bayles, W. Gile, and W. Jesser, “Small particle melting of pure metals,” Thin Solid Films 144, 297 (1986).
[Crossref]

Gong, H.

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

Greene, J. E.

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[Crossref]

Greffet, J.-J.

F. Marquier, K. Joulain, J.-P. Mulet, R. Carminati, J.-J. Greffet, and Y. Chen, “Coherent spontaneous emission of light by thermal sources,” Phys. Rev. B 69, 155412 (2004).
[Crossref]

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

J.-J. Greffet and M. Nieto-Vesperinas, “Field theory for generalized bidirectional reflectivity: derivation of Helmholtz’s reciprocity principle and Kirchhoff’s law,” J. Opt. Soc. Am. A 15, 2735 (1998).
[Crossref]

Guler, U.

U. Guler, A. Boltasseva, and V. M. Shalaev, “Refractory plasmonics,” Science 344(6181), 263 (2014).
[Crossref] [PubMed]

Hatade, K.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Hayden, A.

Ikeda, K.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Inoue, Y.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Jacob, Z.

Jeppesen, C.

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “The effect of Ti and ITO adhesion layers on gold split-ring resonators,” Appl. Phys. Lett. 97, 263103 (2010).
[Crossref]

Jesser, W.

G. Allen, R. Bayles, W. Gile, and W. Jesser, “Small particle melting of pure metals,” Thin Solid Films 144, 297 (1986).
[Crossref]

Jiang, Y.-W.

Johnson, N. P.

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, 045901 (2011).
[Crossref] [PubMed]

Jones, H. G.

H. G. Jones, “Application of thermal imaging and infrared sensing in plant physiology and ecophysiology,” in Incorporating Advances in Plant Pathology, J. A. Callow, ed., vol. 41 of Advances in Botanical Research, pp. 107–163 (Academic, 2004).
[Crossref]

Joulain, K.

F. Marquier, K. Joulain, J.-P. Mulet, R. Carminati, J.-J. Greffet, and Y. Chen, “Coherent spontaneous emission of light by thermal sources,” Phys. Rev. B 69, 155412 (2004).
[Crossref]

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

Jovanovic, N.

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008).
[Crossref]

Kanakugi, T.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Kasaya, T.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Kassakian, J.

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008).
[Crossref]

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

Kitagawa, S.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Kristensen, A.

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “The effect of Ti and ITO adhesion layers on gold split-ring resonators,” Appl. Phys. Lett. 97, 263103 (2010).
[Crossref]

Kwan, A. T.

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[Crossref]

Lahiri, B.

Lai, S. L.

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[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, 071904 (2005).
[Crossref]

Lee, M.-C.

Y.-J. Chen, M.-C. Lee, and C.-M. Wang, “Dielectric function dependence on temperature for Au and Ag,” Jpn. J. Appl. Phys. 53, 08MG02 (2014).
[Crossref]

Lee, S.-C.

Lenert, A.

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljačić, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126 (2014).
[Crossref] [PubMed]

Li, Q.

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

Liang, Y.

Y. Shuai, H. Tan, and Y. Liang, “Polariton-enhanced emittance of metallic–dielectric multilayer structures for selective thermal emitters,” J. Quant. Spectrosc. Radiat. Transfer 135, 50 (2014).
[Crossref]

Lin, S.-Y.

S.-Y. Lin, J.G. Flemming, and I. El-Kady, “Experimental observation of photonic-crystal emission near a photonic band edge,” Appl. Phys. Lett. 83, 593 (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, 045901 (2011).
[Crossref] [PubMed]

Mainguy, S.

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

Marquier, F.

F. Marquier, K. Joulain, J.-P. Mulet, R. Carminati, J.-J. Greffet, and Y. Chen, “Coherent spontaneous emission of light by thermal sources,” Phys. Rev. B 69, 155412 (2004).
[Crossref]

Meng, L.

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

Miyazaki, H.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Molesky, S.

Mortensen, N. A.

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “The effect of Ti and ITO adhesion layers on gold split-ring resonators,” Appl. Phys. Lett. 97, 263103 (2010).
[Crossref]

Mulet, J.-P.

F. Marquier, K. Joulain, J.-P. Mulet, R. Carminati, J.-J. Greffet, and Y. Chen, “Coherent spontaneous emission of light by thermal sources,” Phys. Rev. B 69, 155412 (2004).
[Crossref]

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

Nam, Y.

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljačić, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126 (2014).
[Crossref] [PubMed]

Ni, B.

P. Ben-Abdallah and B. Ni, “Single-defect Bragg stacks for high-power narrow-band thermal emission,” J. Appl. Phys. 97, 104910 (2005).
[Crossref]

Nicodemus, F. E.

Nieto-Vesperinas, M.

Niple, E.

Okada, M.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Olson, E. A.

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[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, 045901 (2011).
[Crossref] [PubMed]

Perreault, D.

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

Planck, M.

M. Planck, “Ueber das Gesetz der Energieverteilung im Normalspectrum,” Ann. Phys. 309, 553 (1901).
[Crossref]

Qiu, M.

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

Schäfer, J.H.

M. Brückner, J.H. Schäfer, C. Schiffer, and J. Uhlenbusch, “Measurements of the optical constants of solid and molten gold and tin at λ = 10.6μm,” J. Appl. Phys. 70, 1642 (1991).
[Crossref]

Schiettekatte, F.

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[Crossref]

Schiffer, C.

M. Brückner, J.H. Schäfer, C. Schiffer, and J. Uhlenbusch, “Measurements of the optical constants of solid and molten gold and tin at λ = 10.6μm,” J. Appl. Phys. 70, 1642 (1991).
[Crossref]

Shalaev, V. M.

U. Guler, A. Boltasseva, and V. M. Shalaev, “Refractory plasmonics,” Science 344(6181), 263 (2014).
[Crossref] [PubMed]

Shea, R.P.

A.S. Gawarikar, R.P. Shea, and J.J. Talghader, “Radiation efficiency of narrowband coherent thermal emitters,” AIP Adv. 2, 032113 (2012).
[Crossref]

Shuai, Y.

Y. Shuai, H. Tan, and Y. Liang, “Polariton-enhanced emittance of metallic–dielectric multilayer structures for selective thermal emitters,” J. Quant. Spectrosc. Radiat. Transfer 135, 50 (2014).
[Crossref]

B. Zhao, L. Wang, Y. Shuai, and Z.M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637 (2013).
[Crossref]

Soljacic, M.

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljačić, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126 (2014).
[Crossref] [PubMed]

Spector, S.

W. Turner, S. Spector, N. Gardiner, M. Fladeland, E. Sterling, and M. Steininger, “Remote sensing for biodiversity science and conservation,” Trends Ecol. Evol. 18(6), 306–314 (2003).
[Crossref]

Srinivasu, K.

S. Tripura Sundari, K. Srinivasu, S. Dash, and A.K. Tyagi, “Temperature evolution of optical constants and their tuning in silver,” Solid State Commun. 167, 36 (2013).
[Crossref]

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, 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, 045901 (2011).
[Crossref] [PubMed]

Steininger, M.

W. Turner, S. Spector, N. Gardiner, M. Fladeland, E. Sterling, and M. Steininger, “Remote sensing for biodiversity science and conservation,” Trends Ecol. Evol. 18(6), 306–314 (2003).
[Crossref]

Sterling, E.

W. Turner, S. Spector, N. Gardiner, M. Fladeland, E. Sterling, and M. Steininger, “Remote sensing for biodiversity science and conservation,” Trends Ecol. Evol. 18(6), 306–314 (2003).
[Crossref]

Talghader, J.J.

A.S. Gawarikar, R.P. Shea, and J.J. Talghader, “Radiation efficiency of narrowband coherent thermal emitters,” AIP Adv. 2, 032113 (2012).
[Crossref]

Tan, H.

Y. Shuai, H. Tan, and Y. Liang, “Polariton-enhanced emittance of metallic–dielectric multilayer structures for selective thermal emitters,” J. Quant. Spectrosc. Radiat. Transfer 135, 50 (2014).
[Crossref]

Tripura Sundari, S.

S. Tripura Sundari, K. Srinivasu, S. Dash, and A.K. Tyagi, “Temperature evolution of optical constants and their tuning in silver,” Solid State Commun. 167, 36 (2013).
[Crossref]

Tsai, D. P.

Tsai, M.-W.

Turner, W.

W. Turner, S. Spector, N. Gardiner, M. Fladeland, E. Sterling, and M. Steininger, “Remote sensing for biodiversity science and conservation,” Trends Ecol. Evol. 18(6), 306–314 (2003).
[Crossref]

Tyagi, A.K.

S. Tripura Sundari, K. Srinivasu, S. Dash, and A.K. Tyagi, “Temperature evolution of optical constants and their tuning in silver,” Solid State Commun. 167, 36 (2013).
[Crossref]

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, 045901 (2011).
[Crossref] [PubMed]

Uhlenbusch, J.

M. Brückner, J.H. Schäfer, C. Schiffer, and J. Uhlenbusch, “Measurements of the optical constants of solid and molten gold and tin at λ = 10.6μm,” J. Appl. Phys. 70, 1642 (1991).
[Crossref]

Ujihara, K.

K. Ujihara, “Reflectivity of metals at high temperatures,” J. Appl. Phys. 43, 2376 (1972).
[Crossref]

Wang, C.-M.

Wang, E. N.

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljačić, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126 (2014).
[Crossref] [PubMed]

Wang, L.

B. Zhao, L. Wang, Y. Shuai, and Z.M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637 (2013).
[Crossref]

L. Wang, S. Basu, and Z. Zhang, “Direct measurement of thermal emission from a Fabry–Perot Cavity resonator,” J. Heat Transfer 134, 072701 (2012).
[Crossref]

Wisleder, T.

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[Crossref]

Yamamoto, K.

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

Yan, M.

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

M. Yan, “Metal–insulator–metal light absorber: a continuous structure,” J. Opt. 15, 025006 (2013).
[Crossref]

Ye, Y.-H.

Zhang, M.

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[Crossref]

Zhang, Z.

L. Wang, S. Basu, and Z. Zhang, “Direct measurement of thermal emission from a Fabry–Perot Cavity resonator,” J. Heat Transfer 134, 072701 (2012).
[Crossref]

Zhang, Z.M.

B. Zhao, L. Wang, Y. Shuai, and Z.M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637 (2013).
[Crossref]

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]

Zhao, B.

B. Zhao, L. Wang, Y. Shuai, and Z.M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637 (2013).
[Crossref]

Zhao, D.

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

AIP Adv. (1)

A.S. Gawarikar, R.P. Shea, and J.J. Talghader, “Radiation efficiency of narrowband coherent thermal emitters,” AIP Adv. 2, 032113 (2012).
[Crossref]

Ann. Phys. (1)

M. Planck, “Ueber das Gesetz der Energieverteilung im Normalspectrum,” Ann. Phys. 309, 553 (1901).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (6)

C. Jeppesen, N. A. Mortensen, and A. Kristensen, “The effect of Ti and ITO adhesion layers on gold split-ring resonators,” Appl. Phys. Lett. 97, 263103 (2010).
[Crossref]

H. Miyazaki, K. Ikeda, T. Kasaya, K. Yamamoto, Y. Inoue, K. Fujimura, T. Kanakugi, M. Okada, K. Hatade, and S. Kitagawa, “Thermal emission of two-color polarized infrared waves from integrated plasmon cavities,” Appl. Phys. Lett. 92, 141114 (2008).
[Crossref]

D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104, 221107 (2014).
[Crossref]

S.-Y. Lin, J.G. Flemming, and I. El-Kady, “Experimental observation of photonic-crystal emission near a photonic band edge,” Appl. Phys. Lett. 83, 593 (2003).
[Crossref]

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]

I. Celanovic, N. Jovanovic, and J. Kassakian, “Two-dimensional tungsten photonic crystals as selective thermal emitters,” Appl. Phys. Lett. 92, 193101 (2008).
[Crossref]

Int. J. Heat Mass Transfer (1)

B. Zhao, L. Wang, Y. Shuai, and Z.M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637 (2013).
[Crossref]

J. Appl. Phys. (3)

P. Ben-Abdallah and B. Ni, “Single-defect Bragg stacks for high-power narrow-band thermal emission,” J. Appl. Phys. 97, 104910 (2005).
[Crossref]

K. Ujihara, “Reflectivity of metals at high temperatures,” J. Appl. Phys. 43, 2376 (1972).
[Crossref]

M. Brückner, J.H. Schäfer, C. Schiffer, and J. Uhlenbusch, “Measurements of the optical constants of solid and molten gold and tin at λ = 10.6μm,” J. Appl. Phys. 70, 1642 (1991).
[Crossref]

J. Heat Transfer (1)

L. Wang, S. Basu, and Z. Zhang, “Direct measurement of thermal emission from a Fabry–Perot Cavity resonator,” J. Heat Transfer 134, 072701 (2012).
[Crossref]

J. Opt. (1)

M. Yan, “Metal–insulator–metal light absorber: a continuous structure,” J. Opt. 15, 025006 (2013).
[Crossref]

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

J. Phys. Chem. B (1)

Y. G. Chushak and L. S. Bartell, “Melting and Freezing of Gold Nanoclusters,” J. Phys. Chem. B 105, 11605 (2001).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

Y. Shuai, H. Tan, and Y. Liang, “Polariton-enhanced emittance of metallic–dielectric multilayer structures for selective thermal emitters,” J. Quant. Spectrosc. Radiat. Transfer 135, 50 (2014).
[Crossref]

Jpn. J. Appl. Phys. (1)

Y.-J. Chen, M.-C. Lee, and C.-M. Wang, “Dielectric function dependence on temperature for Au and Ag,” Jpn. J. Appl. Phys. 53, 08MG02 (2014).
[Crossref]

Nat. Nanotechnol. (1)

A. Lenert, D. M. Bierman, Y. Nam, W. R. Chan, I. Celanović, M. Soljačić, and E. N. Wang, “A nanophotonic solar thermophotovoltaic device,” Nat. Nanotechnol. 9, 126 (2014).
[Crossref] [PubMed]

Nature (1)

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

Opt. Express (3)

Phys. Rev. B (4)

M. Zhang, M.Y. Efremov, F. Schiettekatte, E. A. Olson, A. T. Kwan, S. L. Lai, T. Wisleder, J. E. Greene, and L. H. Allen, “Size-dependent melting point depression of nanostructures: Nanocalorimetric measurements,” Phys. Rev. B 62, 10548 (2000).
[Crossref]

F. Marquier, K. Joulain, J.-P. Mulet, R. Carminati, J.-J. Greffet, and Y. Chen, “Coherent spontaneous emission of light by thermal sources,” Phys. Rev. B 69, 155412 (2004).
[Crossref]

M. Florescu, K. Busch, and J. P. Dowling, “Thermal radiation in photonic crystals,” Phys. Rev. B 75, 201101 (2007).
[Crossref]

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

Phys. Rev. Lett. (1)

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, 045901 (2011).
[Crossref] [PubMed]

Science (1)

U. Guler, A. Boltasseva, and V. M. Shalaev, “Refractory plasmonics,” Science 344(6181), 263 (2014).
[Crossref] [PubMed]

Solid State Commun. (1)

S. Tripura Sundari, K. Srinivasu, S. Dash, and A.K. Tyagi, “Temperature evolution of optical constants and their tuning in silver,” Solid State Commun. 167, 36 (2013).
[Crossref]

Thin Solid Films (1)

G. Allen, R. Bayles, W. Gile, and W. Jesser, “Small particle melting of pure metals,” Thin Solid Films 144, 297 (1986).
[Crossref]

Trends Ecol. Evol. (1)

W. Turner, S. Spector, N. Gardiner, M. Fladeland, E. Sterling, and M. Steininger, “Remote sensing for biodiversity science and conservation,” Trends Ecol. Evol. 18(6), 306–314 (2003).
[Crossref]

Other (1)

H. G. Jones, “Application of thermal imaging and infrared sensing in plant physiology and ecophysiology,” in Incorporating Advances in Plant Pathology, J. A. Callow, ed., vol. 41 of Advances in Botanical Research, pp. 107–163 (Academic, 2004).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a) Working principle of the continuous resonator. Freely propagating waves can couple to the resonator through the optically thin top layer. Inside the resonator, photonic modes are confined in the vertical direction, acquiring reflection and propagation phases, ϕr, top, ϕr, bottom and ϕprop, respectively, as indicated in the right part of (a), creating a resonance when the round-trip phases equal multiples of 2π. (b) Scanning electron micrograph (side view) of a continuous-film Fabry-Perot emitter detached and elevated above its substrate. Note that the 12 nm top gold layer is not well-resolved. (c) The structure of (b), showing the amorphous SiO2-layer (blue), the optically thick bottom gold layer and the optically thin top gold layer (yellow). Not shown are adhesion-promoting layers of 3 nm Ti at the SiO2-gold interfaces.
Fig. 2
Fig. 2 Schematic of the setup used for emission and reflection measurements. The sample is heated in a temperature-controlled microscope stage (HC). For the measurement of blackbody reference spectra, the heated sample cavity (HC) is replaced with a reference blackbody cavity with W1 mounted to the cavity opening. Reflection of sample and silver mirror reference is measured outside of the HC to avoid reflections from window W1, while the frequency shift is monitored inside HC. The numerical aperture (NA) of illumination is controlled with irises AS and FS, while in emission the NA and the area from which light is picked up, are controlled by irises CI and OI.
Fig. 3
Fig. 3 (a) Dependance of the reflectivity on the top gold layer thickness, for a spacer thickness of 472 nm. (b) Dependance of the reflectivity on spacer layer thickness for a top layer thickness of 12 nm. It is obvious that the emitter offers a high degree of tunability. Variation of the spacer thickness influences mainly on the position of the resonance and, to a lesser extent, also the position of the resonance through modification of the reflection phase ϕr, top.
Fig. 4
Fig. 4 Thermal emission measurements. (a) Emission from sample (solid) and blackbody (dashed) at temperatures 673, 723 and 748 K, respectively. It should be noted that intensity measurements incorporate the setup dispersion, leading to an apparent peak at 2 μm. (b) Emissivity calculated from spectra in (a) and extinction measurements (estimated as 1-R) showing an excellent match, in agreement with Kirchhoff’s reciprocity. Inset: The total frequency shift of the resonance is roughly 6 nm and has a low degree of hysteresis.
Fig. 5
Fig. 5 Scanning electron micrographs of heated samples after cooling. (a)–(b) and (c)–(e) show different sample batches, respectively, highlighting the influence of fabrication imperfections. (a) Sample A before heating. Several imperfections can be seen on the sample surface. (b) Sample A heated to 823 K, showing a complicated multitude of phase changes, cracks in the spacer layer and wrinkling of the bottom gold layer. (c), (d) Heated emitter of a fabrication batch with improved surface roughness. (c) The number of imperfections in the unheated sample are visibly reduced compared to (a). (d) Identical to c, heated to 823 K. This sample shows degradation of the top layer only, which has transformed into distinct particles. (e) Identical sample to (c), heated to 923 K, where the SiO2-layer starts to fracture.

Equations (3)

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I ( λ , T ) = ε λ ( T ) B ( λ , T ) = ε λ ( T ) 2 h c 2 λ 5 1 e h c λ k B T 1 ,
λ max ( T ) = b / T = 2898 μ m K / T ,
ϕ r , bottom + ϕ r , top + 2 ϕ prop = 2 m π ,

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