Abstract

Planck’s famous blackbody radiation law was derived under the assumption that the dimensions of the radiating body are significantly larger than the radiated wavelengths. What is unique about Planck's formula is the fact that it is independent of the exact loss mechanism and the geometry. Therefore, for a long period of time, it was regarded as a fundamental property of all materials. Deviations from its predictions were attributed to imperfections and referred to as the emissivity of the specific body, a quantity which was always assumed to be smaller than unity. Recent studies showed that the emission spectrum is affected by the geometry of the body and in fact, in a limited frequency range, the emitted spectrum may exceed Planck's prediction provided the typical size of the body is of the same order of magnitude as the emitted wavelength. For the investigation of the blackbody radiation from an arbitrarily shaped body, we developed a code which incorporates the fluctuation-dissipation theorem (FDT) and the source model technique (SMT). The former determines the correlation between the quasi-microscopic current densities in the body and the latter is used to solve the electromagnetic problem numerically. In this study we present the essence of combining the two concepts. We verify the validity of our code by comparing its results obtained for the case of a sphere against analytic results and discuss how the accuracy of the solution is assessed in the general case. Finally, we illustrate several configurations in which the emitted spectrum exceeds Planck's prediction as well as cases in which the geometrical resonances of the body are revealed.

© 2017 Optical Society of America

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References

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2016 (3)

S. I. Maslovski, C. R. Simovski, and S. A. Tretyakov, “Overcoming blackbody radiation limit in free space: metamaterial superemitter,” New J. Phys. 18(1), 013034 (2016).
[Crossref]

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

S. Edalatpour and M. Francoeur, “Near-field radiative heat transfer between arbitrarily shaped objects and a surface,” Phys. Rev. B 94(4), 045406 (2016).
[Crossref] [PubMed]

2015 (2)

A. G. Polimeridis, M. T. H. Reid, W. Jin, S. G. Johnson, J. K. White, and A. W. Rodriguez, “Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries,” Phys. Rev. B 92(13), 134202 (2015).
[Crossref]

S. Edalatpour, M. Čuma, T. Trueax, R. Backman, and M. Francoeur, “Convergence analysis of the thermal discrete dipole approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(6), 063307 (2015).
[Crossref] [PubMed]

2014 (1)

A. Didari and M. P. Mengüç, “Analysis of near-field radiation transfer within nano-gaps using FDTD method,” J. Quant. Spectrosc. Radiat. Transf. 146, 214–226 (2014).
[Crossref]

2013 (6)

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer: theory and applications,” Phys. Rev. B 88(5), 054305 (2013).
[Crossref]

Y. Tian and C. Y. Zhao, “A review of solar collectors and thermal energy storage in solar thermal applications,” Appl. Energy 104, 538–553 (2013).
[Crossref]

S. A. Biehs, M. Tschikin, R. Messina, and P. Ben-Abdallah, “Super-Planckian near-field thermal emission with phonon-polaritonic hyperbolic metamaterials,” Appl. Phys. Lett. 102(13), 131106 (2013).
[Crossref]

B. Liu and S. Shen, “Broadband near-field radiative thermal emitter/absorber based on hyperbolic metamaterials: Direct numerical simulation by the Wiener chaos expansion method,” Phys. Rev. B 87(11), 115403 (2013).
[Crossref]

A. Reiser and L. Schächter, “Geometric effects on blackbody radiation,” Phys. Rev. A 87(3), 033801 (2013).
[Crossref]

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

2012 (3)

T. T. Chow, G. N. Tiwari, and C. Menezo, “Hybrid solar: a review on photovoltaic and thermal power integration,” Int. J. Photoenergy 2012, 1–17 (2012).
[Crossref]

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
[Crossref]

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer for arbitrary geometries,” Phys. Rev. B 86(22), 220302 (2012).
[Crossref]

2011 (2)

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107(11), 114302 (2011).
[Crossref] [PubMed]

R. Messina and M. Antezza, “Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies,” Phys. Rev. A 84(4), 042102 (2011).
[Crossref]

2009 (1)

2008 (3)

E. Rephaeli and S. Fan, “Tungsten black absorber for solar light with wide angular operation range,” Appl. Phys. Lett. 92(21), 211107 (2008).
[Crossref]

A. Narayanaswamy and G. Chen, “Thermal near-field radiative transfer between two spheres,” Phys. Rev. B 77(7), 075125 (2008).
[Crossref]

H. A. Zondag, “Flat-plate PV-Thermal collectors and systems: A review,” Renew. Sustain. Energy Rev. 12(4), 891–959 (2008).
[Crossref]

2007 (2)

P. G. Charalambous, G. G. Maidment, S. A. Kalogirou, and K. Yiakoumetti, “Photovoltaic thermal (PV/T) collectors: A review,” Appl. Therm. Eng. 27(2), 275–286 (2007).
[Crossref]

S. Basu, Y. B. Chen, and Z. M. Zhang, “Microscale radiation in thermophotovoltaic devices – a review,” Int. J. Energy Res. 31(6–7), 689–716 (2007).
[Crossref]

2004 (1)

A. I. Volokitin and B. N. J. Persson, “Resonant photon tunneling enhancement of the radiative heat transfer,” Phys. Rev. B 69(4), 045417 (2004).
[Crossref]

2003 (1)

A. Narayanaswamy and G. Chen, “Surface modes for near field thermophotovoltaics,” Appl. Phys. Lett. 82(20), 3544–3546 (2003).
[Crossref]

2001 (1)

A. I. Volokitin and B. N. J. Persson, “Radiative heat transfer between nanostructures,” Phys. Rev. B 63(20), 205404 (2001).
[Crossref]

2000 (1)

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[Crossref] [PubMed]

1999 (1)

R. Carminati and J. J. Greffet, “Near-field effects in spatial coherence of thermal sources,” Phys. Rev. Lett. 82(8), 1660–1663 (1999).
[Crossref]

1994 (1)

J. J. Loomis and H. J. Maris, “Theory of heat transfer by evanescent electromagnetic waves,” Phys. Rev. B Condens. Matter 50(24), 18517–18524 (1994).
[Crossref] [PubMed]

1988 (1)

Y. Leviatan, A. Boag, and A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies—Theory and numerical solution,” IEEE Trans. Antenn. Propag. 36(12), 1722–1734 (1988).
[Crossref]

1971 (1)

D. Polder and M. Van Hove, “Theory of radiative heat transfer between closely spaced bodies,” Phys. Rev. B 4(10), 3303–3314 (1971).
[Crossref]

1970 (1)

1955 (1)

F. H. Brownell, “An Extension of Weyl’s Asymptotic Law for Eigenvalues,” Pac. J. Math. 5(4), 483–499 (1955).
[Crossref]

1951 (1)

H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83(1), 34–40 (1951).
[Crossref]

1950 (1)

A. Pleijel, “On the eigenvalues and eigenfunctions of elastic plates,” Commun. Pure Appl. Math. 3(1), 1–10 (1950).
[Crossref]

1912 (1)

H. Weyl, “Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung),” Math. Ann. 71(4), 441–479 (1912).
[Crossref]

Antezza, M.

R. Messina and M. Antezza, “Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies,” Phys. Rev. A 84(4), 042102 (2011).
[Crossref]

Backman, R.

S. Edalatpour, M. Čuma, T. Trueax, R. Backman, and M. Francoeur, “Convergence analysis of the thermal discrete dipole approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(6), 063307 (2015).
[Crossref] [PubMed]

Basu, S.

S. Basu, Y. B. Chen, and Z. M. Zhang, “Microscale radiation in thermophotovoltaic devices – a review,” Int. J. Energy Res. 31(6–7), 689–716 (2007).
[Crossref]

Ben-Abdallah, P.

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

S. A. Biehs, M. Tschikin, R. Messina, and P. Ben-Abdallah, “Super-Planckian near-field thermal emission with phonon-polaritonic hyperbolic metamaterials,” Appl. Phys. Lett. 102(13), 131106 (2013).
[Crossref]

Bermel, P.

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107(11), 114302 (2011).
[Crossref] [PubMed]

Biehs, S. A.

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

S. A. Biehs, M. Tschikin, R. Messina, and P. Ben-Abdallah, “Super-Planckian near-field thermal emission with phonon-polaritonic hyperbolic metamaterials,” Appl. Phys. Lett. 102(13), 131106 (2013).
[Crossref]

Boag, A.

Y. Leviatan, A. Boag, and A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies—Theory and numerical solution,” IEEE Trans. Antenn. Propag. 36(12), 1722–1734 (1988).
[Crossref]

Y. Leviatan, A. Boag, and A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies—Theory and numerical solution,” IEEE Trans. Antenn. Propag. 36(12), 1722–1734 (1988).
[Crossref]

Brownell, F. H.

F. H. Brownell, “An Extension of Weyl’s Asymptotic Law for Eigenvalues,” Pac. J. Math. 5(4), 483–499 (1955).
[Crossref]

Callen, H. B.

H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83(1), 34–40 (1951).
[Crossref]

Carminati, R.

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[Crossref] [PubMed]

R. Carminati and J. J. Greffet, “Near-field effects in spatial coherence of thermal sources,” Phys. Rev. Lett. 82(8), 1660–1663 (1999).
[Crossref]

Celanovic, I.

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107(11), 114302 (2011).
[Crossref] [PubMed]

Charalambous, P. G.

P. G. Charalambous, G. G. Maidment, S. A. Kalogirou, and K. Yiakoumetti, “Photovoltaic thermal (PV/T) collectors: A review,” Appl. Therm. Eng. 27(2), 275–286 (2007).
[Crossref]

Chen, G.

A. Narayanaswamy and G. Chen, “Thermal near-field radiative transfer between two spheres,” Phys. Rev. B 77(7), 075125 (2008).
[Crossref]

A. Narayanaswamy and G. Chen, “Surface modes for near field thermophotovoltaics,” Appl. Phys. Lett. 82(20), 3544–3546 (2003).
[Crossref]

Chen, Y. B.

S. Basu, Y. B. Chen, and Z. M. Zhang, “Microscale radiation in thermophotovoltaic devices – a review,” Int. J. Energy Res. 31(6–7), 689–716 (2007).
[Crossref]

Chow, T. T.

T. T. Chow, G. N. Tiwari, and C. Menezo, “Hybrid solar: a review on photovoltaic and thermal power integration,” Int. J. Photoenergy 2012, 1–17 (2012).
[Crossref]

Cortes, C. L.

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
[Crossref]

Cuma, M.

S. Edalatpour, M. Čuma, T. Trueax, R. Backman, and M. Francoeur, “Convergence analysis of the thermal discrete dipole approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(6), 063307 (2015).
[Crossref] [PubMed]

Didari, A.

A. Didari and M. P. Mengüç, “Analysis of near-field radiation transfer within nano-gaps using FDTD method,” J. Quant. Spectrosc. Radiat. Transf. 146, 214–226 (2014).
[Crossref]

Edalatpour, S.

S. Edalatpour and M. Francoeur, “Near-field radiative heat transfer between arbitrarily shaped objects and a surface,” Phys. Rev. B 94(4), 045406 (2016).
[Crossref] [PubMed]

S. Edalatpour, M. Čuma, T. Trueax, R. Backman, and M. Francoeur, “Convergence analysis of the thermal discrete dipole approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(6), 063307 (2015).
[Crossref] [PubMed]

Eisner, M.

Fan, S.

Francoeur, M.

S. Edalatpour and M. Francoeur, “Near-field radiative heat transfer between arbitrarily shaped objects and a surface,” Phys. Rev. B 94(4), 045406 (2016).
[Crossref] [PubMed]

S. Edalatpour, M. Čuma, T. Trueax, R. Backman, and M. Francoeur, “Convergence analysis of the thermal discrete dipole approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(6), 063307 (2015).
[Crossref] [PubMed]

Greffet, J. J.

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[Crossref] [PubMed]

R. Carminati and J. J. Greffet, “Near-field effects in spatial coherence of thermal sources,” Phys. Rev. Lett. 82(8), 1660–1663 (1999).
[Crossref]

Guo, Y.

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

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
[Crossref]

Ilic, O.

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107(11), 114302 (2011).
[Crossref] [PubMed]

Jacob, Z.

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

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
[Crossref]

Jin, W.

A. G. Polimeridis, M. T. H. Reid, W. Jin, S. G. Johnson, J. K. White, and A. W. Rodriguez, “Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries,” Phys. Rev. B 92(13), 134202 (2015).
[Crossref]

Joannopoulos, J. D.

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107(11), 114302 (2011).
[Crossref] [PubMed]

Johnson, S. G.

A. G. Polimeridis, M. T. H. Reid, W. Jin, S. G. Johnson, J. K. White, and A. W. Rodriguez, “Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries,” Phys. Rev. B 92(13), 134202 (2015).
[Crossref]

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer: theory and applications,” Phys. Rev. B 88(5), 054305 (2013).
[Crossref]

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer for arbitrary geometries,” Phys. Rev. B 86(22), 220302 (2012).
[Crossref]

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107(11), 114302 (2011).
[Crossref] [PubMed]

Joulain, K.

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[Crossref] [PubMed]

Kalogirou, S. A.

P. G. Charalambous, G. G. Maidment, S. A. Kalogirou, and K. Yiakoumetti, “Photovoltaic thermal (PV/T) collectors: A review,” Appl. Therm. Eng. 27(2), 275–286 (2007).
[Crossref]

Kattawar, G. W.

Leviatan, Y.

Y. Leviatan, A. Boag, and A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies—Theory and numerical solution,” IEEE Trans. Antenn. Propag. 36(12), 1722–1734 (1988).
[Crossref]

Liu, B.

B. Liu and S. Shen, “Broadband near-field radiative thermal emitter/absorber based on hyperbolic metamaterials: Direct numerical simulation by the Wiener chaos expansion method,” Phys. Rev. B 87(11), 115403 (2013).
[Crossref]

Loomis, J. J.

J. J. Loomis and H. J. Maris, “Theory of heat transfer by evanescent electromagnetic waves,” Phys. Rev. B Condens. Matter 50(24), 18517–18524 (1994).
[Crossref] [PubMed]

Maidment, G. G.

P. G. Charalambous, G. G. Maidment, S. A. Kalogirou, and K. Yiakoumetti, “Photovoltaic thermal (PV/T) collectors: A review,” Appl. Therm. Eng. 27(2), 275–286 (2007).
[Crossref]

Maris, H. J.

J. J. Loomis and H. J. Maris, “Theory of heat transfer by evanescent electromagnetic waves,” Phys. Rev. B Condens. Matter 50(24), 18517–18524 (1994).
[Crossref] [PubMed]

Maslovski, S. I.

S. I. Maslovski, C. R. Simovski, and S. A. Tretyakov, “Overcoming blackbody radiation limit in free space: metamaterial superemitter,” New J. Phys. 18(1), 013034 (2016).
[Crossref]

Menezo, C.

T. T. Chow, G. N. Tiwari, and C. Menezo, “Hybrid solar: a review on photovoltaic and thermal power integration,” Int. J. Photoenergy 2012, 1–17 (2012).
[Crossref]

Mengüç, M. P.

A. Didari and M. P. Mengüç, “Analysis of near-field radiation transfer within nano-gaps using FDTD method,” J. Quant. Spectrosc. Radiat. Transf. 146, 214–226 (2014).
[Crossref]

Messina, R.

S. A. Biehs, M. Tschikin, R. Messina, and P. Ben-Abdallah, “Super-Planckian near-field thermal emission with phonon-polaritonic hyperbolic metamaterials,” Appl. Phys. Lett. 102(13), 131106 (2013).
[Crossref]

R. Messina and M. Antezza, “Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies,” Phys. Rev. A 84(4), 042102 (2011).
[Crossref]

Molesky, S.

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
[Crossref]

Narayanaswamy, A.

A. Narayanaswamy and G. Chen, “Thermal near-field radiative transfer between two spheres,” Phys. Rev. B 77(7), 075125 (2008).
[Crossref]

A. Narayanaswamy and G. Chen, “Surface modes for near field thermophotovoltaics,” Appl. Phys. Lett. 82(20), 3544–3546 (2003).
[Crossref]

Persson, B. N. J.

A. I. Volokitin and B. N. J. Persson, “Resonant photon tunneling enhancement of the radiative heat transfer,” Phys. Rev. B 69(4), 045417 (2004).
[Crossref]

A. I. Volokitin and B. N. J. Persson, “Radiative heat transfer between nanostructures,” Phys. Rev. B 63(20), 205404 (2001).
[Crossref]

Pleijel, A.

A. Pleijel, “On the eigenvalues and eigenfunctions of elastic plates,” Commun. Pure Appl. Math. 3(1), 1–10 (1950).
[Crossref]

Polder, D.

D. Polder and M. Van Hove, “Theory of radiative heat transfer between closely spaced bodies,” Phys. Rev. B 4(10), 3303–3314 (1971).
[Crossref]

Polimeridis, A. G.

A. G. Polimeridis, M. T. H. Reid, W. Jin, S. G. Johnson, J. K. White, and A. W. Rodriguez, “Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries,” Phys. Rev. B 92(13), 134202 (2015).
[Crossref]

Reid, M. T. H.

A. G. Polimeridis, M. T. H. Reid, W. Jin, S. G. Johnson, J. K. White, and A. W. Rodriguez, “Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries,” Phys. Rev. B 92(13), 134202 (2015).
[Crossref]

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer: theory and applications,” Phys. Rev. B 88(5), 054305 (2013).
[Crossref]

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer for arbitrary geometries,” Phys. Rev. B 86(22), 220302 (2012).
[Crossref]

Reiser, A.

A. Reiser and L. Schächter, “Geometric effects on blackbody radiation,” Phys. Rev. A 87(3), 033801 (2013).
[Crossref]

Rephaeli, E.

Rodriguez, A. W.

A. G. Polimeridis, M. T. H. Reid, W. Jin, S. G. Johnson, J. K. White, and A. W. Rodriguez, “Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries,” Phys. Rev. B 92(13), 134202 (2015).
[Crossref]

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer: theory and applications,” Phys. Rev. B 88(5), 054305 (2013).
[Crossref]

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer for arbitrary geometries,” Phys. Rev. B 86(22), 220302 (2012).
[Crossref]

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107(11), 114302 (2011).
[Crossref] [PubMed]

Schächter, L.

A. Reiser and L. Schächter, “Geometric effects on blackbody radiation,” Phys. Rev. A 87(3), 033801 (2013).
[Crossref]

Shchegrov, A. V.

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[Crossref] [PubMed]

Shen, S.

B. Liu and S. Shen, “Broadband near-field radiative thermal emitter/absorber based on hyperbolic metamaterials: Direct numerical simulation by the Wiener chaos expansion method,” Phys. Rev. B 87(11), 115403 (2013).
[Crossref]

Simovski, C. R.

S. I. Maslovski, C. R. Simovski, and S. A. Tretyakov, “Overcoming blackbody radiation limit in free space: metamaterial superemitter,” New J. Phys. 18(1), 013034 (2016).
[Crossref]

Soljacic, M.

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107(11), 114302 (2011).
[Crossref] [PubMed]

Tian, Y.

Y. Tian and C. Y. Zhao, “A review of solar collectors and thermal energy storage in solar thermal applications,” Appl. Energy 104, 538–553 (2013).
[Crossref]

Tiwari, G. N.

T. T. Chow, G. N. Tiwari, and C. Menezo, “Hybrid solar: a review on photovoltaic and thermal power integration,” Int. J. Photoenergy 2012, 1–17 (2012).
[Crossref]

Tretyakov, S. A.

S. I. Maslovski, C. R. Simovski, and S. A. Tretyakov, “Overcoming blackbody radiation limit in free space: metamaterial superemitter,” New J. Phys. 18(1), 013034 (2016).
[Crossref]

Trueax, T.

S. Edalatpour, M. Čuma, T. Trueax, R. Backman, and M. Francoeur, “Convergence analysis of the thermal discrete dipole approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(6), 063307 (2015).
[Crossref] [PubMed]

Tschikin, M.

S. A. Biehs, M. Tschikin, R. Messina, and P. Ben-Abdallah, “Super-Planckian near-field thermal emission with phonon-polaritonic hyperbolic metamaterials,” Appl. Phys. Lett. 102(13), 131106 (2013).
[Crossref]

Van Hove, M.

D. Polder and M. Van Hove, “Theory of radiative heat transfer between closely spaced bodies,” Phys. Rev. B 4(10), 3303–3314 (1971).
[Crossref]

Volokitin, A. I.

A. I. Volokitin and B. N. J. Persson, “Resonant photon tunneling enhancement of the radiative heat transfer,” Phys. Rev. B 69(4), 045417 (2004).
[Crossref]

A. I. Volokitin and B. N. J. Persson, “Radiative heat transfer between nanostructures,” Phys. Rev. B 63(20), 205404 (2001).
[Crossref]

Welton, T. A.

H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83(1), 34–40 (1951).
[Crossref]

Weyl, H.

H. Weyl, “Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung),” Math. Ann. 71(4), 441–479 (1912).
[Crossref]

White, J. K.

A. G. Polimeridis, M. T. H. Reid, W. Jin, S. G. Johnson, J. K. White, and A. W. Rodriguez, “Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries,” Phys. Rev. B 92(13), 134202 (2015).
[Crossref]

Yiakoumetti, K.

P. G. Charalambous, G. G. Maidment, S. A. Kalogirou, and K. Yiakoumetti, “Photovoltaic thermal (PV/T) collectors: A review,” Appl. Therm. Eng. 27(2), 275–286 (2007).
[Crossref]

Zhang, Z. M.

S. Basu, Y. B. Chen, and Z. M. Zhang, “Microscale radiation in thermophotovoltaic devices – a review,” Int. J. Energy Res. 31(6–7), 689–716 (2007).
[Crossref]

Zhao, C. Y.

Y. Tian and C. Y. Zhao, “A review of solar collectors and thermal energy storage in solar thermal applications,” Appl. Energy 104, 538–553 (2013).
[Crossref]

Zondag, H. A.

H. A. Zondag, “Flat-plate PV-Thermal collectors and systems: A review,” Renew. Sustain. Energy Rev. 12(4), 891–959 (2008).
[Crossref]

Appl. Energy (1)

Y. Tian and C. Y. Zhao, “A review of solar collectors and thermal energy storage in solar thermal applications,” Appl. Energy 104, 538–553 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

S. A. Biehs, M. Tschikin, R. Messina, and P. Ben-Abdallah, “Super-Planckian near-field thermal emission with phonon-polaritonic hyperbolic metamaterials,” Appl. Phys. Lett. 102(13), 131106 (2013).
[Crossref]

E. Rephaeli and S. Fan, “Tungsten black absorber for solar light with wide angular operation range,” Appl. Phys. Lett. 92(21), 211107 (2008).
[Crossref]

A. Narayanaswamy and G. Chen, “Surface modes for near field thermophotovoltaics,” Appl. Phys. Lett. 82(20), 3544–3546 (2003).
[Crossref]

Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-Planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101(13), 131106 (2012).
[Crossref]

Appl. Therm. Eng. (1)

P. G. Charalambous, G. G. Maidment, S. A. Kalogirou, and K. Yiakoumetti, “Photovoltaic thermal (PV/T) collectors: A review,” Appl. Therm. Eng. 27(2), 275–286 (2007).
[Crossref]

Commun. Pure Appl. Math. (1)

A. Pleijel, “On the eigenvalues and eigenfunctions of elastic plates,” Commun. Pure Appl. Math. 3(1), 1–10 (1950).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

Y. Leviatan, A. Boag, and A. Boag, “Generalized formulations for electromagnetic scattering from perfectly conducting and homogeneous material bodies—Theory and numerical solution,” IEEE Trans. Antenn. Propag. 36(12), 1722–1734 (1988).
[Crossref]

Int. J. Energy Res. (1)

S. Basu, Y. B. Chen, and Z. M. Zhang, “Microscale radiation in thermophotovoltaic devices – a review,” Int. J. Energy Res. 31(6–7), 689–716 (2007).
[Crossref]

Int. J. Photoenergy (1)

T. T. Chow, G. N. Tiwari, and C. Menezo, “Hybrid solar: a review on photovoltaic and thermal power integration,” Int. J. Photoenergy 2012, 1–17 (2012).
[Crossref]

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

A. Didari and M. P. Mengüç, “Analysis of near-field radiation transfer within nano-gaps using FDTD method,” J. Quant. Spectrosc. Radiat. Transf. 146, 214–226 (2014).
[Crossref]

Math. Ann. (1)

H. Weyl, “Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung),” Math. Ann. 71(4), 441–479 (1912).
[Crossref]

New J. Phys. (1)

S. I. Maslovski, C. R. Simovski, and S. A. Tretyakov, “Overcoming blackbody radiation limit in free space: metamaterial superemitter,” New J. Phys. 18(1), 013034 (2016).
[Crossref]

Opt. Express (2)

Pac. J. Math. (1)

F. H. Brownell, “An Extension of Weyl’s Asymptotic Law for Eigenvalues,” Pac. J. Math. 5(4), 483–499 (1955).
[Crossref]

Phys. Rev. (1)

H. B. Callen and T. A. Welton, “Irreversibility and generalized noise,” Phys. Rev. 83(1), 34–40 (1951).
[Crossref]

Phys. Rev. A (2)

A. Reiser and L. Schächter, “Geometric effects on blackbody radiation,” Phys. Rev. A 87(3), 033801 (2013).
[Crossref]

R. Messina and M. Antezza, “Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies,” Phys. Rev. A 84(4), 042102 (2011).
[Crossref]

Phys. Rev. B (10)

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer: theory and applications,” Phys. Rev. B 88(5), 054305 (2013).
[Crossref]

A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Fluctuating-surface-current formulation of radiative heat transfer for arbitrary geometries,” Phys. Rev. B 86(22), 220302 (2012).
[Crossref]

A. G. Polimeridis, M. T. H. Reid, W. Jin, S. G. Johnson, J. K. White, and A. W. Rodriguez, “Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries,” Phys. Rev. B 92(13), 134202 (2015).
[Crossref]

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

A. I. Volokitin and B. N. J. Persson, “Resonant photon tunneling enhancement of the radiative heat transfer,” Phys. Rev. B 69(4), 045417 (2004).
[Crossref]

A. Narayanaswamy and G. Chen, “Thermal near-field radiative transfer between two spheres,” Phys. Rev. B 77(7), 075125 (2008).
[Crossref]

A. I. Volokitin and B. N. J. Persson, “Radiative heat transfer between nanostructures,” Phys. Rev. B 63(20), 205404 (2001).
[Crossref]

D. Polder and M. Van Hove, “Theory of radiative heat transfer between closely spaced bodies,” Phys. Rev. B 4(10), 3303–3314 (1971).
[Crossref]

B. Liu and S. Shen, “Broadband near-field radiative thermal emitter/absorber based on hyperbolic metamaterials: Direct numerical simulation by the Wiener chaos expansion method,” Phys. Rev. B 87(11), 115403 (2013).
[Crossref]

S. Edalatpour and M. Francoeur, “Near-field radiative heat transfer between arbitrarily shaped objects and a surface,” Phys. Rev. B 94(4), 045406 (2016).
[Crossref] [PubMed]

Phys. Rev. B Condens. Matter (1)

J. J. Loomis and H. J. Maris, “Theory of heat transfer by evanescent electromagnetic waves,” Phys. Rev. B Condens. Matter 50(24), 18517–18524 (1994).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

S. Edalatpour, M. Čuma, T. Trueax, R. Backman, and M. Francoeur, “Convergence analysis of the thermal discrete dipole approximation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 91(6), 063307 (2015).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

A. W. Rodriguez, O. Ilic, P. Bermel, I. Celanovic, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Frequency-selective near-field radiative heat transfer between photonic crystal slabs: a computational approach for arbitrary geometries and materials,” Phys. Rev. Lett. 107(11), 114302 (2011).
[Crossref] [PubMed]

R. Carminati and J. J. Greffet, “Near-field effects in spatial coherence of thermal sources,” Phys. Rev. Lett. 82(8), 1660–1663 (1999).
[Crossref]

A. V. Shchegrov, K. Joulain, R. Carminati, and J. J. Greffet, “Near-field spectral effects due to electromagnetic surface excitations,” Phys. Rev. Lett. 85(7), 1548–1551 (2000).
[Crossref] [PubMed]

Renew. Sustain. Energy Rev. (1)

H. A. Zondag, “Flat-plate PV-Thermal collectors and systems: A review,” Renew. Sustain. Energy Rev. 12(4), 891–959 (2008).
[Crossref]

Other (9)

J. J. Greffet, P. Bouchon, G. Brucoli, E. Sakat, and F. Marquier, “Generalized Kirchhoff law,” arXiv preprint arXiv:1601.00312 (2016).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 1983)

H. P. Baltes and E. R. Hilf, Spectra of Finite Systems (Bibliographisches Institut, 1976).

R. Courant and D. Hilbert, Methods of Mathematical Physics (Wiley, 1989), Chap. VI, Sec. 4.

T. Carleman, in Proceedings of the Eighth Scandinavian Mathematics Congress, Stockholm (Ohlsson, Lund, 1935), p. 34.

L. D. Landau and E. M. Lifshits, Statistical Physics (Pergamon, 1958).

S. M. Rytov, Theory of Electric Fluctuations and Thermal Radiation, Bedford, Massachusetts: Air-Force Cambridge Reseach Center, 1959.

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

R. F. Harrington, Time-Harmonic Electromagnetic Fields (McGraw-Hill, 1961). Chap. 6, Sec. 2.

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Figures (7)

Fig. 1
Fig. 1 Thermal radiation problem setup, a radiating body of temperature T and dielectric coefficient ε= ε j ε emits radiation due to internal fluctuating electrical and magnetic thermal currents J e th and J m th . We place test magnetic and electrical dipoles J e θ , J e ϕ , J m θ , J m ϕ at point R in order to sample the tangential EM field components using the reciprocity theorem using which the radial Poynting vector and consequently the total radiated power can be found.
Fig. 2
Fig. 2 (a) The conceptual setup; a distribution of current densities in a dielectric body generates radiation inside and outside the body. By virtue of the reciprocity theorem, the emitted power distribution is evaluated by calculating the absorbed power from an incident field generated by test dipole (red arrow) located far ( R ) away from the body. (b) For an assessment of Green's function components, the internal sources generating the reflected (external) fields are located on a surface Γ int . (c) In a similar way, external sources located on Γ ext generate the transmitted (internal) fields.
Fig. 3
Fig. 3 (a) Average boundary conditions error vs radius to wavelength ratio for 80,400,800 and 1600 fictitious sources measured at 40000 validation points (b) same as (a) zoomed for 0-1% error range.
Fig. 4
Fig. 4 Simulation results radiating sphere σ= 10 5 [ Ωm ] 1 at T=1000K, compared to analytic calculation and Planck’s Law (a) Spectral power density of a sphere compared to Planck’s Law and to the analytic result at [44] (solid lines). (b) Spectral power of a sphere of 0.8µm at T=3000K with σ= 10 2 , 10 3 , 10 4 , 10 5 [ Ωm ] 1 . (c) Spectral power density of spheres with 0.8µm at T=1000K with ε r =2,8,16,32 demonstrating the resonant behavior of the spectrum; adjacent to the dielectric, the corresponding total power emitted is marked. (d) Total emitted power to total power predicted by Planck’s Law for a sphere of R=0.1,0.8,10,50,100µm as a function of the conductivity.
Fig. 5
Fig. 5 (a) Contours of the total emitted (SB) power normalized to power predicted by Planck’s Law as function of σ and ε r for R=0.8µm, T=1000K. (b) Same as frame (a) for R=20µm, T=1000K.
Fig. 6
Fig. 6 (a) Power spectrum from a hollow sphere for various internal radius . ε r =2,σ= 10 5 [ Ωm ] 1 (b) Power ratio of hollow sphere to full sphere of the same external radius ε r =2,σ= 10 5 [ Ωm ] 1 as a function of the radii ratio (c) Same as (a) but . ε r =2,σ= 5700 5 [ Ωm ] 1 . Note the resonant character of the spectrum. (d) Same as (b) except ε r =2,σ= 5700 5 [ Ωm ] 1 . Note that the power ratio decreases monotonically.
Fig. 7
Fig. 7 (a) Spectral power density of 2 ellipsoids with the same volume and surface area compared to spheres of the same volume and surface area and the Planckian spectra of same spheres (b) Radiation pattern of the ellipsoids (c) Illustration of the ellipsoids in (a,b).

Equations (5)

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J α e ( ω, r ) J β e* ( ω , r ) =Θ( T,ω ) ω ε 0 ε ( ω ) π δ( ω ω )δ( r r ) δ αβ J α m ( ω, r ) J β m* ( ω , r ) =0, J α e ( ω, r ) J β m* ( ω , r ) =0
E α = β ε αβ J β
S ( E th × H test E test × H th ) d s = V ( E th J e test H th J m test + H test J m th E test J e th ) dV
dW dωdΩ = 2 π ω ε 0 ε ( ω ) R 2 Θ( T,ω ) × V d r Re[ ε ω e θ ( r , R ) ε ω m ϕ ( r , R ) ε ω e ϕ ( r , R ) ε ω m ϕ * ( r , R ) ]
{ t ^ (v) [ E inc ( ρ )+ E ext ( ρ ) E int ( ρ ) ]=0 t ^ (v) [ H inc ( ρ )+ H ext ( ρ ) H int ( ρ ) ]=0 v=1,2

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