Abstract

Near-field radiative transfer between two objects can be computed using Rytov’s theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using the dyadic Green’s function of the vector Helmholtz equation. When the two objects are spheres, the dyadic Green’s function can be expanded in a series of vector spherical waves. Based on comparison with the convergence criterion for the case of radiative transfer between two parallel surfaces, we derive a relation for the number of vector spherical waves required for convergence in the case of radiative transfer between two spheres. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to Rmax/d when d/Rmax → 0, where Rmax is the radius of the larger sphere, and d is the smallest gap between the two spheres. This criterion for convergence applies equally well to other near-field electromagnetic scattering problems.

© 2011 Optical Society of America

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2010 (2)

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

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

2009 (5)

S. Shen, A. Narayanaswamy, and G. Chen, “Surface phonon polaritons mediated energy transfer between nanoscale gaps,” Nano Lett. 9, 2909–2913 (2009).
[CrossRef] [PubMed]

A. Narayanaswamy, S. Shen, L. Hu, X. Chen, and G. Chen, “Breakdown of the planck blackbody radiation law at nanoscale breakdown of the planck blackbody radiation law at nanoscale gaps,” Appl. Phys. A 96, 357–362 (2009).
[CrossRef]

E. Rousseau, A. Siria, G. Jourdan, S. Volz, F. Comin, J. Chevrier, and J.-J. Greffet, “Radiative heat transfer at the nanoscale,” Nat. Photonics 3, 514–517 (2009).
[CrossRef]

S. Basu, Z. Zhang, and C. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Energy Res. 33, 1203–1232 (2009).
[CrossRef]

S. Kawata, Y. Inouye, and P. Verma, “Plasmonics for near-field nano-imaging and superlensing,” Nat. Photonics 3, 388–394 (2009).
[CrossRef]

2008 (7)

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy.” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
[CrossRef]

M. Francoeur and M. P. Menguc, “Role of fluctuational electrodynamics in near-field radiative heat transfer,” J. Quant. Spectrosc. Radiat. Transfer 109, 280–293 (2008).
[CrossRef]

A. Kittel, U. Wischnath, J. Welker, O. Huth, F. Ruting, and S. Biehs, “Near-field thermal imaging of nanostructured surfaces,” Appl. Phys. Lett. 93, 193109 (2008).

M. Francoeur, M. Menguc, and R. Vaillon, “Near-field radiative heat transfer enhancement via surface phonon polaritons coupling in thin films,” Appl. Phys. Lett. 93, 043109 (2008).
[CrossRef]

A. Narayanaswamy, S. Shen, and G. Chen, “Near–field radiative heat transfer between a sphere and a substrate,” Phys. Rev. B 78, 115303 (2008).
[CrossRef]

L. Hu, A. Narayanaswamy, X. Chen, and G. Chen, “Near-field thermal radiation between two closely spaced glass plates exceeding plancks blackbody radiation law,” Appl. Phys. Lett. 92, 133106 (2008).
[CrossRef]

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

2007 (1)

V. Yannopapas and N. Vitanov, “Spontaneous emission of a two-level atom placed within clusters of metallic nanoparticles,” J. Phys.: Condens. Matter 19, 096210 (2007).
[CrossRef]

2006 (3)

M. Laroche, R. Carminati, and J.-J. Greffet, “Near-field thermophotovoltaic energy conversion,” J. of Appl. Phys. 100, 063704 (2006).
[CrossRef]

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[CrossRef] [PubMed]

H. Kimura, L. Kolokolova, and I. Mann, “Light scattering by cometary dust numerically simulated with aggregate particles consisting of identical spheres,” Astron. Astrophys. 449, 1243–1254 (2006).
[CrossRef]

2005 (3)

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[CrossRef]

A. Zayats, I. Smolyaninov, and A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131–314 (2005).
[CrossRef]

R. Yang, A. Narayanaswamy, and G. Chen, “Surface-plasmon coupled nonequilibrium thermoelectric refrigerators and power generators,” J. Comput. Theor. Nanos. 2, 75–87 (2005).

2003 (2)

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

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics.” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

2002 (2)

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative transfer at nanometric distances,” Microscale Thermo. Eng. 6, 209–222 (2002).
[CrossRef]

N. A. Gumerov and R. Duraiswami, “Computation of scattering from n spheres using multipole reexpansion,” J. Acoust. Soc. Am. 112, 2688–2701 (2002).
[CrossRef]

1999 (2)

M. Quinten, A. Pack, and R. Wannemacher, “Scattering and extinction of evanescent waves by small particles,” Appl. Phys. B 68, 87–92 (1999).
[CrossRef]

J. B. Pendry, “Radiative exchange of heat between nanostructures,” J. Phys.: Condens. Matter 11, 6621–6633 (1999).
[CrossRef]

1998 (1)

A. Campion and P. Kambhampati, “Surface-enhanced Raman scattering,” Chem. Soc. Rev. 27, 241 (1998).
[CrossRef]

1995 (1)

1993 (1)

W. C. Chew, “Efficient ways to compute the vector addition theorem,” J. Electromagn. Wave 7, 651–665 (1993).
[CrossRef]

1990 (2)

W. C. Chew, “Derivation of the vector addition theorem,” Microw. Opt. Technol. Let. 3, 256–260 (1990).
[CrossRef]

W. Chew, “A derivation of the vector addition theorem,” Microw. Opt. Technol. Let. 3, 256–260 (1990).
[CrossRef]

1986 (1)

U. Durig, D. W. Pohl, and F. Rohner, “Near-field optical-scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

1984 (1)

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

1973 (1)

C. Hargreaves, “Radiative transfer between closely spaced bodies,” Philips Res. Rep. Suppl. 5, 1–80 (1973).

1971 (2)

J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres Part I–multipole expansion and ray-optical solutions” IEEE Trans. Antenn. Propag. AP-19, 378–390 (1971).
[CrossRef]

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

1967 (1)

C. Liang and Y. T. Lo, “Scattering by two spheres,” Radio Sci. 2, 1481 (1967).

1962 (1)

O. Cruzan, “Translational addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

1961 (1)

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

Alemi, A.

R. Ottens, V. Quetschke, S. Wise, A. Alemi, R. Lundock, G. Mueller, D. Reitze, D. Tanner, and B. Whiting, “Near-field radiative heat transfer between macroscopic planar surfaces,” Arxiv preprint arXiv:1103.2389 (2011).

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics.” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Basu, S.

S. Basu, Z. Zhang, and C. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Energy Res. 33, 1203–1232 (2009).
[CrossRef]

Ben-Abdallah, P.

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

Biehs, S.

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

A. Kittel, U. Wischnath, J. Welker, O. Huth, F. Ruting, and S. Biehs, “Near-field thermal imaging of nanostructured surfaces,” Appl. Phys. Lett. 93, 193109 (2008).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1998).

Bruning, J. H.

J. H. Bruning and Y. T. Lo, “Multiple scattering of EM waves by spheres Part I–multipole expansion and ray-optical solutions” IEEE Trans. Antenn. Propag. AP-19, 378–390 (1971).
[CrossRef]

J. H. Bruning and Y. Lo, “Multiple scattering by spheres” Tech. Rep. Antenna Laboratory Report No. 69-5, University of Illinois, Urbana, Illinois (1969).

Campion, A.

A. Campion and P. Kambhampati, “Surface-enhanced Raman scattering,” Chem. Soc. Rev. 27, 241 (1998).
[CrossRef]

Carminati, R.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[CrossRef] [PubMed]

M. Laroche, R. Carminati, and J.-J. Greffet, “Near-field thermophotovoltaic energy conversion,” J. of Appl. Phys. 100, 063704 (2006).
[CrossRef]

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57, 59–112 (2005).
[CrossRef]

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative transfer at nanometric distances,” Microscale Thermo. Eng. 6, 209–222 (2002).
[CrossRef]

Chen, G.

S. Shen, A. Narayanaswamy, and G. Chen, “Surface phonon polaritons mediated energy transfer between nanoscale gaps,” Nano Lett. 9, 2909–2913 (2009).
[CrossRef] [PubMed]

A. Narayanaswamy, S. Shen, L. Hu, X. Chen, and G. Chen, “Breakdown of the planck blackbody radiation law at nanoscale breakdown of the planck blackbody radiation law at nanoscale gaps,” Appl. Phys. A 96, 357–362 (2009).
[CrossRef]

A. Narayanaswamy, S. Shen, and G. Chen, “Near–field radiative heat transfer between a sphere and a substrate,” Phys. Rev. B 78, 115303 (2008).
[CrossRef]

L. Hu, A. Narayanaswamy, X. Chen, and G. Chen, “Near-field thermal radiation between two closely spaced glass plates exceeding plancks blackbody radiation law,” Appl. Phys. Lett. 92, 133106 (2008).
[CrossRef]

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

R. Yang, A. Narayanaswamy, and G. Chen, “Surface-plasmon coupled nonequilibrium thermoelectric refrigerators and power generators,” J. Comput. Theor. Nanos. 2, 75–87 (2005).

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

A. Narayanaswamy and G. Chen, “Direct computation of thermal emission from nanostructures,” Annual Reviews of Heat Transfer (Begell House, 2005), vol. 14, pp. 169–195.

Chen, X.

A. Narayanaswamy, S. Shen, L. Hu, X. Chen, and G. Chen, “Breakdown of the planck blackbody radiation law at nanoscale breakdown of the planck blackbody radiation law at nanoscale gaps,” Appl. Phys. A 96, 357–362 (2009).
[CrossRef]

L. Hu, A. Narayanaswamy, X. Chen, and G. Chen, “Near-field thermal radiation between two closely spaced glass plates exceeding plancks blackbody radiation law,” Appl. Phys. Lett. 92, 133106 (2008).
[CrossRef]

Chen, Y.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[CrossRef] [PubMed]

Chevrier, J.

E. Rousseau, A. Siria, G. Jourdan, S. Volz, F. Comin, J. Chevrier, and J.-J. Greffet, “Radiative heat transfer at the nanoscale,” Nat. Photonics 3, 514–517 (2009).
[CrossRef]

Chew, W.

W. Chew, “A derivation of the vector addition theorem,” Microw. Opt. Technol. Let. 3, 256–260 (1990).
[CrossRef]

W. Chew, E. Michielssen, J. Song, and J. Jin, Fast and efficient algorithms in computational electromagnetics, (Artech House, Inc., 2001).

Chew, W. C.

W. C. Chew, “Efficient ways to compute the vector addition theorem,” J. Electromagn. Wave 7, 651–665 (1993).
[CrossRef]

W. C. Chew, “Derivation of the vector addition theorem,” Microw. Opt. Technol. Let. 3, 256–260 (1990).
[CrossRef]

W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, 1995).

Comin, F.

E. Rousseau, A. Siria, G. Jourdan, S. Volz, F. Comin, J. Chevrier, and J.-J. Greffet, “Radiative heat transfer at the nanoscale,” Nat. Photonics 3, 514–517 (2009).
[CrossRef]

Crane, R.

R. Crane, “Cooperative scattering by dielectric spheres,” Tech. Rep., Lincoln Laboratory, M.I.T, Lexington, MA (1967).

Cruzan, O.

O. Cruzan, “Translational addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

De Wilde, Y.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[CrossRef] [PubMed]

Denk, W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett. 44, 651–653 (1984).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics.” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Dieringer, J. A.

P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced Raman spectroscopy.” Annu. Rev. Anal. Chem. 1, 601–626 (2008).
[CrossRef]

Duraiswami, R.

N. A. Gumerov and R. Duraiswami, “Computation of scattering from n spheres using multipole reexpansion,” J. Acoust. Soc. Am. 112, 2688–2701 (2002).
[CrossRef]

Durig, U.

U. Durig, D. W. Pohl, and F. Rohner, “Near-field optical-scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics.” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Fan, S.

C. Otey and S. Fan, “Exact microscopic theory of electromagnetic heat transfer between a dielectric sphere and plate,” Arxiv preprint arXiv:1103.2668(2011).

Formanek, F.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740–743 (2006).
[CrossRef] [PubMed]

Francoeur, M.

M. Francoeur and M. P. Menguc, “Role of fluctuational electrodynamics in near-field radiative heat transfer,” J. Quant. Spectrosc. Radiat. Transfer 109, 280–293 (2008).
[CrossRef]

M. Francoeur, M. Menguc, and R. Vaillon, “Near-field radiative heat transfer enhancement via surface phonon polaritons coupling in thin films,” Appl. Phys. Lett. 93, 043109 (2008).
[CrossRef]

Fu, C.

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A. Narayanaswamy, S. Shen, L. Hu, X. Chen, and G. Chen, “Breakdown of the planck blackbody radiation law at nanoscale breakdown of the planck blackbody radiation law at nanoscale gaps,” Appl. Phys. A 96, 357–362 (2009).
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A. Narayanaswamy and G. Chen, “Surface modes for near field thermophotovoltaics,” Appl. Phys. Lett. 82, 3544–3546 (2003).
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L. Hu, A. Narayanaswamy, X. Chen, and G. Chen, “Near-field thermal radiation between two closely spaced glass plates exceeding plancks blackbody radiation law,” Appl. Phys. Lett. 92, 133106 (2008).
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M. Francoeur, M. Menguc, and R. Vaillon, “Near-field radiative heat transfer enhancement via surface phonon polaritons coupling in thin films,” Appl. Phys. Lett. 93, 043109 (2008).
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J. B. Pendry, “Radiative exchange of heat between nanostructures,” J. Phys.: Condens. Matter 11, 6621–6633 (1999).
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M. Francoeur and M. P. Menguc, “Role of fluctuational electrodynamics in near-field radiative heat transfer,” J. Quant. Spectrosc. Radiat. Transfer 109, 280–293 (2008).
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Microscale Thermo. Eng. (1)

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative transfer at nanometric distances,” Microscale Thermo. Eng. 6, 209–222 (2002).
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S. Shen, A. Narayanaswamy, and G. Chen, “Surface phonon polaritons mediated energy transfer between nanoscale gaps,” Nano Lett. 9, 2909–2913 (2009).
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E. Rousseau, A. Siria, G. Jourdan, S. Volz, F. Comin, J. Chevrier, and J.-J. Greffet, “Radiative heat transfer at the nanoscale,” Nat. Photonics 3, 514–517 (2009).
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