Abstract

Near-field radiative heat transfer between isotropic, dielectric-based metamaterials is analyzed. A potassium bromide host medium comprised of silicon carbide (SiC) spheres with a volume filling fraction of 0.4 is considered for the metamaterial. The relative electric permittivity and relative magnetic permeability of the metamaterial are modeled via the Clausius-Mossotti relations linking the macroscopic response of the medium with the polarizabilities of the spheres. We show for the first time that electric and magnetic surface polariton (SP) mediated near-field radiative heat transfer occurs between dielectric-based structures. Magnetic SPs, existing in TE polarization, are physically due to strong magnetic dipole resonances of the spheres. We find that spherical inclusions with radii of 1 μm (or greater) are needed in order to induce SPs in TE polarization. On the other hand, electric SPs existing in TM polarization are generated by surface modes of the spheres, and are thus almost insensitive to the size of the inclusions. We estimate that the total heat flux around SP resonance for the metamaterial comprised of SiC spheres with radii of 1 μm is about 35% greater than the flux predicted between two bulks of SiC, where only surface phonon-polaritons in TM polarization are excited. The results presented in this work show that the near-field thermal spectrum can be engineered via dielectric-based metamaterials, which is crucial in many emerging technologies, such as in nanoscale-gap thermophotovoltaic power generation.

© 2011 OSA

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2011 (6)

Z. Zheng and Y. Xuan, “Theory of near-field radiative heat transfer for stratified magnetic media,” Int. J. Heat Mass Tran. 54(5-6), 1101–1110 (2011).
[CrossRef]

Z. Zheng and Y. Xuan, “Near-field radiative heat transfer between general materials and metamaterials,” Chin. Sci. Bull. 56(22), 2312–2319 (2011).
[CrossRef]

M. Francoeur, R. Vaillon, and M. P. Mengüç, “Thermal impacts on the performance of nanoscale-gap thermophotovoltaic power generators,” IEEE Trans. Energ. Convers. 26(2), 686–698 (2011).
[CrossRef]

S. Basu and M. Francoeur, “Near-field radiative transfer based thermal rectification using doped silicon,” Appl. Phys. Lett. 98(11), 113106 (2011).
[CrossRef]

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

L. P. Wang and Z. M. Zhang, “Phonon-mediated magnetic polaritons in the infrared region,” Opt. Express 19(S2Suppl 2), A126–A135 (2011).
[CrossRef] [PubMed]

2010 (8)

R.-L. Chern and X.-X. Liu, “Effective parameters and quasi-static resonances for periodic arrays of dielectric spheres,” J. Opt. Soc. Am. B 27(3), 488–497 (2010).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coupled magnetic dipole resonances in sub-wavelength dielectric particle clusters,” J. Opt. Soc. Am. B 27(5), 1083–1091 (2010).
[CrossRef]

L.-G. Wang, G.-X. Li, and S.-Y. Zhu, “Thermal emission from layered structures containing a negative-zero-positive index metamaterial,” Phys. Rev. B 81(7), 073105 (2010).
[CrossRef]

M. Francoeur, M. P. Mengüç, and R. Vaillon, “Spectral tuning of near-field radiative heat flux between two silicon carbide films,” J. Phys. D Appl. Phys. 43(7), 075501 (2010).
[CrossRef]

E. Rousseau, M. Laroche, and J.-J. Greffet, “Radiative heat transfer at nanoscale: Closed-form expression for silicon at different doping levels,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1005–1014 (2010).
[CrossRef]

C. R. Otey, W. T. Lau, and S. Fan, “Thermal rectification through vacuum,” Phys. Rev. Lett. 104(15), 154301 (2010).
[CrossRef] [PubMed]

K. Joulain, J. Drevillon, and P. Ben-Abdallah, “Noncontact heat transfer between two metamaterials,” Phys. Rev. B 81(16), 165119 (2010).
[CrossRef]

S. Basu, B. J. Lee, and Z. M. Zhang, “Near-field radiation calculated with an improved dielectric function model for doped silicon,” J. Heat Transfer 132(2), 023302 (2010).
[CrossRef]

2009 (7)

S. Basu, Z. M. Zhang, and C. J. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Energy Res. 33(13), 1203–1232 (2009).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79(7), 073103 (2009).
[CrossRef]

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).
[CrossRef]

M. Francoeur, M. P. Mengüç, and R. Vaillon, “Solution of near-field thermal radiation in one-dimensional layered media using dyadic Green’s function and the scattering matrix method,” J. Quant. Spectrosc. Radiat. Transf. 110(18), 2002–2018 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79(4), 045131 (2009).
[CrossRef]

C. J. Fu and Z. M. Zhang, “Thermal radiative properties of metamaterials and other nanostructured materials: A review,” Front. Energy Power Eng. China 3(1), 11–26 (2009).
[CrossRef]

2008 (4)

C. J. Fu and Z. M. Zhang, “Further investigation of coherent thermal emission from single negative materials,” Nanosc. Microsc. Therm. 12(1), 83–97 (2008).
[CrossRef]

M. Francoeur and M. P. Mengüç, “Role of fluctuational electrodynamics in near-field radiative heat transfer,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 280–293 (2008).
[CrossRef]

B. J. Lee, L. P. Wang, and Z. M. Zhang, “Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film,” Opt. Express 16(15), 11328–11336 (2008).
[CrossRef] [PubMed]

K. Park, S. Basu, W. P. King, and Z. M. Zhang, “Performance analysis of near-field thermophotovoltaic devices considering absorption distribution,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 305–316 (2008).
[CrossRef]

2007 (4)

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99(10), 107401 (2007).
[CrossRef] [PubMed]

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

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
[CrossRef]

F. F. de Medeiros, E. L. Albuquerque, M. S. Vasconcelos, and P. W. Mauriz, “Thermal radiation in quasiperiodic photonic crystals with negative refractive index,” J. Phys. Condens. Matter 19(49), 496212 (2007).
[CrossRef]

2006 (6)

J. Skaar, “On resolving the refractive index and the wave vector,” Opt. Lett. 31(22), 3372–3374 (2006).
[CrossRef] [PubMed]

M. Maksimović and Z. Jakšić, “Emittance and absorptance tailoring by negative refractive index metamaterial-based Cantor multilayers,” J. Opt. A-Pure Appl. Opt. 8, 355–362 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73(4), 045105 (2006).
[CrossRef]

M. Laroche, R. Carminati, and J.-J. Greffet, “Near-field thermophotovoltaic energy conversion,” J. Appl. Phys. 100(6), 063704 (2006).
[CrossRef]

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
[CrossRef] [PubMed]

2005 (5)

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(3-4), 59–112 (2005).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72(19), 193103 (2005).
[CrossRef]

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17(25), 3717–3734 (2005).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

C. J. Fu, Z. M. Zhang, and D. B. Tanner, “Planar heterogeneous structures for coherent emission of radiation,” Opt. Lett. 30(14), 1873–1875 (2005).
[CrossRef] [PubMed]

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

2003 (2)

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
[CrossRef]

S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225(4-6), 233–240 (2003).
[CrossRef]

2002 (3)

S. O’Brien and J. B. Pendry, “Photonics band-gap effects and magnetic activity in dielectric composites,” J. Phys. Condens. Matter 14(15), 4035–4044 (2002).
[CrossRef]

M. D. Whale and E. G. Cravalho, “Modeling and performance of microscale thermophotovoltaic energy conversion devices,” IEEE Trans. Energ. Convers. 17(1), 130–142 (2002).
[CrossRef]

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative heat transfer at nanometric distances,” Microscale Thermophys. Eng. 6(3), 209–222 (2002).
[CrossRef]

2001 (2)

R. S. DiMatteo, P. Greiff, S. L. Finberg, K. A. Young-Waithe, H. K. H. Choy, M. M. Masaki, and C. G. Fonstad, “Enhanced photogeneration of carriers in a semiconductor via coupling across a nonisothermal nanoscale vacuum gap,” Appl. Phys. Lett. 79(12), 1894–1896 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000 (3)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277(1), 61–64 (2000).
[CrossRef]

1994 (1)

L.-W. Li, P.-S. Kooi, M.-S. Leong, and T.-S. Yeo, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE T. Microw. Theory 42(12), 2302–2310 (1994).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

1947 (1)

L. Lewin, “The electrical constants of a material loaded with spherical particles,” Proc. Inst. Electr. Eng. 94, 65–68 (1947).

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coupled magnetic dipole resonances in sub-wavelength dielectric particle clusters,” J. Opt. Soc. Am. B 27(5), 1083–1091 (2010).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79(7), 073103 (2009).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73(4), 045105 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72(19), 193103 (2005).
[CrossRef]

Albuquerque, E. L.

F. F. de Medeiros, E. L. Albuquerque, M. S. Vasconcelos, and P. W. Mauriz, “Thermal radiation in quasiperiodic photonic crystals with negative refractive index,” J. Phys. Condens. Matter 19(49), 496212 (2007).
[CrossRef]

Avitzour, Y.

Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79(4), 045131 (2009).
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Baker-Jarvis, J.

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
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J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
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S. Basu and M. Francoeur, “Near-field radiative transfer based thermal rectification using doped silicon,” Appl. Phys. Lett. 98(11), 113106 (2011).
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S. Basu, B. J. Lee, and Z. M. Zhang, “Near-field radiation calculated with an improved dielectric function model for doped silicon,” J. Heat Transfer 132(2), 023302 (2010).
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S. Basu, Z. M. Zhang, and C. J. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Energy Res. 33(13), 1203–1232 (2009).
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K. Park, S. Basu, W. P. King, and Z. M. Zhang, “Performance analysis of near-field thermophotovoltaic devices considering absorption distribution,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 305–316 (2008).
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K. Joulain, J. Drevillon, and P. Ben-Abdallah, “Noncontact heat transfer between two metamaterials,” Phys. Rev. B 81(16), 165119 (2010).
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J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99(10), 107401 (2007).
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W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
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Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
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M. Laroche, R. Carminati, and J.-J. Greffet, “Near-field thermophotovoltaic energy conversion,” J. Appl. Phys. 100(6), 063704 (2006).
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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(3-4), 59–112 (2005).
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J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative heat transfer at nanometric distances,” Microscale Thermophys. Eng. 6(3), 209–222 (2002).
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M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79(7), 073103 (2009).
[CrossRef]

Chen, Y.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
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Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
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R. S. DiMatteo, P. Greiff, S. L. Finberg, K. A. Young-Waithe, H. K. H. Choy, M. M. Masaki, and C. G. Fonstad, “Enhanced photogeneration of carriers in a semiconductor via coupling across a nonisothermal nanoscale vacuum gap,” Appl. Phys. Lett. 79(12), 1894–1896 (2001).
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S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225(4-6), 233–240 (2003).
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F. F. de Medeiros, E. L. Albuquerque, M. S. Vasconcelos, and P. W. Mauriz, “Thermal radiation in quasiperiodic photonic crystals with negative refractive index,” J. Phys. Condens. Matter 19(49), 496212 (2007).
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Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
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R. S. DiMatteo, P. Greiff, S. L. Finberg, K. A. Young-Waithe, H. K. H. Choy, M. M. Masaki, and C. G. Fonstad, “Enhanced photogeneration of carriers in a semiconductor via coupling across a nonisothermal nanoscale vacuum gap,” Appl. Phys. Lett. 79(12), 1894–1896 (2001).
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K. Joulain, J. Drevillon, and P. Ben-Abdallah, “Noncontact heat transfer between two metamaterials,” Phys. Rev. B 81(16), 165119 (2010).
[CrossRef]

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C. R. Otey, W. T. Lau, and S. Fan, “Thermal rectification through vacuum,” Phys. Rev. Lett. 104(15), 154301 (2010).
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N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
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S. Basu and M. Francoeur, “Near-field radiative transfer based thermal rectification using doped silicon,” Appl. Phys. Lett. 98(11), 113106 (2011).
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M. Francoeur, R. Vaillon, and M. P. Mengüç, “Thermal impacts on the performance of nanoscale-gap thermophotovoltaic power generators,” IEEE Trans. Energ. Convers. 26(2), 686–698 (2011).
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M. Francoeur, M. P. Mengüç, and R. Vaillon, “Spectral tuning of near-field radiative heat flux between two silicon carbide films,” J. Phys. D Appl. Phys. 43(7), 075501 (2010).
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M. Francoeur, M. P. Mengüç, and R. Vaillon, “Solution of near-field thermal radiation in one-dimensional layered media using dyadic Green’s function and the scattering matrix method,” J. Quant. Spectrosc. Radiat. Transf. 110(18), 2002–2018 (2009).
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M. Francoeur and M. P. Mengüç, “Role of fluctuational electrodynamics in near-field radiative heat transfer,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 280–293 (2008).
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S. Basu, Z. M. Zhang, and C. J. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Energy Res. 33(13), 1203–1232 (2009).
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E. Rousseau, M. Laroche, and J.-J. Greffet, “Radiative heat transfer at nanoscale: Closed-form expression for silicon at different doping levels,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1005–1014 (2010).
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Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
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M. Laroche, R. Carminati, and J.-J. Greffet, “Near-field thermophotovoltaic energy conversion,” J. Appl. Phys. 100(6), 063704 (2006).
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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(3-4), 59–112 (2005).
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J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative heat transfer at nanometric distances,” Microscale Thermophys. Eng. 6(3), 209–222 (2002).
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R. S. DiMatteo, P. Greiff, S. L. Finberg, K. A. Young-Waithe, H. K. H. Choy, M. M. Masaki, and C. G. Fonstad, “Enhanced photogeneration of carriers in a semiconductor via coupling across a nonisothermal nanoscale vacuum gap,” Appl. Phys. Lett. 79(12), 1894–1896 (2001).
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C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
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M. Maksimović and Z. Jakšić, “Emittance and absorptance tailoring by negative refractive index metamaterial-based Cantor multilayers,” J. Opt. A-Pure Appl. Opt. 8, 355–362 (2006).
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K. Joulain, J. Drevillon, and P. Ben-Abdallah, “Noncontact heat transfer between two metamaterials,” Phys. Rev. B 81(16), 165119 (2010).
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Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
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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(3-4), 59–112 (2005).
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J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative heat transfer at nanometric distances,” Microscale Thermophys. Eng. 6(3), 209–222 (2002).
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C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
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W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
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K. Park, S. Basu, W. P. King, and Z. M. Zhang, “Performance analysis of near-field thermophotovoltaic devices considering absorption distribution,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 305–316 (2008).
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L.-W. Li, P.-S. Kooi, M.-S. Leong, and T.-S. Yeo, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE T. Microw. Theory 42(12), 2302–2310 (1994).
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C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
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E. Rousseau, M. Laroche, and J.-J. Greffet, “Radiative heat transfer at nanoscale: Closed-form expression for silicon at different doping levels,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1005–1014 (2010).
[CrossRef]

M. Laroche, R. Carminati, and J.-J. Greffet, “Near-field thermophotovoltaic energy conversion,” J. Appl. Phys. 100(6), 063704 (2006).
[CrossRef]

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C. R. Otey, W. T. Lau, and S. Fan, “Thermal rectification through vacuum,” Phys. Rev. Lett. 104(15), 154301 (2010).
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S. Basu, B. J. Lee, and Z. M. Zhang, “Near-field radiation calculated with an improved dielectric function model for doped silicon,” J. Heat Transfer 132(2), 023302 (2010).
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B. J. Lee, L. P. Wang, and Z. M. Zhang, “Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film,” Opt. Express 16(15), 11328–11336 (2008).
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N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
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Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
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L.-W. Li, P.-S. Kooi, M.-S. Leong, and T.-S. Yeo, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE T. Microw. Theory 42(12), 2302–2310 (1994).
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J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
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L.-W. Li, P.-S. Kooi, M.-S. Leong, and T.-S. Yeo, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE T. Microw. Theory 42(12), 2302–2310 (1994).
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M. Maksimović and Z. Jakšić, “Emittance and absorptance tailoring by negative refractive index metamaterial-based Cantor multilayers,” J. Opt. A-Pure Appl. Opt. 8, 355–362 (2006).
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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(3-4), 59–112 (2005).
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R. S. DiMatteo, P. Greiff, S. L. Finberg, K. A. Young-Waithe, H. K. H. Choy, M. M. Masaki, and C. G. Fonstad, “Enhanced photogeneration of carriers in a semiconductor via coupling across a nonisothermal nanoscale vacuum gap,” Appl. Phys. Lett. 79(12), 1894–1896 (2001).
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J. A. Mason, S. Smith, and D. Wasserman, “Strong absorption and selective thermal emission from a midinfrared metamaterial,” Appl. Phys. Lett. 98(24), 241105 (2011).
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F. F. de Medeiros, E. L. Albuquerque, M. S. Vasconcelos, and P. W. Mauriz, “Thermal radiation in quasiperiodic photonic crystals with negative refractive index,” J. Phys. Condens. Matter 19(49), 496212 (2007).
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Mengüç, M. P.

M. Francoeur, R. Vaillon, and M. P. Mengüç, “Thermal impacts on the performance of nanoscale-gap thermophotovoltaic power generators,” IEEE Trans. Energ. Convers. 26(2), 686–698 (2011).
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M. Francoeur, M. P. Mengüç, and R. Vaillon, “Spectral tuning of near-field radiative heat flux between two silicon carbide films,” J. Phys. D Appl. Phys. 43(7), 075501 (2010).
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M. Francoeur, M. P. Mengüç, and R. Vaillon, “Solution of near-field thermal radiation in one-dimensional layered media using dyadic Green’s function and the scattering matrix method,” J. Quant. Spectrosc. Radiat. Transf. 110(18), 2002–2018 (2009).
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M. Francoeur and M. P. Mengüç, “Role of fluctuational electrodynamics in near-field radiative heat transfer,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 280–293 (2008).
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M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coupled magnetic dipole resonances in sub-wavelength dielectric particle clusters,” J. Opt. Soc. Am. B 27(5), 1083–1091 (2010).
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M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79(7), 073103 (2009).
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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(3-4), 59–112 (2005).
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J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative heat transfer at nanometric distances,” Microscale Thermophys. Eng. 6(3), 209–222 (2002).
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D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
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S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225(4-6), 233–240 (2003).
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M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79(7), 073103 (2009).
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D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
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K. Park, S. Basu, W. P. King, and Z. M. Zhang, “Performance analysis of near-field thermophotovoltaic devices considering absorption distribution,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 305–316 (2008).
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[CrossRef]

Skaar, J.

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Smith, S.

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

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Tanner, D. B.

Taubner, T.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99(10), 107401 (2007).
[CrossRef] [PubMed]

Urzhumov, Y. A.

Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79(4), 045131 (2009).
[CrossRef]

Vaillon, R.

M. Francoeur, R. Vaillon, and M. P. Mengüç, “Thermal impacts on the performance of nanoscale-gap thermophotovoltaic power generators,” IEEE Trans. Energ. Convers. 26(2), 686–698 (2011).
[CrossRef]

M. Francoeur, M. P. Mengüç, and R. Vaillon, “Spectral tuning of near-field radiative heat flux between two silicon carbide films,” J. Phys. D Appl. Phys. 43(7), 075501 (2010).
[CrossRef]

M. Francoeur, M. P. Mengüç, and R. Vaillon, “Solution of near-field thermal radiation in one-dimensional layered media using dyadic Green’s function and the scattering matrix method,” J. Quant. Spectrosc. Radiat. Transf. 110(18), 2002–2018 (2009).
[CrossRef]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Vasconcelos, M. S.

F. F. de Medeiros, E. L. Albuquerque, M. S. Vasconcelos, and P. W. Mauriz, “Thermal radiation in quasiperiodic photonic crystals with negative refractive index,” J. Phys. Condens. Matter 19(49), 496212 (2007).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10(4), 509–514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Wang, L. P.

Wang, L.-G.

L.-G. Wang, G.-X. Li, and S.-Y. Zhu, “Thermal emission from layered structures containing a negative-zero-positive index metamaterial,” Phys. Rev. B 81(7), 073105 (2010).
[CrossRef]

Wasserman, D.

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

Whale, M. D.

M. D. Whale and E. G. Cravalho, “Modeling and performance of microscale thermophotovoltaic energy conversion devices,” IEEE Trans. Energ. Convers. 17(1), 130–142 (2002).
[CrossRef]

Wheeler, M. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coupled magnetic dipole resonances in sub-wavelength dielectric particle clusters,” J. Opt. Soc. Am. B 27(5), 1083–1091 (2010).
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M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79(7), 073103 (2009).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73(4), 045105 (2006).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72(19), 193103 (2005).
[CrossRef]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

Xuan, Y.

Z. Zheng and Y. Xuan, “Near-field radiative heat transfer between general materials and metamaterials,” Chin. Sci. Bull. 56(22), 2312–2319 (2011).
[CrossRef]

Z. Zheng and Y. Xuan, “Theory of near-field radiative heat transfer for stratified magnetic media,” Int. J. Heat Mass Tran. 54(5-6), 1101–1110 (2011).
[CrossRef]

Yannopapas, V.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17(25), 3717–3734 (2005).
[CrossRef] [PubMed]

Yeo, T.-S.

L.-W. Li, P.-S. Kooi, M.-S. Leong, and T.-S. Yeo, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE T. Microw. Theory 42(12), 2302–2310 (1994).
[CrossRef]

Young-Waithe, K. A.

R. S. DiMatteo, P. Greiff, S. L. Finberg, K. A. Young-Waithe, H. K. H. Choy, M. M. Masaki, and C. G. Fonstad, “Enhanced photogeneration of carriers in a semiconductor via coupling across a nonisothermal nanoscale vacuum gap,” Appl. Phys. Lett. 79(12), 1894–1896 (2001).
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Zakhidov, A. A.

S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225(4-6), 233–240 (2003).
[CrossRef]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

Zhang, F.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).
[CrossRef]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
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L. P. Wang and Z. M. Zhang, “Phonon-mediated magnetic polaritons in the infrared region,” Opt. Express 19(S2Suppl 2), A126–A135 (2011).
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S. Basu, B. J. Lee, and Z. M. Zhang, “Near-field radiation calculated with an improved dielectric function model for doped silicon,” J. Heat Transfer 132(2), 023302 (2010).
[CrossRef]

C. J. Fu and Z. M. Zhang, “Thermal radiative properties of metamaterials and other nanostructured materials: A review,” Front. Energy Power Eng. China 3(1), 11–26 (2009).
[CrossRef]

S. Basu, Z. M. Zhang, and C. J. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Energy Res. 33(13), 1203–1232 (2009).
[CrossRef]

K. Park, S. Basu, W. P. King, and Z. M. Zhang, “Performance analysis of near-field thermophotovoltaic devices considering absorption distribution,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 305–316 (2008).
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B. J. Lee, L. P. Wang, and Z. M. Zhang, “Coherent thermal emission by excitation of magnetic polaritons between periodic strips and a metallic film,” Opt. Express 16(15), 11328–11336 (2008).
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C. J. Fu and Z. M. Zhang, “Further investigation of coherent thermal emission from single negative materials,” Nanosc. Microsc. Therm. 12(1), 83–97 (2008).
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Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).
[CrossRef]

Zheng, Z.

Z. Zheng and Y. Xuan, “Near-field radiative heat transfer between general materials and metamaterials,” Chin. Sci. Bull. 56(22), 2312–2319 (2011).
[CrossRef]

Z. Zheng and Y. Xuan, “Theory of near-field radiative heat transfer for stratified magnetic media,” Int. J. Heat Mass Tran. 54(5-6), 1101–1110 (2011).
[CrossRef]

Zhou, J.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).
[CrossRef]

Zhu, S.-Y.

L.-G. Wang, G.-X. Li, and S.-Y. Zhu, “Thermal emission from layered structures containing a negative-zero-positive index metamaterial,” Phys. Rev. B 81(7), 073105 (2010).
[CrossRef]

Zia, R.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99(10), 107401 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

R. S. DiMatteo, P. Greiff, S. L. Finberg, K. A. Young-Waithe, H. K. H. Choy, M. M. Masaki, and C. G. Fonstad, “Enhanced photogeneration of carriers in a semiconductor via coupling across a nonisothermal nanoscale vacuum gap,” Appl. Phys. Lett. 79(12), 1894–1896 (2001).
[CrossRef]

S. Basu and M. Francoeur, “Near-field radiative transfer based thermal rectification using doped silicon,” Appl. Phys. Lett. 98(11), 113106 (2011).
[CrossRef]

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

Chin. Sci. Bull. (1)

Z. Zheng and Y. Xuan, “Near-field radiative heat transfer between general materials and metamaterials,” Chin. Sci. Bull. 56(22), 2312–2319 (2011).
[CrossRef]

Front. Energy Power Eng. China (1)

C. J. Fu and Z. M. Zhang, “Thermal radiative properties of metamaterials and other nanostructured materials: A review,” Front. Energy Power Eng. China 3(1), 11–26 (2009).
[CrossRef]

IEEE T. Microw. Theory (1)

L.-W. Li, P.-S. Kooi, M.-S. Leong, and T.-S. Yeo, “Electromagnetic dyadic Green’s function in spherically multilayered media,” IEEE T. Microw. Theory 42(12), 2302–2310 (1994).
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IEEE Trans. Antenn. Propag. (1)

C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antenn. Propag. 51(10), 2596–2603 (2003).
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IEEE Trans. Energ. Convers. (2)

M. Francoeur, R. Vaillon, and M. P. Mengüç, “Thermal impacts on the performance of nanoscale-gap thermophotovoltaic power generators,” IEEE Trans. Energ. Convers. 26(2), 686–698 (2011).
[CrossRef]

M. D. Whale and E. G. Cravalho, “Modeling and performance of microscale thermophotovoltaic energy conversion devices,” IEEE Trans. Energ. Convers. 17(1), 130–142 (2002).
[CrossRef]

Int. J. Energy Res. (1)

S. Basu, Z. M. Zhang, and C. J. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Energy Res. 33(13), 1203–1232 (2009).
[CrossRef]

Int. J. Heat Mass Tran. (1)

Z. Zheng and Y. Xuan, “Theory of near-field radiative heat transfer for stratified magnetic media,” Int. J. Heat Mass Tran. 54(5-6), 1101–1110 (2011).
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M. Laroche, R. Carminati, and J.-J. Greffet, “Near-field thermophotovoltaic energy conversion,” J. Appl. Phys. 100(6), 063704 (2006).
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S. Basu, B. J. Lee, and Z. M. Zhang, “Near-field radiation calculated with an improved dielectric function model for doped silicon,” J. Heat Transfer 132(2), 023302 (2010).
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F. F. de Medeiros, E. L. Albuquerque, M. S. Vasconcelos, and P. W. Mauriz, “Thermal radiation in quasiperiodic photonic crystals with negative refractive index,” J. Phys. Condens. Matter 19(49), 496212 (2007).
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V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17(25), 3717–3734 (2005).
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M. Francoeur, M. P. Mengüç, and R. Vaillon, “Spectral tuning of near-field radiative heat flux between two silicon carbide films,” J. Phys. D Appl. Phys. 43(7), 075501 (2010).
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J. Quant. Spectrosc. Radiat. Transf. (4)

M. Francoeur, M. P. Mengüç, and R. Vaillon, “Solution of near-field thermal radiation in one-dimensional layered media using dyadic Green’s function and the scattering matrix method,” J. Quant. Spectrosc. Radiat. Transf. 110(18), 2002–2018 (2009).
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M. Francoeur and M. P. Mengüç, “Role of fluctuational electrodynamics in near-field radiative heat transfer,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 280–293 (2008).
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K. Park, S. Basu, W. P. King, and Z. M. Zhang, “Performance analysis of near-field thermophotovoltaic devices considering absorption distribution,” J. Quant. Spectrosc. Radiat. Transf. 109(2), 305–316 (2008).
[CrossRef]

Mater. Today (1)

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Mater. Today 12(12), 60–69 (2009).
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Microscale Thermophys. Eng. (1)

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Enhanced radiative heat transfer at nanometric distances,” Microscale Thermophys. Eng. 6(3), 209–222 (2002).
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Nanosc. Microsc. Therm. (1)

C. J. Fu and Z. M. Zhang, “Further investigation of coherent thermal emission from single negative materials,” Nanosc. Microsc. Therm. 12(1), 83–97 (2008).
[CrossRef]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8(7), 568–571 (2009).
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Nat. Photonics (2)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007).
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V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
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Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P.-A. Lemoine, K. Joulain, J.-P. Mulet, Y. Chen, and J.-J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444(7120), 740–743 (2006).
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Opt. Commun. (1)

S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225(4-6), 233–240 (2003).
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Y. Avitzour, Y. A. Urzhumov, and G. Shvets, “Wide-angle infrared absorber based on a negative-index plasmonic metamaterial,” Phys. Rev. B 79(4), 045131 (2009).
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L.-G. Wang, G.-X. Li, and S.-Y. Zhu, “Thermal emission from layered structures containing a negative-zero-positive index metamaterial,” Phys. Rev. B 81(7), 073105 (2010).
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K. Joulain, J. Drevillon, and P. Ben-Abdallah, “Noncontact heat transfer between two metamaterials,” Phys. Rev. B 81(16), 165119 (2010).
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M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72(19), 193103 (2005).
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M. S. Wheeler, J. S. Aitchison, J. I. L. Chen, G. A. Ozin, and M. Mojahedi, “Infrared magnetic response in a random silicon carbide micropowder,” Phys. Rev. B 79(7), 073103 (2009).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73(4), 045105 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99(10), 107401 (2007).
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J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
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D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
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R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
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D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
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Figures (5)

Fig. 1
Fig. 1

Schematic representation of the problem under consideration: two planar half-spaces maintained at temperatures T 0 and T 2 and separated by a vacuum gap of thickness d are exchanging thermal radiation.

Fig. 2
Fig. 2

Real part of the refractive index and sum of the phases of the relative permittivity and permeability of the metamaterial for rs = 1 μm, nh = 1.5 and f = 0.4.

Fig. 3
Fig. 3

Monochromatic radiative heat flux between two metamaterials made of SiC spheres (rs = 1 μm, nh = 1.5, f = 0.4) separated by a vacuum gap of thickness d. The near-field profiles are compared with far-field and blackbody predictions.

Fig. 4
Fig. 4

(a) Real part of the relative electric permittivity and magnetic permeability of the metamaterial for rs = 1 μm, nh = 1.5 and f = 0.4. (b) Comparison between the TM and TE evanescent components of the radiative heat flux for the case shown in Fig. 3 when d = 10 nm.

Fig. 5
Fig. 5

(a) Magnitude of the Mie coefficients a 1 and b 1 for SiC spheres of radii rs of 600 nm, 800 nm and 1 μm in a host medium with nh = 1.5. (b) Monochromatic radiative heat flux between two metamaterials made of SiC spheres (rs = 600 nm, 800 nm and 1 μm, nh = 1.5, f = 0.4) separated by a 10 nm thick vacuum gap. The profiles are compared with the predictions obtained between two SiC bulk materials.

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

E ( r , ω ) = i ω μ μ v V G ¯ ¯ E e ( r , r , ω ) J r , e ( r , ω ) d V V G ¯ ¯ E m ( r , r , ω ) J r , m ( r , ω ) d V
H ( r , ω ) = V G ¯ ¯ H e ( r , r , ω ) J r , e ( r , ω ) d V + i ω ε ε v V G ¯ ¯ H m ( r , r , ω ) J r , m ( r , ω ) d V
E i H j * = i ω μ μ v V d V V d V G i α E e ( r , r , ω ) G j β H e * ( r , r , ω ) J α r , e ( r , ω ) J β r , e * ( r , ω )                                       + i ω ε ε v V d V V d V G i α E m ( r , r , ω ) G j β H m * ( r , r , ω ) J α r , m ( r , ω ) J β r , m * ( r , ω )                                       + k v 2 ε μ V d V V d V G i α E e ( r , r , ω ) G j β H m * ( r , r , ω ) J α r , e ( r , ω ) J β r , m * ( r , ω )                                       V d V V d V G i α E m ( r , r , ω ) G j β H e * ( r , r , ω ) J α r , m ( r , ω ) J β r , e * ( r , ω )
J α r , e ( r , ω ) J β r , e * ( r , ω ) = ω ε v ε π Θ ( ω , T ) δ ( r r ) δ α β
J α r , m ( r , ω ) J β r , m * ( r , ω ) = ω μ v μ π Θ ( ω , T ) δ ( r r ) δ α β
J α r , e ( r , ω ) J β r , m * ( r , ω ) = J α r , m ( r , ω ) J β r , e * ( r , ω ) = 0
q ω ( r ) = S z ( r , ω ) = 2 k v 2 Θ ( ω , T ) π Re { i μ ε V d V [ G x α E e ( r , r , ω ) G y α H e * ( r , r , ω ) G y α E e ( r , r , ω ) G x α H e * ( r , r , ω ) ] + i ε μ V d V [ G x α E m ( r , r , ω ) G y α H m * ( r , r , ω ) G y α E m ( r , r , ω ) G x α H m * ( r , r , ω ) ] }
q ω , 02 = Θ ( ω , T 0 ) Θ ( ω , T 2 ) π 2                                                           × γ = T E , T M [ 0 k v k ρ d k ρ ( 1 | r 10 γ | 2 ) ( 1 | r 12 γ | 2 ) 4 | 1 r 10 γ r 12 γ e 2 i k z 1 d | 2 + k v k ρ d k ρ e 2 k z 1 d Im ( r 10 γ ) Im ( r 12 γ ) | 1 r 10 γ r 12 γ e 2 k z 1 d | 2 ]
a l = m ˜ ψ l ( m ˜ X ) ψ l ( X ) ψ l ( X ) ψ l ( m ˜ X ) m ˜ ψ l ( m ˜ X ) ξ l ( X ) ξ l ( X ) ψ l ( m ˜ X )
b l = ψ l ( m ˜ X ) ψ l ( X ) m ˜ ψ l ( X ) ψ l ( m ˜ X ) ψ l ( m ˜ X ) ξ l ( X ) m ˜ ξ l ( X ) ψ l ( m ˜ X )
ε e f f ε h = 1 + N [ k h 3 i 6 π ( 1 a 1 1 ) N 3 ] 1
μ e f f μ h = 1 + N [ k h 3 i 6 π ( 1 b 1 1 ) N 3 ] 1
b 1 2 i X 3 3 F ( m ˜ X ) 1 F ( m ˜ X ) + 2
F ( m ˜ X ) = 2 [ sin ( m ˜ X ) m ˜ X cos ( m ˜ X ) ] [ ( m ˜ X ) 2 1 ] sin ( m ˜ X ) + m ˜ X cos ( m ˜ X )
λ h , r e s m 2 r s m ˜
ε s = ε ( ω 2 - ω L O 2 + i Γ ω ω 2 - ω T O 2 + i Γ ω )
γ 0 μ 0 + γ 1 μ 1 = 0
k ρ 2 = k v 2 μ 0 μ 1 ( ε 1 μ 0 ε 0 μ 1 ) μ 0 2 μ 1 2
γ j 2 = k v 2 μ j 2 ε 1 μ 1 ε 0 μ 0 μ 0 2 μ 1 2
γ j 2 = k v 2 μ j 2 1 + ε 0 | μ 0 | μ 0 2 1
| μ 0 | > 1 a n d ε 0 > 1 | μ 0 |
| μ 0 | < 1 a n d ε 0 < 1 | μ 0 |
ω r e s m ω L O 2 + Ω 2 ( ω L O 2 + Ω 2 ) 2 4 Ω 2 ω T O 2 2
ω r e s e 2 ε h ω T O 2 + ε ω L O 2 ε + 2 ε h
ω r e s e ε ω L O 2 ε h ω T O 2 ( f 4 f + 2 ) ε ε h ( f 4 f + 2 )

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