Abstract

Using our recently developed method we analyze the radiative heat transfer in micron-thick multilayer stacks of metamaterials with hyperbolic dispersion. The metamaterials are especially designed for prospective thermophotovoltaic systems. We show that the huge transfer of near-infrared thermal radiation across micron layers of metamaterials is achievable and can be optimized. We suggest an approach to the optimal design of such metamaterials taking into account high temperatures of the emitting medium and the heating of the photovoltaic medium by the low-frequency part of the radiation spectrum. We show that both huge values and frequency selectivity are achievable for the radiative heat transfer in hyperbolic multilayer stacks.

© 2013 OSA

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2013 (3)

S. I. Maslovski, C. R. Simovski, and S. A. Tretyakov, “Equivalent circuit model of radiative heat transfer,” Phys. Rev. B87, 155124 (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, 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. B87, 115403 (2013).
[CrossRef]

2012 (6)

S.-A. Biehs, M. Tschikin, and P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett.109, 104301 (2012)
[CrossRef] [PubMed]

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

M. Tschikin, P. Ben-Abdallah, and S.-A. Biehs, “Coherent thermal conductance of 1-D photonic crystals,” Phys. Lett. A376, 3462 (2012).
[CrossRef]

C. R. Simovski, P. A. Belov, A. V. Atraschenko, and Yu. S. Kivshar, “Wire Metamaterials: Physics and Applications,” Adv. Mat.24, 4229–4248 (2012).
[CrossRef]

E. Hasman, V. Kleiner, N. Dahan, Yu. Gorodetski, K. Frischwasser, and I. Balin, “Manipulation of thermal emission by use of micro and nanoscale structures,” J. Heat Transfer134, 031023 (2012).
[CrossRef]

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

2011 (3)

I. Nefedov and C. Simovski, “Giant radiation heat transfer through the micron gaps,” Phys. Rev. B84, 195459 (2011).
[CrossRef]

X. Ni, G. V. Naik, A. V. Kildishev, Y. Barnakov, A. Boltasseva, and V. M. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B103, 553–558 (2011).
[CrossRef]

S. I. Maslovski and M. G. Silveirinha, “Mimicking Boyers-Casimir repulsion with a nanowire material,” Phys. Rev. A83, 022508 (2011).
[CrossRef]

2010 (3)

A. P. Vinogradov, A. V. Dorofeenko, and I. A. Nechepurenko, “Analysis of plasmonic Bloch waves and band structures of 1D plasmonic photonic crystals,” Metamaterials4, 181–200 (2010).
[CrossRef]

S. Levcenko, G. Gurieva, E. J. Friedrich, J. Trigo, J. Ramiro, J. M. Merino, E. Arushanov, and M. Leon, “Optical constants of CuIn1−xAlxSe2 thin films deposited by flash evaporation,” Moldavian Journal of the Physical Sciences, 9148–155 (2010).

P. Bermel, M. Ghebrebrhan, W. Chan, Y.-X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljacic, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Expr.18, A314–A334 (2010).
[CrossRef]

2009 (8)

W. T. Lau, J.-T. Shen, G. Veronis, and S. Fan, “Ultra-Small coherent thermal conductance using multi-layer photonic crystal,” Proc. SPIE7223, 722317 (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, 1203–1210 (2009).
[CrossRef]

S. Basu and Z. M. Zhang, “Maximum energy transfer in near-field thermal radiation at nanometer distances,” J. Appl. Phys.105, 093535 (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, 1203–1232 (2009).
[CrossRef]

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

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nature Mat.8, 867–871 (2009).
[CrossRef]

S. Maslovski and M. Silveirinha, “Nonlocal permittivity from a quasistatic model for a class of wire media,” Phys. Rev. B80, 245101 (2009)
[CrossRef]

N.P. Sergeant, O. Pincon, M. Agrawal, and P. Peumans, “Design of wide-angle solar-selective absorbers using aperiodic metal-dielectric stacks,” Opt. Expr.17, 22800–22812 (2009).
[CrossRef]

2008 (5)

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

K. Park, S. Basu, P. King, and Z.M. Zhang, “Performance analysis of near-field thermo-photovoltaic devices considering absorption distributions,” J. Quantitative Spectros. Radiative Transf.109, 305–310 (2008).
[CrossRef]

K. Joulain, “Near-field heat transfer: A radiative interpretation of thermal conduction,” J. Quantitative Spectroscopy and Radiative Transfer109, 294–304 (2008).
[CrossRef]

M. G. Silveirinha, P. A. Belov, and C. R. Simovski, “Ultimate limit of resolution of subwavelength imaging devices formed by metallic rods,” Opt. Lett.33, 1726–1729 (2008).
[CrossRef] [PubMed]

Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express16, 15439–15448 (2008).
[CrossRef] [PubMed]

2007 (4)

Y.-B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiatiors,” Opt. Comm.269, 411–417 (2007).
[CrossRef]

K. Park, A. Marchenkov, Z. M. Zhang, and W. P. King, “Low-temperature characterization of a heated cantilever,” J. Appl. Phys.101, 094504 (2007).
[CrossRef]

C. Fu and Z. M. Zhang, “Thermal radiative properties of metamaterials and other nanostructured materials: A review,” Frontiers of Energy and Power Engineering in China3, 11–26 (2007).
[CrossRef]

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

2006 (7)

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

S. Feng and J. Elson, “Optical properties of multilayer metal-dielectric nanofilms with all-evanescent modes,” Opt. Express14, 2216–2241 (2006).

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B73, 113110 (2006).
[CrossRef]

J. Elser, R. Wangberg, E. Narimanov, and V. A. Podolskiy, “Nanowire metamaterials with extreme optical anisotropy,” Appl. Phys. Lett.89, 261102 (2006).
[CrossRef]

M. Silveirinha, “Nonlocal homogenization model for a periodic array of epsilon-negative rods,” Phys. Rev. E73, 046612 (2006).
[CrossRef]

M. Meschke, W. Guichard, and J.P. Pekola, “Single-mode heat conduction by photons,” Nature444, 187–190, 2006.
[CrossRef] [PubMed]

A. Haddad-Adel, T. Inokuma, Y. Kurata, and S. Hasegawa, “Optical and structural properties of polycrystalline 3C-SiC films,” Appl. Phys. Lett.89, 181904 (2006)
[CrossRef]

2005 (7)

A. P. Vinogradov and A. V. Dorofeenko, “Near-field Bloch waves in photonic crystals,” Journal of Communication Technology and Electronics50, 1153–1158 (2005).

D. Schurig and D. R. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys.7, 162 (2005).
[CrossRef]

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2000 (2)

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1978 (1)

S. Mattei, P. Masclet, and P. Herve, “Study of complex refractive indices of gold and alloys at high temperature,” High Temperature16, 140–146 (1978).

1977 (1)

E. N. Shestakov, L. N. Latyev, and V. Ia. Chekhovskoi, “Investigation of the optical properties of metals at high temperatures,” Teplofizika Vysokikh Temperatur15, 292–299 (1977), in Russian.

1971 (2)

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Anantha Ramakrishna, S.

S. Anantha Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt.50, 1419 (2003).

Araghchini, M.

P. Bermel, M. Ghebrebrhan, W. Chan, Y.-X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljacic, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Expr.18, A314–A334 (2010).
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R. DiMatteo, P. Greiff, D. Seltzer, D. Meulenberg, E. Brown, E. Carlen, K. Kaiser, S. Finberg, H. Nguyen, J. Azarkevich, P. Baldasaro, J. Beausang, L. Danielson, M. Dashiell, D. DePoy, H. Ehsani, W. Topper, and K. Rahner, “Micron-gap ThermoPhotoVoltaics (MTPV),” in: Proceedings of 6-th AIP Int. Conf. Thermo-Photo-Voltaic Generation of Electricity, A. Gopinath, T.J. Coutts, and J. Luther, Editors, Sept.9–10, 2005, NY, USA, pp. 42–52.

Balin, I.

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Beausang, J.

R. DiMatteo, P. Greiff, D. Seltzer, D. Meulenberg, E. Brown, E. Carlen, K. Kaiser, S. Finberg, H. Nguyen, J. Azarkevich, P. Baldasaro, J. Beausang, L. Danielson, M. Dashiell, D. DePoy, H. Ehsani, W. Topper, and K. Rahner, “Micron-gap ThermoPhotoVoltaics (MTPV),” in: Proceedings of 6-th AIP Int. Conf. Thermo-Photo-Voltaic Generation of Electricity, A. Gopinath, T.J. Coutts, and J. Luther, Editors, Sept.9–10, 2005, NY, USA, pp. 42–52.

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C. R. Simovski, P. A. Belov, A. V. Atraschenko, and Yu. S. Kivshar, “Wire Metamaterials: Physics and Applications,” Adv. Mat.24, 4229–4248 (2012).
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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, 131106 (2013).
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P. Bermel, M. Ghebrebrhan, W. Chan, Y.-X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljacic, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Expr.18, A314–A334 (2010).
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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, 131106 (2013).
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S.-A. Biehs, M. Tschikin, and P. Ben-Abdallah, “Hyperbolic metamaterials as an analog of a blackbody in the near field,” Phys. Rev. Lett.109, 104301 (2012)
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A. Kittel, W. Mller-Hirsch, J. Parisi, S.-A. Biehs, D. Reddig, and M. Holthaus, “Near-field heat transfer in a scanning thermal microscope,” Phys. Rev. Lett.95, 224301 (2005).
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Blasi, B.

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, “Radiation filters and emitters for the NIR based on periodically structured metal surfaces,” J. Mod. Opt.47, 2399–2419 (2000).

Boerner, V.

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, “Radiation filters and emitters for the NIR based on periodically structured metal surfaces,” J. Mod. Opt.47, 2399–2419 (2000).

Boltasseva, A.

X. Ni, G. V. Naik, A. V. Kildishev, Y. Barnakov, A. Boltasseva, and V. M. Shalaev, “Effect of metallic and hyperbolic metamaterial surfaces on electric and magnetic dipole emission transitions,” Appl. Phys. B103, 553–558 (2011).
[CrossRef]

Brown, E.

R. DiMatteo, P. Greiff, D. Seltzer, D. Meulenberg, E. Brown, E. Carlen, K. Kaiser, S. Finberg, H. Nguyen, J. Azarkevich, P. Baldasaro, J. Beausang, L. Danielson, M. Dashiell, D. DePoy, H. Ehsani, W. Topper, and K. Rahner, “Micron-gap ThermoPhotoVoltaics (MTPV),” in: Proceedings of 6-th AIP Int. Conf. Thermo-Photo-Voltaic Generation of Electricity, A. Gopinath, T.J. Coutts, and J. Luther, Editors, Sept.9–10, 2005, NY, USA, pp. 42–52.

Caballero, R.

R. Caballero and C. Guillen, “Optical and electrical properties of CuIn1−xAlxSe2 thin films obtained by selenization of sequentially evaporated metallic layers,” Thin Solid Films, 431/432200–204 (2003).
[CrossRef]

Carlen, E.

R. DiMatteo, P. Greiff, D. Seltzer, D. Meulenberg, E. Brown, E. Carlen, K. Kaiser, S. Finberg, H. Nguyen, J. Azarkevich, P. Baldasaro, J. Beausang, L. Danielson, M. Dashiell, D. DePoy, H. Ehsani, W. Topper, and K. Rahner, “Micron-gap ThermoPhotoVoltaics (MTPV),” in: Proceedings of 6-th AIP Int. Conf. Thermo-Photo-Voltaic Generation of Electricity, A. Gopinath, T.J. Coutts, and J. Luther, Editors, Sept.9–10, 2005, NY, USA, pp. 42–52.

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M. Laroche, R. Carminati, and J.-J. Greffet, “Near-field thermo-photovoltaic energy conversion,” J. 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,” Surface Science Reports57, 59–112 (2005).
[CrossRef]

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, “Nanoscale radiative heat transfer between a small particle and a plane surface,” Appl. Phys. Lett.78, 2931 (2001).
[CrossRef]

Celanovic, I.

P. Bermel, M. Ghebrebrhan, W. Chan, Y.-X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljacic, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Expr.18, A314–A334 (2010).
[CrossRef]

F. OSullivan, I. Celanovic, N. Jovanovic, J. Kassakian, S. Akiyama, and K. Wada, “Optical characteristics of 1D Si/SiO2photonic crystals for thermophotovoltaic applications,” J. Appl. Phys.97, 033529 (2005).
[CrossRef]

I. Celanovic, F. OSullivan, M. Ilak, J. Kassakian, and D. Perreault, “Design and optimization of one-dimensional photonic crystals for thermophotovoltaic applications,” Opt. Lett.29, 863–866 (2004).
[CrossRef] [PubMed]

Chan, W.

P. Bermel, M. Ghebrebrhan, W. Chan, Y.-X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljacic, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Expr.18, A314–A334 (2010).
[CrossRef]

Chekhovskoi, V. Ia.

E. N. Shestakov, L. N. Latyev, and V. Ia. Chekhovskoi, “Investigation of the optical properties of metals at high temperatures,” Teplofizika Vysokikh Temperatur15, 292–299 (1977), in Russian.

Chen, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E69, 066607 (2004).
[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, 689–716 (2007).
[CrossRef]

Y.-B. Chen and Z. M. Zhang, “Design of tungsten complex gratings for thermophotovoltaic radiatiors,” Opt. Comm.269, 411–417 (2007).
[CrossRef]

Chen, Y.-Y.

Y.-Y. Chen, Z.-M. Huang, and Q. Wang, “Photon tunneling in one-dimensional metamaterial photonic crystals,” J. Opt. A: Pure Appl. Opt.7(9), 519–524 (2005).
[CrossRef]

Choi, B. I.

M. I. Flik, B. I. Choi, and K. E. Goodson, “Heat-transfer regimes in microstructures,” J. Heat Transfer114, 666–674 (1992).
[CrossRef]

Cleland, A. N.

D. R. Schmidt, R. J. Schoelkopf, and A. N. Cleland, “Photon-mediated thermal relaxation of electrons in nanostructures,” Phys. Rev. Lett.93, 045901 (2004).
[CrossRef] [PubMed]

Collins, R. W.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92, 2424–2436 (2002).
[CrossRef]

Cortes, C. L.

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

Cravalho, E. G.

M. D. Whale and E. G. Cravalho, “Modeling and performance of microscale thermo-photovoltaic energy conversion devices,” IEEE Trans. Energy Conversion17, 130–137 (2002).
[CrossRef]

Dahan, N.

E. Hasman, V. Kleiner, N. Dahan, Yu. Gorodetski, K. Frischwasser, and I. Balin, “Manipulation of thermal emission by use of micro and nanoscale structures,” J. Heat Transfer134, 031023 (2012).
[CrossRef]

Danielson, L.

R. DiMatteo, P. Greiff, D. Seltzer, D. Meulenberg, E. Brown, E. Carlen, K. Kaiser, S. Finberg, H. Nguyen, J. Azarkevich, P. Baldasaro, J. Beausang, L. Danielson, M. Dashiell, D. DePoy, H. Ehsani, W. Topper, and K. Rahner, “Micron-gap ThermoPhotoVoltaics (MTPV),” in: Proceedings of 6-th AIP Int. Conf. Thermo-Photo-Voltaic Generation of Electricity, A. Gopinath, T.J. Coutts, and J. Luther, Editors, Sept.9–10, 2005, NY, USA, pp. 42–52.

Dashiell, M.

R. DiMatteo, P. Greiff, D. Seltzer, D. Meulenberg, E. Brown, E. Carlen, K. Kaiser, S. Finberg, H. Nguyen, J. Azarkevich, P. Baldasaro, J. Beausang, L. Danielson, M. Dashiell, D. DePoy, H. Ehsani, W. Topper, and K. Rahner, “Micron-gap ThermoPhotoVoltaics (MTPV),” in: Proceedings of 6-th AIP Int. Conf. Thermo-Photo-Voltaic Generation of Electricity, A. Gopinath, T.J. Coutts, and J. Luther, Editors, Sept.9–10, 2005, NY, USA, pp. 42–52.

Demichelis, F.

F. Demichelis, E. Minettimezzetti, M. Agnello, and E. Tresso, “Evaluation of thermophotovoltaic conversion efficiency,” J. Appl. Phys.53, 9098–9104 (1982).
[CrossRef]

Deng, X.

A. S. Ferlauto, G. M. Ferreira, J. M. Pearce, C. R. Wronski, R. W. Collins, X. Deng, and G. Ganguly, “Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics,” J. Appl. Phys.92, 2424–2436 (2002).
[CrossRef]

DePoy, D.

R. DiMatteo, P. Greiff, D. Seltzer, D. Meulenberg, E. Brown, E. Carlen, K. Kaiser, S. Finberg, H. Nguyen, J. Azarkevich, P. Baldasaro, J. Beausang, L. Danielson, M. Dashiell, D. DePoy, H. Ehsani, W. Topper, and K. Rahner, “Micron-gap ThermoPhotoVoltaics (MTPV),” in: Proceedings of 6-th AIP Int. Conf. Thermo-Photo-Voltaic Generation of Electricity, A. Gopinath, T.J. Coutts, and J. Luther, Editors, Sept.9–10, 2005, NY, USA, pp. 42–52.

DePoy, D. M.

B. Wernsman, R. R. Siergiej, S. D. Link, R. G. Mahorter, M. N. Palmisiano, R. J. Wehrer, R. W. Schultz, G. P. Schmuck, R. L. Messham, S. Murray, C. S. Murray, F. Newman, D. Taylor, D. M. DePoy, and T. Rahmlow, “Greater than 20% radiant heat conversion efficiency of a thermophotovoltaic radiator/module system using reflective spectral control,” IEEE Trans. Electron. Dev.51, 512–515 (2004).
[CrossRef]

DiMatteo, R.

R. DiMatteo, P. Greiff, D. Seltzer, D. Meulenberg, E. Brown, E. Carlen, K. Kaiser, S. Finberg, H. Nguyen, J. Azarkevich, P. Baldasaro, J. Beausang, L. Danielson, M. Dashiell, D. DePoy, H. Ehsani, W. Topper, and K. Rahner, “Micron-gap ThermoPhotoVoltaics (MTPV),” in: Proceedings of 6-th AIP Int. Conf. Thermo-Photo-Voltaic Generation of Electricity, A. Gopinath, T.J. Coutts, and J. Luther, Editors, Sept.9–10, 2005, NY, USA, pp. 42–52.

DiMatteo, R. S.

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Figures (8)

Fig. 1
Fig. 1

(a) – Sketch of the general design solution. (b) – The homogenization model under study.

Fig. 2
Fig. 2

(a) – The equivalent scheme of the radiative heat transfer across the layer of medium 2 formed by nanowires in the air gap. (b) – The equivalent circuit that allows one to simplify the evaluation of the thermal power absorbed in the medium 3.

Fig. 3
Fig. 3

(a) – Real and imaginary parts of the axial effective permittivity of media 1–3, optimized for gold nanowires at temperatures T1 = 400° K (medium 1) and T3 = 300° K (medium 3). (b) – Same for the transverse effective permittivity.

Fig. 4
Fig. 4

(a) – Spatial spectrum N(q/k) of the heat transfer function for the gap h = 1 μm (here and below k = k0 = ω/c). Gold nanowires in media 1–3 are under temperatures T1 = 400° K, T2 = 350° K, T3 = 300° K). N(q) is calculated for four sets of the volume fractions of gold in media 1–3: p1,2,3 = 0, p1,2,3 = 0.3, 3) p1,3 = 0, p2 = 0.16, and p1 = 0.22, p2 = 0.16, p3 = 0.28 (optimal case). (b) – Gain G13 in the spectral density of RHT due to the presence of nanowires calculated for p1,2,3 = 0.3, p1 = p3 = 0, p2 = 0.16, and p1 = 0.22, p2 = 0.16, p3 = 0.28 (optimal case).

Fig. 5
Fig. 5

(a) – Spatial spectrum N(q/k) of the heat transfer function for the gap h = 1 μm. Gold nanowires in media 1–3 are at temperatures T1 = 1300° K, T2 = 800° K, and T3 = 300° K. N(q/k) is calculated for 3 cases p1,2,3 = 0, p1,2,3 = 0.4, and p1 = 0.37, p2 = 0.33, p3 = 0.40. (b) – Gain G13 in the spectral density of RHT due to the presence of nanowires calculated for p1,2,3 = 0.4 and for the optimal case p1 = 0.37, p2 = 0.33, p3 = 0.40.

Fig. 6
Fig. 6

(a) – Gain G123 in the RHT across the gap h = 5 μm taking into account the contribution of medium 2 in comparison with G13 calculated neglecting this contribution. Design parameters of the original structure were optimized for the gap h = 1 μm. (a) – Nanowires in media 1–3 are under temperatures T1 = 400° K, T2 = 350° K, and T3 = 300° K. (b) – Nanowires in media 1–3 are under temperatures T1 = 1300° K, T2 = 350° K, and T3 = 300° K.

Fig. 7
Fig. 7

(a) – A seven-layer structure that may offer the frequency selective enhanced RHT across five internal micron-thick layers. (b) – A homogenization model for this structure. Host medium of three internal effective-medium layers is vacuum.

Fig. 8
Fig. 8

The gain G = G13(λ) due to the presence of nanowires and the RHT spectrum g in the absence of nanowires normalized to that between two black bodies. The black-body radiation spectrum Bλ corresponding to the temperature of medium 1 is shown in arbitrary units. (a) – Host media of layers H1,3 are same as media 1 and 3, respectively, and G is given in absolute units. (b) – Host medium of layers H1,3 is silicon, and G is given in dB.

Equations (36)

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B ω = k 0 2 4 π 3 Θ , Θ = h ¯ ω ( e h ¯ ω k B T 1 ) ,
Z 12 = Z 21 = j Z 2 sin β 2 h , Z 11 = Z 22 = j Z 2 tan β 2 h .
| 1 , 3 | 2 ¯ d ( e 1 , 3 ) 2 ¯ d ω = 2 π Θ 1 , 3 R 1 , 3 , | 2 ± | 2 ¯ d ( e 2 ± ) 2 ¯ d ω = 2 π Θ 2 R 11 = 2 π Θ 2 R 22 .
2 2 + * ¯ d ( e 2 e 2 + ) ¯ d ω = 2 π Θ 2 R 12 = 2 π Θ 2 R 21 .
Z h = Z 22 Z 21 2 Z 11 + Z 1 = Z 2 Z 1 + j Z 2 tan β 2 h Z 2 + j Z 1 tan β 2 h .
I + = 3 + 2 + + 2 1 Z d + Z 3 .
| 1 | 2 ¯ = 2 π Θ 1 R 1 | Z 12 Z 11 + Z 1 | 2 , | 2 | 2 ¯ = 2 π Θ 2 R 11 | Z 12 Z 11 + Z 1 | 2 , 2 2 + * ¯ = 2 π Θ 2 R 12 .
| I ¯ + | 2 = | 3 | 2 ¯ + | 2 + | 2 ¯ + 2 2 + * ¯ + | 1 | 2 ¯ | Z h + Z 3 | 2 .
P 3 = P 33 + P 23 + P 13 ,
P 33 = 2 π Θ 3 R 3 2 | Z h + Z 3 | 2 ,
P 23 = 2 π Θ 2 R 3 | Z h + Z 3 | 2 ( R 11 + R 12 ) ,
P 13 = 2 π Θ 1 | Z 12 Z 11 + Z 1 | 2 R 1 R 3 | Z h + Z 3 | 2 .
S 3 = 0 d ω s 3 ( ω ) = d 2 k t ( 2 π ) 2 0 d ω P 3 ( ω , k t ) = 1 2 π 0 d ω 0 q d q P 3 ( ω , q ) .
S 13 = 1 π 2 0 d ω 0 q d q N ( ω , q ) Θ 1
N ( ω , q ) = 4 | Z 2 | 2 R 1 R 3 e 2 Im ( β 2 ) h | ( Z 1 + Z 2 ) ( Z 2 + Z 3 ) + ( Z 1 Z 2 ) ( Z 2 Z 3 ) e 2 j β 2 h | 2 .
Γ 12 , 32 = ( Z 1 , 3 Z 2 ) / ( Z 1 , 3 + Z 2 ) ,
N ( ω , q ) = | 1 Γ 12 | 2 | 1 Γ 32 | 2 | e j β 2 h | 2 | 1 Γ 12 Γ 32 e 2 j β 2 h | 2 R 1 R 3 4 | Z 2 | 2 .
| 1 Γ 12 | 2 | 1 Γ 32 | 2 | e j β 2 h | 2 | 1 Γ 12 Γ 32 e 2 j β 2 h | 2 = | τ Z 2 Z 3 | 2 ,
N ( ω , q ) = | τ | 2 R 1 R 3 4 | Z 3 | 2 .
N ( ω , q ) R 1 R 2 | Z 1 + Z 2 | 2 , q < k 0 ; N ( ω , q ) 0 , q > k 0 .
E ω = 4 k 0 2 0 k 0 N ( ω , q ) q d q = 0 π / 2 cos θ sin θ ( 1 | Γ 12 | 2 ) d θ .
Z i T M = η β i T M k 0 ε i , β i T M = ε i ε i | | ( k 0 2 ε i | | q 2 ) ,
Z i T E = η k 0 β i , β i T E = k 0 2 ε i q 2 .
R 2 ( R 1 R 3 ) sin β 2 h = cos β 2 h ( R 1 X 3 + R 3 X 1 ) .
P 13 = 2 π Θ 1 R 2 4 ( R 2 + X ¯ 2 ) + 1 2 X ¯ 2 F , X ¯ X 1 + X 3 2 .
F = ( 1 + X 1 X 3 4 R 2 ) ( 1 cos 2 β 2 d ) X ¯ R sin 2 β 2 d .
Re k 0 2 ε 2 | | q 2 ε 2 | | ε 2 = Re k 0 2 ε 1 , 3 | | q 2 ε 1 , 3 | | ε 1 , 3 .
Re ( ε 1 ) = Re ( ε 2 ) = Re ( ε 3 ) ,
Re ( ε 1 | | ) = Re ( ε 2 | | ) = Re ( ε 3 | | ) < 0 .
ε | | ε h = 1 + 1 ε h p ( ε m ε h ) k h 2 β 2 k p 2 .
ε ε h = 1 + 2 ε m + ε h p ( ε m ε h ) 1 .
ε | | ε h = 1 k p 2 k h 2 + k h Y β 2 , Y 4 k p 2 a 2 π k 0 b 2 ( ε h ε m ) .
S 13 1 2 π ω min ω max d ω 0 q max P 13 ( ω , q ) q d q , S 13 ( 0 ) 1 2 π ω min ω max d ω 0 P 13 ( 0 ) ( ω , q ) q d q .
G 13 int = ω min ω max d ω 0 q max N ( ω , q ) q d q ω min ω max d ω 0 N ( 0 ) ( ω , q ) q d q .
G 13 ( ω ) = M 13 M 13 ( 0 ) = 0 q max N ( ω , q ) q d q 0 N ( 0 ) ( ω , q ) q d q .
G 123 ( ω ) = 0 q max [ P 13 ( ω , q ) + P 23 ( ω , q ) ] q d q 0 P 13 ( 0 ) ( ω , q ) q d q G 13 ( ω ) + G 23 ( ω ) .

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