Abstract

Radiative heat transfer between uniform plates is bounded by the narrow range and limited contribution of surface waves. Using a combination of analytical calculations and numerical gradient-based optimization, we show that such a limitation can be overcome in complicated multilayer geometries, allowing the scattering and coupling rates of slab resonances to be altered over a broad range of evanescent wavevectors. We conclude that while the radiative flux between two inhomogeneous slabs can only be weakly enhanced, the flux between a dipolar particle and an inhomogeneous slab—proportional to the local density of states—can be orders of magnitude larger, albeit at the expense of increased frequency selectivity. A brief discussion of hyperbolic metamaterials shows that they provide far less enhancement than optimized inhomogeneous slabs.

© 2017 Optical Society of America

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2017 (4)

V. Fernández-Hurtado, F. J. García-Vidal, S. Fan, and J. C. Cuevas, “Enhancing near-field radiative heat transfer with si-based metasurfaces,” Phys. Rev. Lett. 118, 203901 (2017).
[Crossref] [PubMed]

R. Messina, A. Noto, B. Guizal, and M. Antezza, “Radiative heat transfer between metallic gratings using adaptive spatial resolution,” Phys. Rev. B 95, 125404 (2017).
[Crossref]

Y. Li, C. J. Zhang, T.-B. Wang, J.-T. Liu, T.-B. Yu, Q.-H. Liao, and N.-H. Liu, “Modulation of electromagnetic local density of states by coupling of surface phonon-polariton,” Mod. Phys. Lett. B 31, 1750050 (2017).
[Crossref]

S.-A. Biehs and P. Ben-Abdallah, “Near-field heat transfer between multilayer hyperbolic metamaterials,” Z. Naturforsch. A 72, 115–127 (2017).
[Crossref]

2016 (10)

C. Khandekar, W. Jin, O. D. Miller, A. Pick, and A. W. Rodriguez, “Giant frequency-selective near-field energy transfer in active–passive structures,” Phys. Rev. B 94, 115402 (2016).
[Crossref]

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

O. Ilic, P. Bermel, G. Chen, J. D. Joannopoulos, I. Celanovic, and M. Soljačić, “Tailoring high-temperature radiation and the resurrection of the incandescent source,” Nat. Nanotech. 11, 320 (2016).
[Crossref]

A. Seyedzahedi, A. Moradian, and M. Setare, “Intensifying the casimir force between two silicon substrates within three different layers of materials,” Phys. Lett. A 380, 1475–1480 (2016).
[Crossref]

O. D. Miller, A. G. Polimeridis, M. H. Reid, C. W. Hsu, B. G. DeLacy, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Fundamental limits to optical response in absorptive systems,” Opt. Express 24, 3329 (2016).
[Crossref] [PubMed]

H. Chalabi, A. Alù, and M. L. Brongersma, “Focused thermal emission from a nanostructured sic surface,” Phys. Rev. B 94, 094307 (2016).
[Crossref]

O. Ramezan Choubdar and M. Nikbakht, “Radiative heat transfer between nanoparticles: Shape dependence and three-body effect,” J. Appl. Phys. 120, 144303 (2016).
[Crossref]

J. Dai, S. A. Dyakov, and M. Yan, “Radiative heat transfer between two dielectric-filled metal gratings,” Phys. Rev. B 93, 155403 (2016).
[Crossref]

J. Dai, S. A. Dyakov, S. I. Bozhevolnyi, and M. Yan, “Near-field radiative heat transfer between metasurfaces: A full-wave study based on two-dimensional grooved metal plates,” Phys. Rev. B 94, 125431 (2016).
[Crossref]

Y. Yang and L. Wang, “Spectrally enhancing near-field radiative transfer between metallic gratings by exciting magnetic polaritons in nanometric vacuum gaps,” Phys. Rev. Lett. 117, 044301 (2016).
[Crossref] [PubMed]

2015 (8)

X. Liu, B. Zhao, and Z. M. Zhang, “Enhanced near-field thermal radiation and reduced casimir stiction between doped-si gratings,” Phys. Rev. A 91, 062510 (2015).
[Crossref]

H. Chalabi, E. Hasman, and M. L. Brongersma, “Effect of shape in near-field thermal transfer for periodic structures,” Phys. Rev. B 91, 174304 (2015).
[Crossref]

H. Chalabi, E. Hasman, and M. L. Brongersma, “Near-field radiative thermal transfer between a nanostructured periodic material and a planar substrate,” Phys. Rev. B 91, 014302 (2015).
[Crossref]

S. Bhargava and E. Yablonovitch, “Lowering hamr near-field transducer temperature via inverse electromagnetic design,” IEEE Trans. Magn. 51, 3100407 (2015).
[Crossref]

X. Liu, L. Wang, and Z. M. Zhang, “Near-field thermal radiation: Recent progress and outlook,” Nanoscale Microscale Thermophys. Eng. 19, 98 (2015).
[Crossref]

O. D. Miller, S. G. Johnson, and A. W. Rodriguez, “Shape-independent limits to near-field radiative heat transfer,” Phys. Rev. Lett. 115, 204302 (2015).
[Crossref] [PubMed]

P. D. Anderson and M. L. Povinelli, “Optimized emission in nanorod arrays through quasi-aperiodic inverse design,” Opt. Lett. 40, 2672 (2015).
[Crossref] [PubMed]

J. Dai, S. A. Dyakov, and M. Yan, “Enhanced near-field radiative heat transfer between corrugated metal plates: Role of spoof surface plasmon polaritons,” Phys. Rev. B 92, 035419 (2015).
[Crossref]

2014 (6)

O. D. Miller, S. G. Johnson, and A. W. Rodriguez, “Effectiveness of thin films in lieu of hyperbolic metamaterials in the near field,” Phys. Rev. Lett. 112, 157402 (2014).
[Crossref] [PubMed]

R. Messina and M. Antezza, “Three-body radiative heat transfer and casimir-lifshitz force out of thermal equilibrium for arbitrary bodies,” Phys. Rev. A 89, 052104 (2014).
[Crossref]

V. Ganapati, O. D. Miller, and E. Yablonovitch, “Light trapping textures designed by electromagnetic optimization for subwavelength thick solar cells,” IEEE J. Photovolt. 4, 175–182 (2014).
[Crossref]

X. Ling, W. Fang, Y.-H. Lee, P. T. Araujo, X. Zhang, J. F. Rodriguez-Nieva, Y. Lin, J. Zhang, J. Kong, and M. S. Dresselhaus, “Raman enhancement effect on two-dimensional layered materials: graphene, h-bn and mos2,” Nano Lett. 14, 3033–3040 (2014).
[Crossref] [PubMed]

C. R. Otey, L. Zhu, S. Sandhu, and S. Fan, “Fluctuational electrodynamics calculations of near-field heat transfer in non-planar geometries: A brief overview,” J. Quant. Spectrosc. Radiat. Transf. 132, 3 (2014).
[Crossref]

X. L. Liu and Z. M. Zhang, “Graphene-assisted near-field radiative heat transfer between corrugated polar materials,” Appl. Phys. Lett. 104, 251911 (2014).
[Crossref]

2013 (5)

E. Nefzaoui, Y. Ezzahri, J. Drevillon, and K. Joulain, “Maximal near-field radiative heat transfer between two plates,” Eur. Phys. J. Appl. Phys. 63, 30902 (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]

C. Simovski, S. Maslovski, I. Nefedov, and S. Tretyakov, “Optimization of radiative heat transfer in hyperbolic metamaterials for thermophotovoltaic applications,” Opt. Express 21, 14988 (2013).
[Crossref] [PubMed]

P. Wang and R. Menon, “Optimization of generalized dielectric nanostructures for enhanced light trapping in thin-film photovoltaics via boosting the local density of optical states,” Opt. Express 22, A99 (2013).
[Crossref]

R. Messina, J.-P. Hugonin, J.-J. Greffet, F. Marquier, Y. De Wilde, A. Belarouci, L. Frechette, Y. Cordier, and P. Ben-Abdallah, “Tuning the electromagnetic local density of states in graphene-covered systems via strong coupling with graphene plasmons,” Phys. Rev. B 87, 085421 (2013).
[Crossref]

2012 (5)

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

E. Nefzaoui, J. Drevillon, and K. Joulain, “Selective emitters design and optimization for thermophotovoltaic applications,” J. Appl. Phys. 11, 084316 (2012).
[Crossref]

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12, 1616–1619 (2012).
[Crossref] [PubMed]

Y. Zhao, G. H. Tang, and Z. Y. Li, “Parametric investigation for suppressing near-field thermal radiation between two spherical nanoparticles,” Int. Commun. Heat Mass Transf. 39, 918 (2012).
[Crossref]

R. Guérout, J. Lussange, F. S. S. Rosa, J.-P. Hugonin, D. A. R. Dalvit, J.-J. Greffet, A. Lambrecht, and S. Reynaud, “Enhanced near-field thermal radiation and reduced casimir stiction between doped-si gratings,” Phys. Rev. B 85, 180301 (2012).
[Crossref]

2011 (6)

S. Chen, H. Cheng, H. Yang, J. Li, X. Duan, C. Gu, and J. Tian, “Polarization insensitive and omnidirectional broadband near perfect planar metamaterial absorber in the near infrared regime,” Appl. Phys. Lett. 99, 253104 (2011).
[Crossref]

S. Basu and M. Francoeur, “Maximum near-field radiative heat transfer between thin films,” Appl. Phys. Lett. 98, 243120 (2011).
[Crossref]

L. Wang, S. Basu, and Z. Zhang, “Direct and indirect methods for calculating thermal emission from layered structures with nonuniform temperatures,” J. Heat Transf. 133, 072701 (2011).
[Crossref]

J. S. Jensen and O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5, 308–321 (2011).
[Crossref]

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2010 (3)

P. Bermel, W. Ghebrebrhan, M. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18, A314 (2010).
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Y.-B. Chen and K.-H. Tan, “The profile optimization of periodic nano-structures for wavelength-selective thermophotovoltaic emitters,” Int. J. Heat Mass Transf. 53, 5542–5551 (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 Transf. 132, 023302 (2010).
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P. Ben-Abdallah, K. Joulain, J. Drevillon, and G. Domingues, “Tailoring the local density of states of nonradiative field at the surface of nanolayered materials,” Appl. Phys. Lett. 94, 153117 (2009).
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S. Basu, Z. Zhang, and C. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Ener. Res. 33, 1203 (2009).
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X. J. Wang, S. Basu, and Z. M. Zhang, “Parametric optimization of dielectric functions for maximizing nanoscale radiative transfer,” J. Phys. D: Appl. Phys. 42, 245403 (2009).
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P. Ben-Abdallah, K. Joulain, J. Drevillon, and G. Domingues, “Near-field heat transfer mediated by surface wave hybridization between two films,” J. Appl. Phys. 106, 044306 (2009).
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M. Ghebrebrhan, P. Bermel, Y. Avniel, J. D. Joannopoulos, and S. G. Johnson, “Global optimization of silicon photovoltaic cell front coatings,” Opt. Express 17, 7505 (2009).
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N. P. Sergeant, O. Pincon, M. Agrawal, and P. Peumans, “Design of wide-angle solar-selective absorbers using aperiodic metal-dielectric stacks,” Opt. Express 17, 22800 (2009).
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X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7, 435 (2008).
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C. Fu and Z. Zhang, “Nanoscale radiation heat transfer for silicon at different doping levels,” Int. J. Heat Mass Transf.  49, 1703 (2006).
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2005 (1)

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 (2005).
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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 Transf. 132, 023302 (2010).
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X. J. Wang, S. Basu, and Z. M. Zhang, “Parametric optimization of dielectric functions for maximizing nanoscale radiative transfer,” J. Phys. D: Appl. Phys. 42, 245403 (2009).
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S. Basu, Z. Zhang, and C. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Ener. Res. 33, 1203 (2009).
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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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H. Chalabi, A. Alù, and M. L. Brongersma, “Focused thermal emission from a nanostructured sic surface,” Phys. Rev. B 94, 094307 (2016).
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Celanovic, I.

Chalabi, H.

H. Chalabi, A. Alù, and M. L. Brongersma, “Focused thermal emission from a nanostructured sic surface,” Phys. Rev. B 94, 094307 (2016).
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H. Chalabi, E. Hasman, and M. L. Brongersma, “Near-field radiative thermal transfer between a nanostructured periodic material and a planar substrate,” Phys. Rev. B 91, 014302 (2015).
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H. Chalabi, E. Hasman, and M. L. Brongersma, “Effect of shape in near-field thermal transfer for periodic structures,” Phys. Rev. B 91, 174304 (2015).
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O. Ilic, P. Bermel, G. Chen, J. D. Joannopoulos, I. Celanovic, and M. Soljačić, “Tailoring high-temperature radiation and the resurrection of the incandescent source,” Nat. Nanotech. 11, 320 (2016).
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S. V. Boriskina, J. K. Tong, Y. Huang, J. Zhou, V. Chiloyan, and G. Chen, “Enhancement and tunability of near-field radiative heat transfer mediated by surface plasmon polaritons in thin plasmonic films,” in “Photonics,”, vol. 2 (Multidisciplinary Digital Publishing Institute, 2015), vol. 2, p. 659.
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S. Chen, H. Cheng, H. Yang, J. Li, X. Duan, C. Gu, and J. Tian, “Polarization insensitive and omnidirectional broadband near perfect planar metamaterial absorber in the near infrared regime,” Appl. Phys. Lett. 99, 253104 (2011).
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Chen, Y.-B.

Y.-B. Chen and K.-H. Tan, “The profile optimization of periodic nano-structures for wavelength-selective thermophotovoltaic emitters,” Int. J. Heat Mass Transf. 53, 5542–5551 (2010).
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Cheng, H.

S. Chen, H. Cheng, H. Yang, J. Li, X. Duan, C. Gu, and J. Tian, “Polarization insensitive and omnidirectional broadband near perfect planar metamaterial absorber in the near infrared regime,” Appl. Phys. Lett. 99, 253104 (2011).
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Chiloyan, V.

S. V. Boriskina, J. K. Tong, Y. Huang, J. Zhou, V. Chiloyan, and G. Chen, “Enhancement and tunability of near-field radiative heat transfer mediated by surface plasmon polaritons in thin plasmonic films,” in “Photonics,”, vol. 2 (Multidisciplinary Digital Publishing Institute, 2015), vol. 2, p. 659.
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L. Hu and S. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66, 085108 (2002).
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R. Messina, J.-P. Hugonin, J.-J. Greffet, F. Marquier, Y. De Wilde, A. Belarouci, L. Frechette, Y. Cordier, and P. Ben-Abdallah, “Tuning the electromagnetic local density of states in graphene-covered systems via strong coupling with graphene plasmons,” Phys. Rev. B 87, 085421 (2013).
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Y. Guo, C. L. Cortes, S. Molesky, and Z. Jacob, “Broadband super-planckian thermal emission from hyperbolic metamaterials,” Appl. Phys. Lett. 101, 131106 (2012).
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V. Fernández-Hurtado, F. J. García-Vidal, S. Fan, and J. C. Cuevas, “Enhancing near-field radiative heat transfer with si-based metasurfaces,” Phys. Rev. Lett. 118, 203901 (2017).
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Cui, Y.

K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12, 1616–1619 (2012).
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Dai, J.

J. Dai, S. A. Dyakov, S. I. Bozhevolnyi, and M. Yan, “Near-field radiative heat transfer between metasurfaces: A full-wave study based on two-dimensional grooved metal plates,” Phys. Rev. B 94, 125431 (2016).
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J. Dai, S. A. Dyakov, and M. Yan, “Radiative heat transfer between two dielectric-filled metal gratings,” Phys. Rev. B 93, 155403 (2016).
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J. Dai, S. A. Dyakov, and M. Yan, “Enhanced near-field radiative heat transfer between corrugated metal plates: Role of spoof surface plasmon polaritons,” Phys. Rev. B 92, 035419 (2015).
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R. Guérout, J. Lussange, F. S. S. Rosa, J.-P. Hugonin, D. A. R. Dalvit, J.-J. Greffet, A. Lambrecht, and S. Reynaud, “Enhanced near-field thermal radiation and reduced casimir stiction between doped-si gratings,” Phys. Rev. B 85, 180301 (2012).
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David, A.

A. David, H. Benisty, and C. Weisbuch, “Optimization of light-diffracting photonic-crystals for high extraction efficiency leds,” J. Displ. Technol. 3, 133 (2007).
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R. Messina, J.-P. Hugonin, J.-J. Greffet, F. Marquier, Y. De Wilde, A. Belarouci, L. Frechette, Y. Cordier, and P. Ben-Abdallah, “Tuning the electromagnetic local density of states in graphene-covered systems via strong coupling with graphene plasmons,” Phys. Rev. B 87, 085421 (2013).
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Domingues, G.

P. Ben-Abdallah, K. Joulain, J. Drevillon, and G. Domingues, “Tailoring the local density of states of nonradiative field at the surface of nanolayered materials,” Appl. Phys. Lett. 94, 153117 (2009).
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P. Ben-Abdallah, K. Joulain, J. Drevillon, and G. Domingues, “Near-field heat transfer mediated by surface wave hybridization between two films,” J. Appl. Phys. 106, 044306 (2009).
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X. Ling, W. Fang, Y.-H. Lee, P. T. Araujo, X. Zhang, J. F. Rodriguez-Nieva, Y. Lin, J. Zhang, J. Kong, and M. S. Dresselhaus, “Raman enhancement effect on two-dimensional layered materials: graphene, h-bn and mos2,” Nano Lett. 14, 3033–3040 (2014).
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E. Nefzaoui, Y. Ezzahri, J. Drevillon, and K. Joulain, “Maximal near-field radiative heat transfer between two plates,” Eur. Phys. J. Appl. Phys. 63, 30902 (2013).
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P. Ben-Abdallah, K. Joulain, J. Drevillon, and G. Domingues, “Tailoring the local density of states of nonradiative field at the surface of nanolayered materials,” Appl. Phys. Lett. 94, 153117 (2009).
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J. Drevillon and P. Ben-Abdallah, “Ab initio design of coherent thermal sources,” J. Appl. Phys. 102, 114305 (2007).
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S. Chen, H. Cheng, H. Yang, J. Li, X. Duan, C. Gu, and J. Tian, “Polarization insensitive and omnidirectional broadband near perfect planar metamaterial absorber in the near infrared regime,” Appl. Phys. Lett. 99, 253104 (2011).
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J. Dai, S. A. Dyakov, and M. Yan, “Radiative heat transfer between two dielectric-filled metal gratings,” Phys. Rev. B 93, 155403 (2016).
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J. Dai, S. A. Dyakov, S. I. Bozhevolnyi, and M. Yan, “Near-field radiative heat transfer between metasurfaces: A full-wave study based on two-dimensional grooved metal plates,” Phys. Rev. B 94, 125431 (2016).
[Crossref]

J. Dai, S. A. Dyakov, and M. Yan, “Enhanced near-field radiative heat transfer between corrugated metal plates: Role of spoof surface plasmon polaritons,” Phys. Rev. B 92, 035419 (2015).
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E. Nefzaoui, Y. Ezzahri, J. Drevillon, and K. Joulain, “Maximal near-field radiative heat transfer between two plates,” Eur. Phys. J. Appl. Phys. 63, 30902 (2013).
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V. Fernández-Hurtado, F. J. García-Vidal, S. Fan, and J. C. Cuevas, “Enhancing near-field radiative heat transfer with si-based metasurfaces,” Phys. Rev. Lett. 118, 203901 (2017).
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K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12, 1616–1619 (2012).
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[Crossref] [PubMed]

Fernández-Hurtado, V.

V. Fernández-Hurtado, F. J. García-Vidal, S. Fan, and J. C. Cuevas, “Enhancing near-field radiative heat transfer with si-based metasurfaces,” Phys. Rev. Lett. 118, 203901 (2017).
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Frandsen, L. H.

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R. Messina, J.-P. Hugonin, J.-J. Greffet, F. Marquier, Y. De Wilde, A. Belarouci, L. Frechette, Y. Cordier, and P. Ben-Abdallah, “Tuning the electromagnetic local density of states in graphene-covered systems via strong coupling with graphene plasmons,” Phys. Rev. B 87, 085421 (2013).
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S. Basu, Z. Zhang, and C. Fu, “Review of near-field thermal radiation and its application to energy conversion,” Int. J. Ener. Res. 33, 1203 (2009).
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C. Fu and Z. Zhang, “Nanoscale radiation heat transfer for silicon at different doping levels,” Int. J. Heat Mass Transf.  49, 1703 (2006).
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Ghebrebrhan, W.

Greffet, J.-J.

R. Messina, J.-P. Hugonin, J.-J. Greffet, F. Marquier, Y. De Wilde, A. Belarouci, L. Frechette, Y. Cordier, and P. Ben-Abdallah, “Tuning the electromagnetic local density of states in graphene-covered systems via strong coupling with graphene plasmons,” Phys. Rev. B 87, 085421 (2013).
[Crossref]

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[Crossref]

E. Rousseau, M. Laroche, and J.-J. Greffet, “Radiative heat transfer at nanoscale mediated by surface plasmons for highly doped silicon,” Appl. Phys. Lett. 95, 231913 (2009).
[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 (2005).
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S. Chen, H. Cheng, H. Yang, J. Li, X. Duan, C. Gu, and J. Tian, “Polarization insensitive and omnidirectional broadband near perfect planar metamaterial absorber in the near infrared regime,” Appl. Phys. Lett. 99, 253104 (2011).
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R. Guérout, J. Lussange, F. S. S. Rosa, J.-P. Hugonin, D. A. R. Dalvit, J.-J. Greffet, A. Lambrecht, and S. Reynaud, “Enhanced near-field thermal radiation and reduced casimir stiction between doped-si gratings,” Phys. Rev. B 85, 180301 (2012).
[Crossref]

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R. Messina, A. Noto, B. Guizal, and M. Antezza, “Radiative heat transfer between metallic gratings using adaptive spatial resolution,” Phys. Rev. B 95, 125404 (2017).
[Crossref]

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

Hamam, R.

Harpoth, A.

Hasman, E.

H. Chalabi, E. Hasman, and M. L. Brongersma, “Effect of shape in near-field thermal transfer for periodic structures,” Phys. Rev. B 91, 174304 (2015).
[Crossref]

H. Chalabi, E. Hasman, and M. L. Brongersma, “Near-field radiative thermal transfer between a nanostructured periodic material and a planar substrate,” Phys. Rev. B 91, 014302 (2015).
[Crossref]

Hsu, C. W.

Hu, L.

L. Hu and S. Chui, “Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials,” Phys. Rev. B 66, 085108 (2002).
[Crossref]

Huang, Y.

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of two inhomogeneous ε(z) slabs (A and B) separated by a vacuum gap of size d along the z direction. The radiative heat transfer (RHT) rate between them depends on their local temperatures TA,B and reflection coefficients A   , B. Associated with each slab is a coordinate system centered at the slab–vacuum interface and pointing away from the gap. (b) Enhancement factor comparing RHT between optimized inhomogeneous (solid lines) or optimized uniform (dashed lines) slabs against that of semi-infinite uniform plates of Re[ε] = −1, at a fixed vacuum wavelength λ = 8 μm, as a function of material loss Im[ε], and for two representative separations d = 10 nm (red) and 500 nm (blue). The black dotted line shows the theoretical bound described by Eq. (3). (c) Transmission coefficient Z corresponding to uniform semi-infinite slabs of ε = 1 (black), finite slabs of optimal thickness topt and permittivity εopt (blue), and inhomogeneous slabs resulting from optimization (red), as a function of the dimensionless wavevector kβ d at fixed d = 10 nm and Im[ε] = 10−2. The inset shows a typical dielectric profile Re[ε(z)] needed to achieve Z 1 over a broad range of kβ. To enhance the readability, two different x-scales are used in the ranges [0, 20] nm and [20, 100] nm, and the points resulting from numerical optimization are connected with segments.

Fig. 2
Fig. 2

(a) Schematic of an inhomogeneous ε(z) slab and a dipole separated by a vacuum gap of size d along the z direction. (b) Dielectric profile Re[ε(z)] corresponding to inhomogeneous slabs optimized to increase RHT from a dipole a distance d = 1 μm away from their z = 0 interface, at a fixed vacuum wavelength λ = 8 μm (frequency ω ≈ 0.785c/d). The profiles are obtained under different constraints on the maximum possible permittivity εmax ≡ max|Re ε| = {5, 40} uniform (upper and lower figures) but correspond to the same Im[ε] = 10−3. (c) Imaginary part of the reflection coefficient Im [ ( k β ) ] at frequency ω as a function of kβ, for optimized inhomogeneous slabs [red and green solid lines, corresponding to the ε profiles in panel (b)], optimized uniform slabs (blue solid line), along with the theoretical bound (black dotted line) described by Eq. (8). (d) LDOS ( k β ) (in SI units) at the location of the dipole and at frequency ω, with the same color convention of panel (c). The inset in (d) shows the kβ-integrated spectrum ( ω ) near ω as a function of the dimensionless frequency (ω′ − ω) Im[ε], indicating that contributions from smaller kβ are increasingly sensitive to the wavelength.

Fig. 3
Fig. 3

(a) Peak LDOS of optimized inhomogeneous slabs (solid lines) and optimized uniform slabs (dashed lines), normalized by the vacuum LDOS 0 ( ω ) = ω 2 π 2 c 3, as a function of the dimensionless separation ωd/c, for multiple material loss rates Im[ε] = {10−1, 10−2, 10−3} (black, blue, and red, respectively). The green dotted line marks the largest possible LDOS in the far field, given by Eq. (10). (b) Enhancement factor comparing the peak LDOS of optimized inhomogeneous and uniform slabs.

Equations (13)

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d R ( z ) d z = 2 i k z m ( z ) 1 r 2 ( z ) [ r ( z ) ( 1 + R 2 ( z ) ) ( 1 + r 2 ( z ) ) R ( z ) ] ,
Z ( k β , ω ) = 4 Im [ A ] Im [ B ] e 2 Im [ k z ] d | 1 A B e 2 Im [ k z ] d | 2
Φ ˜ 0 Φ 0 = 1 8 ln [ | χ spp | 4 4 ( Im χ spp ) 2 ] + 1 2 ,
ε = ( ε ε ε ) , μ = ( μ μ μ ) .
r p i ε / ε ε 1 i ε / ε ε + 1 ,
Im [ ε iso ] 1 2 ( Re [ ε ] Re [ ε ] + Re [ ε ] Re [ ε ] ) Im [ ε ] Im [ ε ] .
D x x = D y y = i 2 0 d k β k z k β ( 1 e 2 i k z d ) , D z z = i 0 d k β k β 3 k z ( 1 + e 2 i k z d ) ,
Im [ ( k ) ] = 1 Im [ ε ] 2 + 4 k 2 ( k 2 1 ) + 2 1 + 4 k 2 ( k 2 1 ) ( k 2 1 ) 1 + 4 k 2 ( k 2 1 ) ,
Re [ ε ( k ) ] = 1 + 1 + 4 k 2 ( k 2 1 ) 2 ( k 2 1 ) .
max { prop } = ( 4 3 + 2 3 ) ω 2 π 2 c 3 ,
p prop = ω 2 π 2 c 3 + ω 2 π 2 c 3 0 k 0 d k β ( k β 3 k z k β k z ) Re [ R p e 2 i k z d ] 2 ω 2 3 π 2 c 3 ( 1 + 2 ) ,
Im [ I ] 2 k 2 1 ε 1 ε 1 ε 2 k 2 ε 1 ( k 2 1 ) + 1 1 ε 2 k 2 1 ,
Im [ II ] 4 ε 1 ε 2 ( ε 2 1 ) ε 1 1 + ε 2 ε 2 2 1 Im [ ε ]

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