Research Papers: Radiative Heat Transfer

Application Conditions of Effective Medium Theory in Near-Field Radiative Heat Transfer Between Multilayered Metamaterials

[+] Author and Article Information
X. L. Liu, T. J. Bright

George W. Woodruff
School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332

Z. M. Zhang

George W. Woodruff
School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: zhuomin.zhang@me.gatech.edu

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 20, 2014; final manuscript received May 14, 2014; published online June 27, 2014. Assoc. Editor: Zhixiong Guo.

J. Heat Transfer 136(9), 092703 (Jun 27, 2014) (8 pages) Paper No: HT-14-1143; doi: 10.1115/1.4027802 History: Received March 20, 2014; Revised May 14, 2014

This work addresses the validity of the local effective medium theory (EMT) in predicting the near-field radiative heat transfer between multilayered metamaterials, separated by a vacuum gap. Doped silicon and germanium are used to form the metallodielectric superlattice. Different configurations are considered by setting the layers adjacent to the vacuum spacer as metal–metal (MM), metal–dielectric (MD), or dielectric–dielectric (DD) (where M refers to metallic doped silicon and D refers to dielectric germanium). The calculation is based on fluctuational electrodynamics using the Green's function formulation. The cutoff wave vectors for surface plasmon polaritons (SPPs) and hyperbolic modes are evaluated. Combining the Bloch theory with the cutoff wave vector, the application condition of EMT in predicting near-field radiative heat transfer is presented quantitatively and is verified by exact calculations based on the multilayer formulation.

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Shalaev, V. M., 2007, “Optical Negative-Index Metamaterials,” Nat. Photonics, 1, pp. 41–48. [CrossRef]
Noginov, M., Lapine, M., Podolskiy, V., and Kivshar, Y., 2013, “Focus Issue: Hyperbolic Metamaterials,” Opt. Express, 21, pp. 14895–14897. [CrossRef] [PubMed]
Liu, X. L., and Zhang, Z. M., 2013, “Metal-Free Low-Loss Negative Refraction in the Mid-Infrared Region,” Appl. Phys. Lett., 103, p. 103101. [CrossRef]
Yao, J., Liu, Z. W., Liu, Y. M., Wang, Y., Sun, C., Bartal, G., Stacy, A. M., and Zhang, X., 2008, “Optical Negative Refraction in Bulk Metamaterials of Nanowires,” Science, 321, p. 930. [CrossRef] [PubMed]
Jacob, Z., Alekseyev, L. V., and Narimanov, E., 2006, “Optical Hyperlens: Far-Field Imaging Beyond the Diffraction Limit,” Opt. Express, 14, pp. 8247–8256. [CrossRef] [PubMed]
Liu, Z. W., Lee, H., Xiong, Y., Sun, C., and Zhang, X., 2007, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science, 315, p. 1686. [CrossRef] [PubMed]
Liu, X. L., Wang, L. P., and Zhang, Z. M., 2013, “Wideband Tunable Omnidirectional Infrared Absorbers Based on Doped-Silicon Nanowire Arrays,” ASME J. Heat Transfer, 135(6), p. 061602. [CrossRef]
Choy, T. C., 1999, Effective Medium Theory: Principles and Applications, Oxford University, Oxford, UK.
Narayanaswamy, A., Shen, S., Hu, L., Chen, X. Y., and Chen, G., 2009, “Breakdown of the Planck Blackbody Radiation Law at Nanoscale Gaps,” Appl. Phys. A: Mater. Sci. Process., 96, pp. 357–362. [CrossRef]
Rousseau, E., Siria, A., Jourdan, G., Volz, S., Comin, F., Chevrier, J., and Greffet, J. J., 2009, “Radiative Heat Transfer at the Nanoscale,” Nat. Photonics, 3, pp. 514–517. [CrossRef]
Ottens, R. S., Quetschke, V., Wise, S., Alemi, A. A., Lundock, R., Mueller, G., Reitze, D. H., Tanner, D. B., and Whiting, B. F., 2011, “Near-Field Radiative Heat Transfer Between Macroscopic Planar Surfaces,” Phys. Rev. Lett., 107, p. 014301. [CrossRef] [PubMed]
Kralik, T., Hanzelka, P., Zobac, M., Musilova, V., Fort, T., and Horak, M., 2012, “Strong Near-Field Enhancement of Radiative Heat Transfer Between Metallic Surfaces,” Phys. Rev. Lett., 109, p. 224302. [CrossRef] [PubMed]
Zhang, Z. M., 2007, Nano/Microscale Heat Transfer, McGraw-Hill, New York.
Liu, B., and Shen, S., 2013, “Broadband Near-Field Radiative Thermal Emitter/Absorber Based on Hyperbolic Metamaterials: Direct Numerical Simulation by the Wiener Chaos Expansion Method,” Phys. Rev. B, 87, p. 115403. [CrossRef]
Liu, X. L., Zhang, R. Z., and Zhang, Z. M., 2013, “Near-Field Thermal Radiation Between Hyperbolic Metamaterials: Graphite and Carbon Nanotubes,” Appl. Phys. Lett., 103, p. 213102. [CrossRef]
Biehs, S. A., Tschikin, M., and Ben-Abdallah, P., 2012, “Hyperbolic Metamaterials as an Analog of a Blackbody in the Near Field,” Phys. Rev. Lett., 109, p. 104301. [CrossRef] [PubMed]
Dimatteo, R. S., Greiff, P., Finberg, S. L., Young-Waithe, K. A., Choy, H. K. H., Masaki, M. M., and Fonstad, C. G., 2001, “Enhanced Photogeneration of Carriers in a Semiconductor Via Coupling Across a Nonisothermal Nanoscale Vacuum Gap,” Appl. Phys. Lett., 79, pp. 1894–1896. [CrossRef]
Laroche, M., Carminati, R., and Greffet, J. J., 2006, “Near-Field Thermophotovoltaic Energy Conversion,” J. Appl. Phys., 100, p. 063704. [CrossRef]
Park, K., Basu, S., King, W. P., and Zhang, Z. M., 2008, “Performance Analysis of Near-Field Thermophotovoltaic Devices Considering Absorption Distribution,” J. Quant. Spectrosc. Radiat. Transfer, 109, pp. 305–316. [CrossRef]
Simovski, C., Maslovski, S., Nefedov, I., and Tretyakov, S., 2013, “Optimization of Radiative Heat Transfer in Hyperbolic Metamaterials for Thermophotovoltaic Applications,” Opt. Express, 21, pp. 14988–15013. [CrossRef] [PubMed]
Messina, R., and Ben-Abdallah, P., 2013, “Graphene-Based Photovoltaic Cells for Near-Field Thermal Energy Conversion,” Sci. Rep., 3, p. 1083. [CrossRef]
Francoeur, M., Vaillon, R., and Mengüç, M. P., 2011, “Thermal Impacts on the Performance of Nanoscale-Gap Thermophotovoltaic Power Generators,” IEEE Trans. Energy Convers., 26, pp. 686–698. [CrossRef]
Bright, T. J., Wang, L. P., and Zhang, Z. M., 2014, “Performance of Near-Field Thermophotovoltaic Cells Enhanced With a Backside Reflector,” ASME J. Heat Transfer, 136, p. 062701. [CrossRef]
Ilic, O., Jablan, M., Joannopoulos, J. D., Celanovic, I., and Soljačić, M., 2012, “Overcoming the Black Body Limit in Plasmonic and Graphene Near-Field Thermophotovoltaic Systems,” Opt. Express, 20, pp. A366–A384. [CrossRef] [PubMed]
Otey, C. R., Lau, W. T., and Fan, S., 2010, “Thermal Rectification Through Vacuum,” Phys. Rev. Lett., 104, p. 154301. [CrossRef] [PubMed]
Basu, S., and Francoeur, M., 2011, “Near-Field Radiative Transfer Based Thermal Rectification Using Doped Silicon,” Appl. Phys. Lett., 98, p. 113106. [CrossRef]
Zhu, L., Otey, C. R., and Fan, S., 2013, “Ultrahigh-Contrast and Large-Bandwidth Thermal Rectification in Near-Field Electromagnetic Thermal Transfer Between Nanoparticles,” Phys. Rev. B, 88, p. 184301. [CrossRef]
Yang, Y., Basu, S., and Wang, L., 2013, “Radiation-Based Near-Field Thermal Rectification With Phase Transition Materials,” Appl. Phys. Lett., 103, p. 163101. [CrossRef]
Wang, L. P., and Zhang, Z. M., 2013, “Thermal Rectification Enabled by Near-Field Radiative Heat Transfer Between Intrinsic Silicon and a Dissimilar Material,” Nanoscale Microscale Thermophys. Eng., 17, pp. 337–348. [CrossRef]
Biehs, S.-A., Rosa, F. S. S., and Ben-Abdallah, P., 2011, “Modulation of Near-Field Heat Transfer Between Two Gratings,” Appl. Phys. Lett., 98, p. 243102. [CrossRef]
Cui, L., Huang, Y., Wang, J., and Zhu, K.-Y., 2013, “Ultrafast Modulation of Near-Field Heat Transfer With Tunable Metamaterials,” Appl. Phys. Lett., 102, p. 053106. [CrossRef]
Van Zwol, P. J., Joulain, K., Abdallah, P. B., Greffet, J. J., and Chevrier, J., 2011, “Fast Nanoscale Heat-Flux Modulation With Phase-Change Materials,” Phys. Rev. B, 83, p. 201404. [CrossRef]
Ben-Abdallah, P., and Biehs, S.-A., 2014, “Near-Field Thermal Transistor,” Phys. Rev. Lett., 112, p. 044301. [CrossRef] [PubMed]
Biehs, S. A., Ben-Abdallah, P., Rosa, F. S. S., Joulain, K., and Greffet, J. J., 2011, “Nanoscale Heat Flux Between Nanoporous Materials,” Opt. Express, 19, pp. A1088–A1103. [CrossRef] [PubMed]
Guo, Y., Cortes, C. L., Molesky, S., and Jacob, Z., 2012, “Broadband Super-Planckian Thermal Emission From Hyperbolic Metamaterials,” Appl. Phys. Lett., 101, p. 131106. [CrossRef]
Guo, Y., and Jacob, Z., 2013, “Thermal Hyperbolic Metamaterials,” Opt. Express, 21, pp. 15014–15019. [CrossRef] [PubMed]
Liu, B., Shi, J., Liew, K., and Shen, S., 2014, “Near-Field Radiative Heat Transfer for Si Based Metamaterials,” Opt. Commun., 314, pp. 57–65. [CrossRef]
Orlov, A. A., Voroshilov, P. M., Belov, P. A., and Kivshar, Y. S., 2011, “Engineered Optical Nonlocality in Nanostructured Metamaterials,” Phys. Rev. B, 84, p. 045424. [CrossRef]
Tschikin, M., Biehs, S. A., Messina, R., and Ben-Abdallah, P., 2013, “On the Limits of the Effective Description of Hyperbolic Materials in the Presence of Surface Waves,” J. Opt., 15, p. 105101. [CrossRef]
Basu, S., Lee, B. J., and Zhang, Z. M., 2010, “Infrared Radiative Properties of Heavily Doped Silicon at Room Temperature,” ASME J. Heat Transfer, 132(2), p. 023301. [CrossRef]
Liu, X. L., Zhang, R. Z., and Zhang, Z. M., 2014, “Near-Field Radiative Heat Transfer With Doped-Silicon Nanostructured Metamaterials,” Int. J. Heat Mass Transfer, 73, pp. 389–398. [CrossRef]
Francoeur, M., Menguc, M. P., and Vaillon, R., 2009, “Solution of Near-Field Thermal Radiation in One-Dimensional Layered Media Using Dyadic Green's Functions and the Scattering Matrix Method,” J. Quant. Spectrosc. Radiat. Transfer, 110, pp. 2002–2018. [CrossRef]
Zheng, Z., and Xuan, Y., 2011, “Theory of Near-Field Radiative Heat Transfer for Stratified Magnetic Media,” Int. J. Heat Mass Transfer, 54, pp. 1101–1110. [CrossRef]
Narayanaswamy, A., and Chen, G., 2004, “Thermal Emission Control With One-Dimensional Metallodielectric Photonic Crystals,” Phys. Rev. B, 70, p. 125101. [CrossRef]
Bimonte, G., and Santamato, E., 2007, “General Theory of Electromagnetic Fluctuations Near a Homogeneous Surface in Terms of Its Reflection Amplitudes,” Phys. Rev. A, 76, p. 013810. [CrossRef]
Guérout, R., Lussange, J., Rosa, F. S. S., Hugonin, J. P., Dalvit, D. A. R., Greffet, J. J., Lambrecht, A., and Reynaud, S., 2012, “Enhanced Radiative Heat Transfer Between Nanostructured Gold Plates,” Phys. Rev. B, 85, p. 180301. [CrossRef]
Bright, T. J., Liu, X. L., and Zhang, Z. M., 2014, “Energy Streamlines in Near-Field Radiative Heat Transfer Between Hyperbolic Metamaterials,” Opt. Express22, pp. A1112–A1127. [CrossRef] [PubMed]
Kidwai, O., Zhukovsky, S. V., and Sipe, J. E., 2012, “Effective-Medium Approach to Planar Multilayer Hyperbolic Metamaterials: Strengths and Limitations,” Phys. Rev. A, 85, p. 053842. [CrossRef]
Basu, S., and Zhang, Z. M., 2009, “Ultrasmall Penetration Depth in Nanoscale Thermal Radiation,” Appl. Phys. Lett., 95, pp. 133103–133104. [CrossRef]
Mulet, J.-P., Joulain, K., Carminati, R., and Greffet, J.-J., 2002, “Enhanced Radiative Heat Transfer at Nanometric Distances,” Microscale Thermophys. Eng., 6, pp. 209–222. [CrossRef]
Francoeur, M., Mengüç, M. P., and Vaillon, R., 2011, “Coexistence of Multiple Regimes for Near-Field Thermal Radiation Between Two Layers Supporting Surface Phonon Polaritons in the Infrared,” Phys. Rev. B, 84, p. 075436. [CrossRef]
Shen, S., Mavrokefalos, A., Sambegoro, P., and Chen, G., 2012, “Nanoscale Thermal Radiation Between Two Gold Surfaces,” Appl. Phys. Lett., 100, p. 233114. [CrossRef]
Wang, X. J., Basu, S., and Zhang, Z. M., 2009, “Parametric Optimization of Dielectric Functions for Maximizing Nanoscale Radiative Transfer,” J. Phys. D: Appl. Phys., 42, p. 245403. [CrossRef]
Basu, S., and Zhang, Z. M., 2009, “Maximum Energy Transfer in Near-Field Thermal Radiation at Nanometer Distances,” J. Appl. Phys., 105, p. 093535. [CrossRef]
Biehs, S. A., Rousseau, E., and Greffet, J. J., 2010, “Mesoscopic Description of Radiative Heat Transfer at the Nanoscale,” Phys. Rev. Lett., 105, p. 234301. [CrossRef] [PubMed]
Pendry, J. B., 1999, “Radiative Exchange of Heat Between Nanostructures,” J. Phys.: Condens. Matter, 11, pp. 6621–6633. [CrossRef]


Grahic Jump Location
Fig. 1

Illustration of radiative heat transfer between two multilayered metamaterials (at temperatures T1 and T2, respectively) separated by a vacuum gap of distance d. Note that tm and td are the thicknesses of D-Si (metallic behavior) and Ge (dielectric), respectively. The resulting period is P = tm + td.

Grahic Jump Location
Fig. 2

Effective dielectric function components for (a) f = 0.5 and (b) f = 0.8. Shaded regions denote hyperbolic dispersion (type I or type II).

Grahic Jump Location
Fig. 3

Total near-field radiative heat flux for different configurations as a function of gap distance: (a) s-polarization, f = 0.5; (b) s-polarization, f = 0.8; (c) p-polarization, f = 0.5 and (d) p-polarization, f = 0.8. The frequency region covering most of thermal radiation is chosen from 2 × 1012 rad/s to 4 × 1014 rad/s.

Grahic Jump Location
Fig. 4

Spectral near-field radiative heat flux for different configurations at gap distance d = 10 nm for f = 0.5: (a) s-polarization and (b) p-polarization

Grahic Jump Location
Fig. 5

Spectral heat flux at different distances for p-polarization with f = 0.5: (a) d = 100 nm; (b) d = 200 nm; and (c) d = 300 nm

Grahic Jump Location
Fig. 6

Transmission coefficient contours ξp(ω,β) for (a) effective medium, different hyperbolic region are delineated; (b) MM; (c) MD; and (d) DD

Grahic Jump Location
Fig. 7

Loss-dependent cutoff wave vector at the surface resonance frequency. The numerically calculated values are based on Eq. (10). The fitted curve given in Eq. (11) and that from Biehs et al. [55] are also shown.




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