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Thermal meta-device in analogue of zero-index photonics

Nature Materials volume 18, pages 48–54 (2019)Cite this article

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Abstract

Inspired by the developments in photonic metamaterials, the concept of thermal metamaterials has promised new avenues for manipulating the flow of heat. In photonics, the existence of natural materials with both positive and negative permittivities has enabled the creation of metamaterials with a very wide range of effective parameters. In contrast, in conductive heat transfer, the available range of thermal conductivities in natural materials is far narrower, strongly restricting the effective parameters of thermal metamaterials and limiting possible applications in extreme environments. Here, we identify a rigorous correspondence between zero index in Maxwell’s equations and infinite thermal conductivity in Fourier’s law. We also propose a conductive system with an integrated convective element that creates an extreme effective thermal conductivity, and hence by correspondence a thermal analogue of photonic near-zero-index metamaterials, a class of metamaterials with crucial importance in controlling light. Synergizing the general properties of zero-index metamaterials and the specific diffusive nature of thermal conduction, we theoretically and experimentally demonstrate a thermal zero-index cloak. In contrast with conventional thermal cloaks, this meta-device can operate in a highly conductive background and the cloaked object preserves great sensitivity to external temperature changes. Our work demonstrates a thermal metamaterial which greatly enhances the capability for molding the flow of heat.

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Fig. 1: The origin of thermal NZIM and its effect in thermal cloaking.
Fig. 2: Steady-state temperature profiles.
Fig. 3: Transient temperature profiles at 500 s and the central temperature evolution with time.
Fig. 4: Experimental verification of a convective thermal zero-index cloak.

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Data availability

The data that support the findings of this study are available from the corresponding author C.-W.Q. upon reasonable request.

References

  1. Narayana, S. & Sato, Y. Heat flux manipulation with engineered thermal materials. Phys. Rev. Lett. 108, 214303 (2012).

    Article  Google Scholar 

  2. Han, T. et al. Theoretical realization of an ultra-efficient thermal-energy harvesting cell made of natural materials. Energy Environ. Sci. 6, 3537–3541 (2013).

    Article  CAS  Google Scholar 

  3. Han, T., Bai, X., Thong, J. T. L., Li, B. & Qiu, C.-W. Full control and manipulation of heat signatures: Cloaking, camouflage and thermal metamaterials. Adv. Mater. 26, 1731–1734 (2014).

    Article  CAS  Google Scholar 

  4. Fan, C. Z., Gao, Y. & Huang, J. P. Shaped graded materials with an apparent negative thermal conductivity. Appl. Phys. Lett. 92, 251907 (2008).

    Article  Google Scholar 

  5. Guenneau, S., Amra, C. & Veynante, D. Transformation thermodynamics: cloaking and concentrating heat flux. Opt. Express 20, 8207–8218 (2012).

    Article  Google Scholar 

  6. Vemuri, K. P. & Bandaru, P. R. Geometrical considerations in the control and manipulation of conductive heat flux in multilayered thermal metamaterials. Appl. Phys. Lett. 103, 133111 (2013).

    Article  Google Scholar 

  7. Schittny, R., Kadic, M., Guenneau, S. & Wegener, M. Experiments on transformation thermodynamics: molding the flow of heat. Phys. Rev. Lett. 110, 195901 (2013).

    Article  Google Scholar 

  8. Xu, H., Shi, X., Gao, F., Sun, H. & Zhang, B. Ultrathin three-dimensional thermal cloak. Phys. Rev. Lett. 112, 054301 (2014).

    Article  Google Scholar 

  9. Han, T. et al. Experimental demonstration of a bilayer thermal cloak. Phys. Rev. Lett. 112, 054302 (2014).

    Article  Google Scholar 

  10. Ma, Y., Liu, Y., Raza, M., Wang, Y. & He, S. Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously. Phys. Rev. Lett. 113, 205501 (2014).

    Article  Google Scholar 

  11. Li, Y., Bai, X., Yang, T., Luo, H. & Qiu, C.-W. Structured thermal surface for radiative camouflage. Nat. Commun. 9, 273 (2018).

    Article  Google Scholar 

  12. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006).

    Article  CAS  Google Scholar 

  13. Li, Y. et al. Temperature-dependent transformation thermotics: from switchable thermal cloaks to macroscopic thermal diodes. Phys. Rev. Lett. 115, 195503 (2015).

    Article  Google Scholar 

  14. Yang, T. Z. et al. Invisible sensors: Simultaneous sensing and camouflaging in multiphysical fields. Adv. Mater. 27, 7752–7758 (2015).

    Article  CAS  Google Scholar 

  15. Liberal, I. & Engheta, N. Near-zero refractive index photonics. Nat. Photon. 11, 149–158 (2017).

    Article  CAS  Google Scholar 

  16. Shalaev, V. M. Optical negative-index metamaterials. Nat. Photon. 1, 41–48 (2007).

    Article  CAS  Google Scholar 

  17. Silveirinha, M. & Engheta, N. Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials. Phys. Rev. Lett. 97, 157403 (2006).

    Article  Google Scholar 

  18. Mahmoud, A. M. & Engheta, N. Wave–matter interactions in epsilon-and-mu-near-zero structures. Nat. Commun. 5, 5638 (2014).

    Article  CAS  Google Scholar 

  19. Suchowski, H. et al. Phase mismatch-free nonlinear propagation in optical zero-index materials. Science 342, 1223–1226 (2013).

    Article  CAS  Google Scholar 

  20. Liberal, I., Mahmoud, A. M., Li, Y., Edwards, B. & Engheta, N. Photonic doping of epsilon-near-zero media. Science 355, 1058–1062 (2017).

    Article  CAS  Google Scholar 

  21. Chu, H. et al. A hybrid invisibility cloak based on integration of transparent metasurfaces and zero-index materials. Light Sci. Appl. 7, 50 (2018).

    Article  Google Scholar 

  22. Alam, M. Z., Schulz, S. A., Upham, J., Leon, I. D. & Boyd, R. W. Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material. Nat. Photon. 12, 79–83 (2018).

    Article  CAS  Google Scholar 

  23. Liberal, I. & Engheta, N. Manipulating thermal emission with spatially static fluctuating fields in arbitrarily shaped epsilon-near-zero bodies. Proc. Natl Acad. Sci. USA 115, 2878–2883 (2018).

    Article  CAS  Google Scholar 

  24. Alam, M. Z., De Leon, I. & Boyd, R. W. Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region. Science 352, 795–797 (2016).

    Article  CAS  Google Scholar 

  25. Huang, X., Lai, Y., Hang, Z. H., Zheng, H. & Chan, C. T. Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nat. Mater. 10, 582–586 (2011).

    Article  CAS  Google Scholar 

  26. Li, Y. et al. On-chip zero-index metamaterials. Nat. Photon. 9, 738–742 (2015).

    Article  CAS  Google Scholar 

  27. Maas, R., Parsons, J., Engheta, N. & Polman, A. Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths. Nat. Photon. 7, 907–912 (2013).

    Article  CAS  Google Scholar 

  28. Leonhardt, U. Optical conformal mapping. Science 312, 1777–1780 (2006).

    Article  CAS  Google Scholar 

  29. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).

    Article  CAS  Google Scholar 

  30. Alù, A. & Engheta, N. Achieving transparency with plasmonic and metamaterial coatings. Phys. Rev. E 72, 016623 (2005).

    Article  Google Scholar 

  31. Bejan, A. Convection Heat Transfer (Wiley, Hoboken, 2013).

  32. Olver, F. W. J. & Maximon, L. C. in NIST Digital Library of Mathematical Functions Ch. 10 (Version 1.0.18, release date 27 March 2018); http://dlmf.nist.gov/10release1.0.18 of2018-03-27.

  33. Torrent, D., Poncelet, O. & Batsale, J.-C. Nonreciprocal thermal material by spatiotemporal modulation. Phys. Rev. Lett. 120, 125501 (2018).

    Article  Google Scholar 

  34. Shen, X. Y. & Huang, J. P. Thermally hiding an object inside a cloak with feeling. Int. J. Heat Mass Trans. 78, 1–6 (2014).

    Article  Google Scholar 

  35. Garnett, J. C. M. Colours in metal glasses, in metallic films, and in metallic solutions. II. Phil. Trans. R. Soc. A 205, 238–288 (1906).

    Article  Google Scholar 

Download references

Acknowledgements

Y.L. and C.-W.Q. acknowledge financial support from the Ministry of Education, Singapore (Project No. R-263-000-C05-112). K.-J.Z. and H.C. are supported by National Key Research Program of China (2016YFA0301101), National Natural Science Foundation of China (61621001), and Natural Science Foundation of Shanghai (18JC1410900). Y.-G.P. and X.-F.Z. are supported by the National Natural Science Foundation of China (Grant Nos. 11690030, 11690032 and 11674119). W.L. and S.F. are supported by Department of Energy Grant No. DE-FG-07ER46426.

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Author notes

  1. These authors contributed equally: Ying Li, Ke-Jia Zhu, Yu-Gui Peng.

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore

    Ying Li, Ke-Jia Zhu, Yu-Gui Peng, He-Xiu Xu & C.-W. Qiu

  2. Key Laboratory of Advanced Micro-structure Materials (MOE) and School of Physics Sciences and Engineering, Tongji University, Shanghai, China

    Ke-Jia Zhu & Hong Chen

  3. School of Physics and Innovation Institute, Huazhong University of Science and Technology, Wuhan, China

    Yu-Gui Peng & Xue-Feng Zhu

  4. Department of Electrical Engineering, Ginzton Laboratory, Stanford University, Stanford, CA, USA

    Wei Li & Shanhui Fan

  5. Department of Mechanics, Tianjin University, Tianjin, China

    Tianzhi Yang

  6. Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, China

    Tianzhi Yang

  7. Air and Missile Defense College, Air Force Engineering University, Xi’an, China

    He-Xiu Xu

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  1. Ying Li
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Contributions

Y.L. and C.-W.Q. conceived the idea. Y.L. designed and performed numerical simulations and theoretical derivations. Y.L., K.-J.Z. and Y.-G.P. performed the experiments. Y.L., W.L., S.F. and C.-W.Q. analysed the numerical results. C.-W.Q. supervised the project. All the authors contributed to the manuscript writing.

Corresponding authors

Correspondence to Shanhui Fan or C.-W. Qiu.

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Supplementary Information

Supplementary Note 1, Supplementary Reference 1, Supplementary Figures 1–5

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Li, Y., Zhu, KJ., Peng, YG. et al. Thermal meta-device in analogue of zero-index photonics. Nature Mater 18, 48–54 (2019). https://doi.org/10.1038/s41563-018-0239-6

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