volume | PIER Journals

Abstract

Most three-dimensional omnidirectional cloaks proposed to date (using optics, electromagnetics, and acoustics) are not easily realized, as they possess inhomogeneous and singular parameters imposed by the transformation-optic method. In this study, we theoretically demonstrate that a thermodynamic spherical cloak with homogeneous and finite conductivity and employing only naturally available conductive materials may be achieved. More interestingly, the thermal localization inside the coating layer can be tuned by anisotropy, which may lead to nearly perfect functionality in an incomplete cloak. The practical realization of such a homogeneous thermal cloak by using two naturally occurring materials has been suggested, which provides an unprecedentedly plausible way to flexibly achieve a thermal cloak and manipulate heat flow. Numerical experiments validate the excellent performance of the proposed homogeneous cloak functions.

1. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, 1780-1782, 2006.
doi:10.1126/science.1125907

2. Leonhardt, U., "Science," Science, Vol. 312, 1777-1780, 2006.
doi:10.1126/science.1126493

3. Schurig, D., J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science, Vol. 314, 977-980, 2006.
doi:10.1126/science.1133628

4. Kante, B., D. Germain, and A. Lustrac, "Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies," Phys. Rev. B, Vol. 80, 201104, 2009.
doi:10.1103/PhysRevB.80.201104

5. Han, T. C., X. H. Tang, and F. Xiao, "The petal-shaped cloak," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 14--15, 2055-2062, 2009.
doi:10.1163/156939309789932511

6. Han, T. C., C.-W. Qiu, and X. H. Tang, "Creating rigorous open cloaks," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 13, 1839-1847, 2010.

7. Cummer, S. A., R. P. Liu, and T. J. Cui, "A rigorous and nonsingular two dimensional cloaking coordinate transformation," J. of Appl. Phys., Vol. 105, 056102, 2009.
doi:10.1063/1.3080155

8. Li, J. and J. B. Pendry, "Hiding under the carpet: A new strategy for cloaking," Phys. Rev. Lett., Vol. 101, 203901, 2008.
doi:10.1103/PhysRevLett.101.203901

9. Liu, R., C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, "Broadband ground-plane cloak," Science, Vol. 323, 366-369, 2009.
doi:10.1126/science.1166949

10. Valentine, J., J. Li, T. Zentgraf, G. Bartal, and X. Zhang, "An optical cloak made of dielectrics," Nat. Mater., Vol. 8, 568-571, 2009.
doi:10.1038/nmat2461

11. Gabrielli, L. H., J. Cardenas, C. B. Poitras, and M. Lipson, "Silicon nanostructure cloak operating at optical frequencies," Nat. Photon., Vol. 3, 461-463, 2009.
doi:10.1038/nphoton.2009.117

12. Zhang, B., Y. Luo, X. Liu, and G. Barbastathis, "Macroscopic invisibility cloak for visible light," Phys. Rev. Lett., Vol. 106, 033901, 033901.

13. Chen, X., Y. Luo, J. Zhang, K. Jiang, J. B. Pendry, and S. Zhang, "Macroscopic invisibility cloaking of visible light," Nat. Commun., Vol. 2, 176, 2011.
doi:10.1038/ncomms1176

14. Ma, T. J. Cui and T. J. Cui, "Three-dimensional broadband ground-plane cloak made of metamaterials," Nat. Commun., Vol. 1, No. 21, 2010.

15. Ergin, T., N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, "Three-dimensional invisibility cloak at optical wavelengths," Science, Vol. 328, 337-339, 2010.
doi:10.1126/science.1186351

16. Sanchez, A., C. Navau, J. Prat-Camps, and D. X. Chen, "Antimagnets: Controlling magnetic fields with superconductor- metamaterial hybrids," New J. Phys., Vol. 13, 093034, 2011.
doi:10.1088/1367-2630/13/9/093034

17. Gomory, , F., M. Solovyov, J. ·Souc, C. Navau, J. Part-Camps, and A. Sanchez, "Experimental realization of a magnetic cloak," Science, Vol. 335, 1466-1468, 2012.
doi:10.1126/science.1218316

18. Jiang, W. X., C. Y. Luo, Z. L. Mei, and T. J. Cui, "An ultrathin but nearly perfect direct current electric cloak," Appl. Phys. Lett. , Vol. 102, 014102, 2013.
doi:10.1063/1.4774301

19. Chen, H. and C. T. Chan, "Acoustic cloaking in three dimensions using acoustic metamaterials," Appl. Phys. Lett., Vol. 91, 183518, 2007.
doi:10.1063/1.2803315

20. Zhang, S., C. Xia, and N. Fang, "Broadband acoustic cloak for ultrasound waves," Phys. Rev. Lett., Vol. 106, 24301, 2011.
doi:10.1103/PhysRevLett.106.024301

21. Zhang, S., D. A. Genov, C. Sun, and X. Zhang, "Cloaking of matter waves," Phys. Rev. Lett., Vol. 100, 123002, 2008.
doi:10.1103/PhysRevLett.100.123002

22. Brun, M., S. Guenneau, and A. B. Movchan, "Achieving control of in-plane elastic waves," Appl. Phys. Lett., Vol. 94, 061903, 2009.
doi:10.1063/1.3068491

23. Milton, G. W., M. Briane, and J. R. Willis, "On cloaking for elasticity and physical equations with a transformation invariant form," New J. Phys., Vol. 8, 248, 2006.
doi:10.1088/1367-2630/8/10/248

24. Fan, C., Y. Gao, and J. Huang, "Shaped graded materials with an apparent negative thermal conductivity," Appl. Phys. Lett. , Vol. 92, 251907, 2008.
doi:10.1063/1.2951600

25. Chen, T., C. N. Weng, and J. S. Chen, "Cloak for curvilinearly anisotropic media in conduction," Appl. Phys. Lett., Vol. 93, 114103, 2008.
doi:10.1063/1.2988181

26. Li, J., Y. Gao, and J. Huang, "A bifunctional cloak using transformation media," J. Appl. Phys., Vol. 108, 074504, 2010.
doi:10.1063/1.3490226

27. Guenneau, S., C. Amra, and D. Veynante, "Transformation thermodynamics: Cloaking and concentrating heat flux," Opt. Express, Vol. 20, 8207-8218, 2012.
doi:10.1364/OE.20.008207

28. Schittny, R., M. Kadic, S. Guenneau, and M. Wegener, "Experiments on transformation thermodynamics: Molding the flow of heat," Phys. Rev. Lett., Vol. 110, 195901, 2013.
doi:10.1103/PhysRevLett.110.195901

29. Narayana, S. and Y. Sato, "Heat flux manipulation with engineered thermal materials," Phys. Rev. Lett., Vol. 108, 214303, 2012.
doi:10.1103/PhysRevLett.108.214303

30. Han, T. C., T. Yuan, B. W. Li, and C. W. Qiu, "Homogeneous thermal cloak with constant conductivity and tunable heat localization," Scientific Reports, Vol. 3, 1593, 2013.

31. Guenneau, S. and T. M. Puvirajesinghe, "Fick's second law transformed: One path to cloaking in mass diffusion," J. R. Soc. Interface, Vol. 10, 20130106, 2013.

Dr. Tiancheng Han

Dr. Zheng-Mao Wu