Design of diamond-shaped transient thermal cloaks with homogeneous isotropic materials

Abstract

Transformation thermodynamics as a major extension of transformation optics has recently received considerable attention. In this paper, we present two-dimensional (2D) and three-dimensional (3D) diamond-shaped transient thermal cloaks with non-singular homogeneous material parameters. The absence of singularity in the parameters results from the fact that the linear coordinate transformation is performed by expanding a line segment rather than a point into a region, while the mechanism behind the homogeneity is the homogeneous stretching and compression along orthogonal directions during the transformation. Although the derived parameters remain anisotropic, we further show that this can be circumvented by considering a layered structure composed of only four types of isotropic materials based on the effective medium theory. Numerical simulation results confirm the good performance of the proposed cloaks.

Keywords

transformation thermodynamics / metamaterials / thermal cloak / effective medium theory

References

[1] J. B. Pendry, D. Schurig, and D. R. Smith, Controlling electromagnetic fields, Science 312(5781), 1780 (2006)

[2] U. Leonhardt, Optical conformal mapping, Science 312(5781), 1777 (2006)

[3] H. Y. Chen, C. T. Chan, and P. Sheng, Transformation optics and metamaterials, Nat. Mater. 9(5), 387 (2010)

[4] D. H. Werner and D. H. Kwon, Transformation Electromagnetics and Metamaterials, London: Springer-Verlag, 2015

[5] W. Li, J. G. Guan, Z. G. Sun, W. Wang, and Q. J. Zhang, A near-perfect invisibility cloak constructed with homogeneous materials, Opt. Express 17(26), 23410 (2009)

[6] D. Bao, E. Kallos, W. X. Tang, C. Argyropoulos, Y. Hao, and T. J. Cui, A broadband simplified free space cloak realized by nonmagnetic dielectric cylinders, Front. Phys. 5(3), 319 (2010)

[7] M. R. Forouzeshfard and M. Hosseini Farzad, Twin invisibility cloak at a distance and its illusory properties, Plasmonics 10(1), 125 (2015)

[8] M. M. Sadeghi, H. Nadgaran, and H. Y. Chen, Perfect field concentrator using zero index metamaterials and perfect electric conductors, Front. Phys. 9(1), 90 (2014)

[9] J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, Coherent beam control with an all-dielectric transformation optics based lens, Sci. Rep. 6, 18819 (2016)

[10] F. Sun and S. L. He, Overlapping illusions by transformation optics without any negative refraction material, Sci. Rep. 6, 19130 (2016)

[11] H. Y. Chen and C. T. Chan, Acoustic cloaking and transformation acoustics, J. Phys. D Appl. Phys. 43(11), 113001 (2010)

[12] M. Farhat, S. Guenneau, and S. Enoch, Ultrabroadband elastic cloaking in thin plates, Phys. Rev. Lett. 103(2), 024301 (2009)

[13] G. R. Mohammadi, A. G. Moghaddam, and R. Mohammadkhani, Coordinate transformations and matter waves cloaking, Phys. Lett. A 380(9–10), 1093 (2016)

[14] W. R. Zhu, I. D. Rukhlenko, and M. Premaratne, Linear transformation optics for plasmonics, J. Opt. Soc. Am. B 29(10), 2659 (2012)

[15] L. W. Zeng and R. X. Song, Controlling chloride ions diffusion in concrete, Sci. Rep. 3, 3359 (2013)

[16] U. Leonhardt, Applied physics: Cloaking of heat, Nature 498(7455), 440 (2013)

[17] C. Z. Fan, Y. Gao, and J. P. Huang, Shaped graded materials with an apparent negative thermal conductivity, Appl. Phys. Lett. 92(25), 251907 (2008)

[18] G. X. Yu, Y. F. Lin, G. Q. Zhang, Z. Yu, L. L. Yu, and J. Su, Design of square-shaped heat flux cloaks and concentrators using method of coordinate transformation, Front. Phys. 6(1), 70 (2011)

[19] T. Z. Yang, L. J. Huang, F. Chen, and W. K. Xu, Heat flux and temperature field cloaks for arbitrarily shaped objects, J. Phys. D Appl. Phys. 46(30), 305102 (2013)

[20] F. C. Mao, T. H. Li, M. Huang, J. J. Yang, and J. C. Chen, Research and design of thermal cloak in arbitary shape, Acta Physica Sinica 63(1), 014401 (2014) (in Chinese)

[21] T. C. Han, T. Yuan, B. W. Li, and C. W. Qiu, Homogeneous thermal cloak with constant conductivity and tunable heat localization, Sci. Rep. 3, 1593 (2013)

[22] S. Narayana and Y. Sato, Heat flux manipulation with engineered thermal materials, Phys. Rev. Lett. 108(21), 214303 (2012)

[23] E. H. Ooi and V. Popov, Transformation thermodynamics for heat flux management based on segmented thermal cloaks, Eur. Phys. J. Appl. Phys. 63(1), 10903 (2013)

[24] S. Guenneau, C. Amra, and D. Veynante, Transformation thermodynamics: Cloaking and concentrating heat flux, Opt. Express 20(7), 8207 (2012)

[25] R. Schittny, M. Kadic, S. Guenneau, and M. Wegener, Experiments on transformation thermodynamics: Molding the flow of heat, Phys. Rev. Lett. 110(19), 195901 (2013)

[26] T. C. Han, X. Bai, J. T. L. Thong, B. W. Li, and C. W. Qiu, Full control and manipulation of heat signatures: Cloaking, camouflage and thermal metamaterials, Adv. Mater. 26(11), 1731 (2014)

[27] T. C. Han, X. Bai, D. L. Gao, J. T. L. Thong, B. W. Li, and C. W. Qiu, Experimental demonstration of a bilayer thermal cloak, Phys. Rev. Lett. 112(5), 054302 (2014)

[28] H. Y. Xu, X. H. Shi, F. Gao, H. D. Sun, and B. L. Zhang, Ultrathin three-dimensional thermal cloak, Phys. Rev. Lett. 112(5), 054301 (2014)

[29] Y. G. Ma, L. Lan, W. Jiang, F. Sun, and S. L. He, A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity, NPG Asia Mater. 5(11), e73 (2013)

[30] X. He and L. Z. Wu, Design of two-dimensional open cloaks with finite material parameters for thermodynamics, Appl. Phys. Lett. 102(21), 211912 (2013)

[31] Y. Gao and J. P. Huang, Unconventional thermal cloak hiding an object outside the cloak, Europhys. Lett. 104(4), 44001 (2013)

[32] R. Hu, X. L. Wei, J. Y. Hu, and X. B. Luo, Local heating realization by reverse thermal cloak, Sci. Rep. 4, 3600 (2014)

[33] D. M. Nguyen, H. Y. Xu, Y. M. Zhang, and B. L. Zhang, Active thermal cloak, Appl. Phys. Lett. 107(12), 121901 (2015)

[34] S. Guenneau and C. Amra, Anisotropic conductivity rotates heat fluxes in transient regimes, Opt. Express 21(5), 6578 (2013)

[35] T. C. Han, J. J. Zhao, T. Yuan, D. Y. Lei, B. W. Li, and C. W. Qiu, Theoretical realization of an ultra-efficient thermalenergy harvesting cell made of natural materials, Energy Environ. Sci. 6(12), 3537 (2013)

[36] Y. C. Liu, F. Sun, and S. L. He, Novel thermal lens for remote heating/cooling designed with transformation optics, Opt. Express 24(6), 5683 (2016)

RIGHTS & PERMISSIONS

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg