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How to control and manipulate the heat flow in a flexible way is a hotspot of current research. Based on Laplace's equation, we propose a method to design thermal cloak of arbitrary shape. For a thermal cloak of regular shape, the thermal conductivity expression is derived by analytically solving the Laplace's equation under certain boundary conditions; for a thermal cloak of irregular shape, the distribution of thermal conductivity can also be obtained based on the numerical solution of Laplace's equation. Results of full wave simulation show that no heat fluxes emerge in the internal stealth area both for two-dimensional and three-dimensional thermal cloak of arbitrary shape. Meanwhile, the heat fluxes return to their original pathways, resulting in a perfect thermal invisible effect. This research provides a feasible method to design a thermal cloak of non-conformal cross section and has a guiding significance for the design and manufacturing of thermal cloak.
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Keywords:
- thermal cloak /
- Laplace equation /
- arbitrary shape /
- metamaterials
[1] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[2] Pendry J B 2000 Phy. Rev. Lett. 85 3966
[3] Yang J J, Huang M, Yang C F, Xiao Z, Peng J H 2009 Optics Express 17 19656
[4] Wu Q, Zhang K, Meng F Y, Li L W 2010 Acta Phys. Sin. 59 6071(in Chinese) [吴群, 张狂, 孟繁义, 李乐伟 2010 59 6071]
[5] Zheludev N I, Kivshar Y S 2012 Nature Materials 11 917
[6] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[7] Hu J, Zhou X M, Hu G K 2009 Optics Express 17 1308
[8] Luo X Y, Liu D Y, Liu J J, Dong J F 2014 Chin. Phys. B 23 054101
[9] Yan M, Yan W, Qiu M 2008 Phys. Rev. B 78 125113
[10] Li C, Meng X K, Liu X, Li F, Fang G Y, Chen H Y, Chan C T 2010 Phys. Rev. Lett. 105 233906
[11] Yu G X, Cui T J, Jiang W 2009 J. Infrared. Millim. W. 30 633
[12] Chen H Y, Chan C T, Sheng P 2010 Nature materials 9 387
[13] Wang Z, Dong J F, Liu J J, Luo X Y 2012 Acta Phys. Sin. 61 204101(in Chinese) [王战, 董建峰, 刘锦景, 罗孝阳 2012 61 204101]
[14] Fan C Z, Gao Y, Huang J P 2008 Appl. Phys. Lett. 92 251907
[15] Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901
[16] Guenneau S, Amra C, Veynante D 2012 Optics Express 20 8207
[17] Yang T Z, Huang L J, Chen F, Xu W K 2013 J. Phys. D: Appl. Phys. 46 305102
[18] Han T C, Yuan T, Li B W, Qiu C W 2013 Scientific Reports 3 1593
[19] Mao F C, Li T H, Huang M, Yang J J, Chen J C 2014 Acta Phys. Sin. 63 014401(in Chinese) [毛福春, 李廷华, 黄铭, 杨晶晶, 陈俊昌 2014 63 014401]
[20] Courant R, Hilbert D 1991 Methods of Mathematical Physics (Weinheim: Wiley-VCH) pp110-112
[21] Hu J, Zhou X M, Hu G K 2009 Comput. Mater. Sci. 46 708
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[1] Shelby R A, Smith D R, Schultz S 2001 Science 292 77
[2] Pendry J B 2000 Phy. Rev. Lett. 85 3966
[3] Yang J J, Huang M, Yang C F, Xiao Z, Peng J H 2009 Optics Express 17 19656
[4] Wu Q, Zhang K, Meng F Y, Li L W 2010 Acta Phys. Sin. 59 6071(in Chinese) [吴群, 张狂, 孟繁义, 李乐伟 2010 59 6071]
[5] Zheludev N I, Kivshar Y S 2012 Nature Materials 11 917
[6] Pendry J B, Schurig D, Smith D R 2006 Science 312 1780
[7] Hu J, Zhou X M, Hu G K 2009 Optics Express 17 1308
[8] Luo X Y, Liu D Y, Liu J J, Dong J F 2014 Chin. Phys. B 23 054101
[9] Yan M, Yan W, Qiu M 2008 Phys. Rev. B 78 125113
[10] Li C, Meng X K, Liu X, Li F, Fang G Y, Chen H Y, Chan C T 2010 Phys. Rev. Lett. 105 233906
[11] Yu G X, Cui T J, Jiang W 2009 J. Infrared. Millim. W. 30 633
[12] Chen H Y, Chan C T, Sheng P 2010 Nature materials 9 387
[13] Wang Z, Dong J F, Liu J J, Luo X Y 2012 Acta Phys. Sin. 61 204101(in Chinese) [王战, 董建峰, 刘锦景, 罗孝阳 2012 61 204101]
[14] Fan C Z, Gao Y, Huang J P 2008 Appl. Phys. Lett. 92 251907
[15] Schittny R, Kadic M, Guenneau S, Wegener M 2013 Phys. Rev. Lett. 110 195901
[16] Guenneau S, Amra C, Veynante D 2012 Optics Express 20 8207
[17] Yang T Z, Huang L J, Chen F, Xu W K 2013 J. Phys. D: Appl. Phys. 46 305102
[18] Han T C, Yuan T, Li B W, Qiu C W 2013 Scientific Reports 3 1593
[19] Mao F C, Li T H, Huang M, Yang J J, Chen J C 2014 Acta Phys. Sin. 63 014401(in Chinese) [毛福春, 李廷华, 黄铭, 杨晶晶, 陈俊昌 2014 63 014401]
[20] Courant R, Hilbert D 1991 Methods of Mathematical Physics (Weinheim: Wiley-VCH) pp110-112
[21] Hu J, Zhou X M, Hu G K 2009 Comput. Mater. Sci. 46 708
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