Abstract

Remote thermal focusing/refrigeration by suppressing thermal diffusion can be achieved with the help of the novel thermal lens proposed in this paper. Our thermal lens is designed using transformation optics, and has several advantages. Firstly, it is a remote controlling device, i.e. the temperature is increased or decreased only in the heat/cold source and the target points, and the temperature in the area between the source and target points is not influenced. Secondly, the heat/cold sources can move freely inside the lens, and hence the focused points outside the lens can be adjusted dynamically. Numerical simulations are given to verify the novel properties (such as thermal focusing effect, remote refrigeration and remote thermal diffusion suppressing) of the proposed device, which cannot be achieved by any other traditional method.

© 2016 Optical Society of America

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    [Crossref]
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2016 (1)

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

2015 (4)

F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagnetics Res. 151, 169–173 (2015).
[Crossref]

F. Sun and S. He, “Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5, 16032 (2015).
[Crossref] [PubMed]

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

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

2014 (5)

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
[Crossref]

F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014).
[Crossref] [PubMed]

2013 (5)

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013).
[Crossref]

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

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).
[Crossref] [PubMed]

2012 (4)

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

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
[Crossref]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
[Crossref] [PubMed]

2011 (3)

X. Zang and C. Jiang, “Overlapped optics, illusion optics, and an external cloak based on shifting media,” J. Opt. Soc. Am. B 28(8), 1994–2000 (2011).
[Crossref]

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref] [PubMed]

2010 (1)

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

2009 (4)

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

2008 (7)

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

W. Wang, L. Lin, X. Yang, J. Cui, C. Du, and X. Luo, “Design of oblate cylindrical perfect lens using coordinate transformation,” Opt. Express 16(11), 8094–8105 (2008).
[Crossref] [PubMed]

D. H. Kwon and D. H. Werner, “Polarization splitter and polarization rotator designs based on transformation optics,” Opt. Express 16(23), 18731–18738 (2008).
[Crossref] [PubMed]

2007 (3)

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007).
[Crossref]

V. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

2006 (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

2004 (2)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Alekseyev, L. V.

Alù, A.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

Amra, C.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
[Crossref] [PubMed]

Ao, X.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Bagci, H.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

Bao, L.

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

Brun, M.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

Burokur, S. N.

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

Cai, B.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Castaldi, G.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Chan, C.

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

Chan, C. T.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007).
[Crossref]

Chen, H.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007).
[Crossref]

Chen, P. Y.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

Chen, S.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Cui, J.

Cummer, S. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref] [PubMed]

de Lustrac, A.

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

Du, C.

Enoch, S.

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

Fang, G.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Fang, N.

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref] [PubMed]

Farhat, M.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

Galdi, V.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Gao, F.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Genov, D. A.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Guenneau, S.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 5, 9876 (2015).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
[Crossref]

S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
[Crossref] [PubMed]

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

Han, D.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Han, T.

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

He, S.

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

F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagnetics Res. 151, 169–173 (2015).
[Crossref]

F. Sun and S. He, “Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5, 16032 (2015).
[Crossref] [PubMed]

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
[Crossref]

F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014).
[Crossref] [PubMed]

F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013).
[Crossref]

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Hou, B.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Iacobucci, A.

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

Jacob, Z.

Jiang, C.

Jiang, W.

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Kadic, M.

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).
[Crossref] [PubMed]

Kong, J.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Kwon, D. H.

Lai, Y.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Lan, L.

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Legoll, F.

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Li, B.

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

Li, C.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Li, F.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Li, Z.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Lin, L.

Liu, X.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Liu, Y.

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

Luo, X.

Luo, Y.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Ma, Y.

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Meng, X.

C. Li, X. Meng, X. Liu, F. Li, G. Fang, H. Chen, and C. T. Chan, “Experimental realization of a circuit-based broadband illusion-optics analogue,” Phys. Rev. Lett. 105(23), 233906 (2010).
[Crossref] [PubMed]

Moccia, M.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Movchan, A. B.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

M. Farhat, S. Enoch, S. Guenneau, and A. B. Movchan, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid,” Phys. Rev. Lett. 101(13), 134501 (2008).
[Crossref] [PubMed]

Narayana, S.

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

Narimanov, E.

Ng, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Nguyen, D.

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

Olla, S.

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

Pendry, J.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref] [PubMed]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Popa, B. I.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref] [PubMed]

Qiu, C. W.

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

Rahm, M.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Ran, L.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

Raza, M.

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Sato, Y.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

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

Savo, S.

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
[Crossref]

Schittny, R.

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).
[Crossref] [PubMed]

Schurig, D.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Shalaev, V.

V. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

Shi, C.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Shi, X.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Smith, D. R.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Starr, A.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, J. Pendry, M. Rahm, and A. Starr, “Scattering theory derivation of a 3D acoustic cloaking shell,” Phys. Rev. Lett. 100(2), 024301 (2008).
[Crossref] [PubMed]

Stenger, N.

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
[Crossref] [PubMed]

Stoltz, G.

A. Iacobucci, F. Legoll, S. Olla, and G. Stoltz, “Negative thermal conductivity of chains of rotors with mechanical forcing,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 84(6), 061108 (2011).
[Crossref] [PubMed]

Sun, C.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Sun, F.

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

F. Sun and S. He, “Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5, 16032 (2015).
[Crossref] [PubMed]

F. Sun and S. He, “Homogenous optic-null medium performs as optical surface transformation,” Prog. Electromagnetics Res. 151, 169–173 (2015).
[Crossref]

F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014).
[Crossref] [PubMed]

F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
[Crossref]

F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013).
[Crossref]

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Sun, H.

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Tichit, P.-H.

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

Veynante, D.

Wang, W.

Wang, Y.

Y. Ma, Y. Liu, M. Raza, Y. Wang, and S. He, “Experimental demonstration of a multiphysics cloak: manipulating heat flux and electric current simultaneously,” Phys. Rev. Lett. 113(20), 205501 (2014).
[Crossref] [PubMed]

Wegener, M.

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).
[Crossref] [PubMed]

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
[Crossref] [PubMed]

Wen, W.

H. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. 102(18), 183903 (2009).
[Crossref] [PubMed]

Werner, D. H.

Wilhelm, M.

N. Stenger, M. Wilhelm, and M. Wegener, “Experiments on elastic cloaking in thin plates,” Phys. Rev. Lett. 108(1), 014301 (2012).
[Crossref] [PubMed]

Xia, C.

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref] [PubMed]

Xiao, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Xu, H.

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

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Xue, X.

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

Yang, X.

Yuan, T.

T. Han, T. Yuan, B. Li, and C. W. Qiu, “Homogeneous thermal cloak with constant conductivity and tunable heat localization,” Sci. Rep. 3(4), 1593 (2013).
[PubMed]

Zang, X.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

X. Zang and C. Jiang, “Overlapped optics, illusion optics, and an external cloak based on shifting media,” J. Opt. Soc. Am. B 28(8), 1994–2000 (2011).
[Crossref]

Zhang, B.

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

H. Xu, X. Shi, F. Gao, H. Sun, and B. Zhang, “Experimental demonstration of an ultra-thin three-dimensional thermal cloak,” Phys. Rev. Lett. 112(5), 054301 (2014).
[Crossref] [PubMed]

Zhang, J.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
[Crossref]

Zhang, S.

F. Sun, S. Zhang, and S. He, “A general method for designing a radome to enhance the scanning angle of a phased array antenna,” Prog. Electromagnetics Res. 145, 203–212 (2014).
[Crossref]

S. Zhang, C. Xia, and N. Fang, “Broadband acoustic cloak for ultrasound waves,” Phys. Rev. Lett. 106(2), 024301 (2011).
[Crossref] [PubMed]

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Zhang, X.

S. Zhang, D. A. Genov, C. Sun, and X. Zhang, “Cloaking of matter waves,” Phys. Rev. Lett. 100(12), 123002 (2008).
[Crossref] [PubMed]

Zhang, Y.

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

Zhang, Z. Q.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Zhu, Y.

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

Appl. Phys. Lett. (4)

H. Chen and C. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007).
[Crossref]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” Appl. Phys. Lett. 91(18), 183518 (2007).
[Crossref]

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94(6), 061903 (2009).
[Crossref]

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

J. Appl. Phys. (1)

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Ultradirective antenna via transformation optics,” J. Appl. Phys. 105(10), 104912 (2009).
[Crossref]

J. Glaciology Geocryology (1)

L. Ran, X. Xue, and L. Bao, “Applications and Technical Characteristics of Thermal Pipe Subgrade in Qinghai-Tibet Railway Design,” J. Glaciology Geocryology 26, 151–154 (2004).

J. Opt. Soc. Am. B (1)

Nat. Photonics (1)

V. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

NPG Asia Mater. (1)

Y. Ma, L. Lan, W. Jiang, F. Sun, and S. He, “A transient thermal cloak experimentally realized through a rescaled diffusion equation with anisotropic thermal diffusivity,” NPG Asia Mater. 5, e75 (2013).

Opt. Commun. (1)

Z. Li, X. Zang, B. Cai, C. Shi, and Y. Zhu, “Cloaks and antiobject-independent illusion optics based on illusion media,” Opt. Commun. 308(11), 95–99 (2013).
[Crossref]

Opt. Express (4)

Photonics Nanostruct. Fundam. Appl. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photonics Nanostruct. Fundam. Appl. 6(1), 87–95 (2008).
[Crossref]

Phys. Rev. B (2)

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77(12), 125127 (2008).
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M. Farhat, S. Guenneau, and S. Enoch, “Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates,” Phys. Rev. B 85(2), 020301 (2012).
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Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

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Phys. Rev. Lett. (13)

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Phys. Rev. X (1)

M. Moccia, G. Castaldi, S. Savo, Y. Sato, and V. Galdi, “Independent manipulation of heat and electrical current via bifunctional metamaterials,” Phys. Rev. X 4(2), 021025 (2014).
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F. Sun and S. He, “DC magnetic concentrator and omnidirectional cascaded cloak by using only one or two homogeneous anisotropic materials of positive permeability,” Prog. Electromagnetics Res. 142, 683–699 (2013).
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Sci. Rep. (5)

F. Sun and S. He, “Optical Surface Transformation: Changing the optical surface by homogeneous optic-null medium at will,” Sci. Rep. 5, 16032 (2015).
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F. Sun and S. He, “Extending the scanning angle of a phased array antenna by using a null-space medium,” Sci. Rep. 4, 6832 (2014).
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Figures (5)

Fig. 1
Fig. 1 The basic scheme of the thermal lens by transformation optics. The blue lines form squares with the size denoted by the length of their diagonal lines: 2a and 2b. The yellow suns in the blue line squares denote the thermal sources in the virtual space (a) and the real space (b), respectively. (a) The whole virtual space is the free space (i.e. no thermal materials are utilized). (b) The sun in the dotted line square is the image of the real heat source in the green thermal lens in the real space. The green shell is the proposed thermal lens that can transform the thermal source in real space to its image position, which is consistent with the same position in the virtual space outside the shell.
Fig. 2
Fig. 2 Simulation result of the thermal focusing effect, represented by a plot of the temperature distribution. The two arrows point to the thermal source and the focusing point, respectively.
Fig. 3
Fig. 3 Simulation result of the remote refrigeration effect, represented by a plot of the temperature distribution. The two arrows point to the cold source and the refrigeration point, respectively.
Fig. 4
Fig. 4 Numerical simulation results for remotely suppressing thermal diffusion: (a) with the thermal lens and a source with low temperature; (b) without the lens and the cold source; (c) temperature distribution on the line that has been marked in (a) and (b) along the y-direction near the thermal source.
Fig. 5
Fig. 5 Thermal conductivity distribution of the thermal lens. (a), (b) and (c) denote three components of the thermal conductivity tensor. (a) shows the x-x component, κxx = −5.11 for regions I & IV, and κxx = 2.68 for regions II & III. (b) shows the x-y component, κxy = 3.20 for regions I & II, and κxy = −3.20 for regions III & IV. (c) shows the y-y component, κyy = −2.20 for regions I & IV, and κyy = 4.20 for regions II & III.

Equations (6)

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x ' = { b a d b + a x d d b + a y + d d b + a b ,for region I b a d + b a x + d d b + a y d d + b a b ,for region II b a d + b a x d d + b a y d d + b a b ,for region III b a d b + a x + d d b + a y + d d b + a b ,for region IV y ' = y , z ' = z ,
κ ' = [ ( P 2 + Q 2 ) P Q P Q P 1 P ] κ ,
s i g n ( x ) = { 1 x > 0 0 x = 0 - 1 x < 0 .
[ κ 0 0 κ ] = [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] [ κ x x κ x y κ x y κ y y ] [ cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) ] ,
θ = 1 2 arc tan ( 2 κ x y κ x x κ y y ) ,
{ κ = cos 2 θ κ x x + sin 2 θ κ y y + 2 sin θ cos θ κ x y κ = sin 2 θ κ x x + cos 2 θ κ y y 2 sin θ cos θ κ x y .

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