Abstract

In the context of scattering cancellation, design of an arbitrarily-shaped cloak for simultaneous manipulations of thermal and electric fields has been proposed. The integral equations governing the static thermal and electric phenomena for the objects with arbitrary shapes are formulated, respectively, and the discrete dipole approximation (DDA) approach is used to solve the thermal and electric field integral equations. An eigenvalue analysis has been developed to explore the relationship of the thermal-electric fields with the eigenvalues of the matrices obtained by the DDA. With the relationship, an analytical formulation is derived to determine the thermal and electric constitute parameters of the cloak. An optimization procedure is developed to achieve an optimal performance of the cloak. Some numerical examples are given to demonstrate good performance of the proposed bifunctional cloak.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

2016 (4)

L. Zhang, Y. Shi, and C. H. Liang, “Achieving illusion and invisibility of inhomogeneous cylinders and spheres,” J. Opt. 18(8), 085101 (2016).
[Crossref]

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Corrigendum: Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 6(1), 19321 (2016).
[Crossref] [PubMed]

C. W. Lan, K. Bi, Z. H. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

L. Zhang, Y. Shi, and C. H. Liang, “Optimal illusion and invisibility of multilayered anisotropic cylinders and spheres,” Opt. Express 24(20), 23333–23352 (2016).
[Crossref] [PubMed]

2015 (9)

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensor: Simultaneous sensing and camflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

M. Raza, Y. Liu, and Y. Ma, “A multi-cloak bifunctional device,” J. Appl. Phys. 117(2), 4130 (2015).
[Crossref]

F. Yang, Z. L. Mei, W. X. Jiang, and T. J. Cui, “Electromagnetic illusion with isotropic and homogeneous materials through scattering manipulation,” J. Opt. 17(10), 105610 (2015).
[Crossref]

N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015).
[Crossref]

J. C. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alu, “Multiband and wideband bilayer mantle cloaks,” IEEE Trans. Antenn. Propag. 63(7), 3235–3240 (2015).
[Crossref]

M. D. Guild, A. J. Hicks, M. R. Haberman, A. Alù, and P. S. Wilson, “Acoustic scattering cancellation of irregular objects surrounded by spherical layers in the resonant regime,” J. Appl. Phys. 118(16), 016623 (2015).
[Crossref]

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

Y. Shi, W. Tang, L. Li, and C. H. Liang, “Three-dimensional complementary invisibility cloak with arbitrary shapes,” IEEE Antennas Wirel. Propag. Lett. 14, 1550–1553 (2015).
[Crossref]

Y. Shi, L. Zhang, W. Tang, L. Li, and C. H. Liang, “Design of a minimized complementary illusion cloak with arbitrary position,” Int. J. Antenn. Propag. 2015, 932495 (2015).

2014 (4)

Y. Shi, W. Tang, and C. H. Liang, “A minimized invisibility complementary cloak with a composite shape,” IEEE Antennas Wirel. Propag. Lett. 13, 1800–1803 (2014).
[Crossref]

K. P. Vemuri, F. M. Canbazoglu, and P. R. Bandaru, “Guiding conductive heat flux through thermal meatmaterials,” Appl. Phys. Lett. 105(19), 193904 (2014).
[Crossref]

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. 26(5), e73 (2014).

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]

2013 (2)

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]

W. X. Jiang, C. W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusion using wave dynamics in meatmaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

2012 (1)

W. Akl and A. Baz, “Analysis and experimental demonstration of an active acoustic metamaterial cell,” J. Appl. Phys. 111(4), 044505 (2012).
[Crossref]

2011 (2)

P. Y. Chen and A. Alú, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 3825–3833 (2011).
[Crossref]

V. L. Y. Vincent, M. P. Mengüç, and T. A. Nieminen, “Discrete-dipole approximation with surface interaction: Computational toolbox for MATLAB,” J. Quant. Spectrosc. Ra. 112(11), 1711–1725 (2011).
[Crossref]

2010 (1)

J. Y. Li, Y. Gao, and J. P. Huang, “A bifunctional cloak using transformation media,” J. Appl. Phys. 108(7), 074504 (2010).
[Crossref]

2009 (1)

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

2008 (4)

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).
[Crossref]

T. Chen, C. N. Weng, and J. S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93(11), 685 (2008).
[Crossref]

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

W. Yan, M. Yan, Z. Ruan, and M. Liu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[Crossref]

2007 (1)

2006 (3)

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

D. Schurig, 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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8(10), 248 (2006).
[Crossref]

2005 (1)

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

1994 (1)

1991 (1)

1973 (1)

E. Purcell and C. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186(2), 705–714 (1973).
[Crossref]

1968 (1)

V. G. Leselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Phys. Uspekhi 10(4), 509–514 (1968).
[Crossref]

Akl, W.

W. Akl and A. Baz, “Analysis and experimental demonstration of an active acoustic metamaterial cell,” J. Appl. Phys. 111(4), 044505 (2012).
[Crossref]

Alu, A.

J. C. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alu, “Multiband and wideband bilayer mantle cloaks,” IEEE Trans. Antenn. Propag. 63(7), 3235–3240 (2015).
[Crossref]

Alú, A.

P. Y. Chen and A. Alú, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 3825–3833 (2011).
[Crossref]

Alù, A.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Corrigendum: Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 6(1), 19321 (2016).
[Crossref] [PubMed]

M. D. Guild, A. J. Hicks, M. R. Haberman, A. Alù, and P. S. Wilson, “Acoustic scattering cancellation of irregular objects surrounded by spherical layers in the resonant regime,” J. Appl. Phys. 118(16), 016623 (2015).
[Crossref]

A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights,” Opt. Express 15(6), 3318–3332 (2007).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

Amra, C.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Corrigendum: Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 6(1), 19321 (2016).
[Crossref] [PubMed]

Bagci, H.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Corrigendum: Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 6(1), 19321 (2016).
[Crossref] [PubMed]

Bai, X.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensor: Simultaneous sensing and camflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Bandaru, P. R.

K. P. Vemuri, F. M. Canbazoglu, and P. R. Bandaru, “Guiding conductive heat flux through thermal meatmaterials,” Appl. Phys. Lett. 105(19), 193904 (2014).
[Crossref]

Baz, A.

W. Akl and A. Baz, “Analysis and experimental demonstration of an active acoustic metamaterial cell,” J. Appl. Phys. 111(4), 044505 (2012).
[Crossref]

Bi, K.

C. W. Lan, K. Bi, Z. H. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

Bilotti, F.

J. C. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alu, “Multiband and wideband bilayer mantle cloaks,” IEEE Trans. Antenn. Propag. 63(7), 3235–3240 (2015).
[Crossref]

Briane, M.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8(10), 248 (2006).
[Crossref]

Calvo, D. C.

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

Canbazoglu, F. M.

K. P. Vemuri, F. M. Canbazoglu, and P. R. Bandaru, “Guiding conductive heat flux through thermal meatmaterials,” Appl. Phys. Lett. 105(19), 193904 (2014).
[Crossref]

Chen, H. B.

N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015).
[Crossref]

Chen, J. S.

T. Chen, C. N. Weng, and J. S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93(11), 685 (2008).
[Crossref]

Chen, P. Y.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Corrigendum: Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 6(1), 19321 (2016).
[Crossref] [PubMed]

P. Y. Chen and A. Alú, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 3825–3833 (2011).
[Crossref]

Chen, T.

T. Chen, C. N. Weng, and J. S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93(11), 685 (2008).
[Crossref]

Cheng, Q.

N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015).
[Crossref]

Cui, T. J.

N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015).
[Crossref]

F. Yang, Z. L. Mei, W. X. Jiang, and T. J. Cui, “Electromagnetic illusion with isotropic and homogeneous materials through scattering manipulation,” J. Opt. 17(10), 105610 (2015).
[Crossref]

W. X. Jiang, C. W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusion using wave dynamics in meatmaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Cummer, S. A.

D. Schurig, 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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Draine, B. T.

Engheta, N.

A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights,” Opt. Express 15(6), 3318–3332 (2007).
[Crossref] [PubMed]

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[Crossref] [PubMed]

Enoch, S.

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

Fan, C. Z.

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).
[Crossref]

Farhat, M.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Corrigendum: Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 6(1), 19321 (2016).
[Crossref] [PubMed]

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

Flatau, P. J.

Gao, D.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensor: Simultaneous sensing and camflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Gao, Y.

J. Y. Li, Y. Gao, and J. P. Huang, “A bifunctional cloak using transformation media,” J. Appl. Phys. 108(7), 074504 (2010).
[Crossref]

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).
[Crossref]

Gao, Z. H.

C. W. Lan, K. Bi, Z. H. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

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]

Goodman, J. J.

Guenneau, S.

M. Farhat, P. Y. Chen, H. Bagci, C. Amra, S. Guenneau, and A. Alù, “Corrigendum: Thermal invisibility based on scattering cancellation and mantle cloaking,” Sci. Rep. 6(1), 19321 (2016).
[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, “Ultrabroadband elastic cloaking in thin plates,” Phys. Rev. Lett. 103(2), 024301 (2009).
[Crossref] [PubMed]

Guild, M. D.

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

M. D. Guild, A. J. Hicks, M. R. Haberman, A. Alù, and P. S. Wilson, “Acoustic scattering cancellation of irregular objects surrounded by spherical layers in the resonant regime,” J. Appl. Phys. 118(16), 016623 (2015).
[Crossref]

Haberman, M. R.

M. D. Guild, A. J. Hicks, M. R. Haberman, A. Alù, and P. S. Wilson, “Acoustic scattering cancellation of irregular objects surrounded by spherical layers in the resonant regime,” J. Appl. Phys. 118(16), 016623 (2015).
[Crossref]

Han, T. C.

W. X. Jiang, C. W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusion using wave dynamics in meatmaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

He, S.

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]

He, S. L.

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. 26(5), e73 (2014).

Hicks, A. J.

M. D. Guild, A. J. Hicks, M. R. Haberman, A. Alù, and P. S. Wilson, “Acoustic scattering cancellation of irregular objects surrounded by spherical layers in the resonant regime,” J. Appl. Phys. 118(16), 016623 (2015).
[Crossref]

Huang, J. P.

J. Y. Li, Y. Gao, and J. P. Huang, “A bifunctional cloak using transformation media,” J. Appl. Phys. 108(7), 074504 (2010).
[Crossref]

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).
[Crossref]

Jiang, W.

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. 26(5), e73 (2014).

Jiang, W. X.

N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015).
[Crossref]

F. Yang, Z. L. Mei, W. X. Jiang, and T. J. Cui, “Electromagnetic illusion with isotropic and homogeneous materials through scattering manipulation,” J. Opt. 17(10), 105610 (2015).
[Crossref]

W. X. Jiang, C. W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusion using wave dynamics in meatmaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Justice, B. J.

D. Schurig, 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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

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]

Lan, C. W.

C. W. Lan, K. Bi, Z. H. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

Lan, L.

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. 26(5), e73 (2014).

Layman, C. N.

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

Leselago, V. G.

V. G. Leselago, “The electrodynamics of substances with simultaneously negative values of permittivity and permeability,” Phys. Uspekhi 10(4), 509–514 (1968).
[Crossref]

Li, B.

C. W. Lan, K. Bi, Z. H. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensor: Simultaneous sensing and camflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Li, J. Y.

J. Y. Li, Y. Gao, and J. P. Huang, “A bifunctional cloak using transformation media,” J. Appl. Phys. 108(7), 074504 (2010).
[Crossref]

Li, L.

Y. Shi, W. Tang, L. Li, and C. H. Liang, “Three-dimensional complementary invisibility cloak with arbitrary shapes,” IEEE Antennas Wirel. Propag. Lett. 14, 1550–1553 (2015).
[Crossref]

Y. Shi, L. Zhang, W. Tang, L. Li, and C. H. Liang, “Design of a minimized complementary illusion cloak with arbitrary position,” Int. J. Antenn. Propag. 2015, 932495 (2015).

Liang, C. H.

L. Zhang, Y. Shi, and C. H. Liang, “Achieving illusion and invisibility of inhomogeneous cylinders and spheres,” J. Opt. 18(8), 085101 (2016).
[Crossref]

L. Zhang, Y. Shi, and C. H. Liang, “Optimal illusion and invisibility of multilayered anisotropic cylinders and spheres,” Opt. Express 24(20), 23333–23352 (2016).
[Crossref] [PubMed]

Y. Shi, L. Zhang, W. Tang, L. Li, and C. H. Liang, “Design of a minimized complementary illusion cloak with arbitrary position,” Int. J. Antenn. Propag. 2015, 932495 (2015).

Y. Shi, W. Tang, L. Li, and C. H. Liang, “Three-dimensional complementary invisibility cloak with arbitrary shapes,” IEEE Antennas Wirel. Propag. Lett. 14, 1550–1553 (2015).
[Crossref]

Y. Shi, W. Tang, and C. H. Liang, “A minimized invisibility complementary cloak with a composite shape,” IEEE Antennas Wirel. Propag. Lett. 13, 1800–1803 (2014).
[Crossref]

Liu, M.

W. Yan, M. Yan, Z. Ruan, and M. Liu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[Crossref]

Liu, Y.

M. Raza, Y. Liu, and Y. Ma, “A multi-cloak bifunctional device,” J. Appl. Phys. 117(2), 4130 (2015).
[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]

Ma, H. F.

N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015).
[Crossref]

Ma, Y.

M. Raza, Y. Liu, and Y. Ma, “A multi-cloak bifunctional device,” J. Appl. Phys. 117(2), 4130 (2015).
[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]

Ma, Y. G.

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. 26(5), e73 (2014).

Martin, T. P.

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

Mei, Z. L.

F. Yang, Z. L. Mei, W. X. Jiang, and T. J. Cui, “Electromagnetic illusion with isotropic and homogeneous materials through scattering manipulation,” J. Opt. 17(10), 105610 (2015).
[Crossref]

Mengüç, M. P.

V. L. Y. Vincent, M. P. Mengüç, and T. A. Nieminen, “Discrete-dipole approximation with surface interaction: Computational toolbox for MATLAB,” J. Quant. Spectrosc. Ra. 112(11), 1711–1725 (2011).
[Crossref]

Milton, G. W.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8(10), 248 (2006).
[Crossref]

Mock, J. J.

D. Schurig, 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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Monti, A.

J. C. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alu, “Multiband and wideband bilayer mantle cloaks,” IEEE Trans. Antenn. Propag. 63(7), 3235–3240 (2015).
[Crossref]

Naify, C. J.

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

Niarchos, D.

R. Tarkhanyan and D. Niarchos, “Coexisting of thermal and electric cloaking effects in bi-layer nanoporous composite,” International Congress on Advanced Electromagnetic Materials in Microwave and Optics (Oxford, 2015), pp. 304–306.
[Crossref]

Nicholas, M.

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

Nieminen, T. A.

V. L. Y. Vincent, M. P. Mengüç, and T. A. Nieminen, “Discrete-dipole approximation with surface interaction: Computational toolbox for MATLAB,” J. Quant. Spectrosc. Ra. 112(11), 1711–1725 (2011).
[Crossref]

Orris, G. J.

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

Pendry, J. B.

D. Schurig, 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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

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

Pennypacker, C.

E. Purcell and C. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186(2), 705–714 (1973).
[Crossref]

Purcell, E.

E. Purcell and C. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186(2), 705–714 (1973).
[Crossref]

Qiu, C. W.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensor: Simultaneous sensing and camflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

W. X. Jiang, C. W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusion using wave dynamics in meatmaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Raza, M.

M. Raza, Y. Liu, and Y. Ma, “A multi-cloak bifunctional device,” J. Appl. Phys. 117(2), 4130 (2015).
[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]

Rohde, C. A.

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

Ruan, Z.

W. Yan, M. Yan, Z. Ruan, and M. Liu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[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.

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

D. Schurig, 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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Shi, Y.

Y. Shi and L. Zhang, “Cloaking design for arbitrarily shape objects based on characteristic mode method,” Opt. Express 25(26), 32263–32279 (2017).
[Crossref]

L. Zhang, Y. Shi, and C. H. Liang, “Optimal illusion and invisibility of multilayered anisotropic cylinders and spheres,” Opt. Express 24(20), 23333–23352 (2016).
[Crossref] [PubMed]

L. Zhang, Y. Shi, and C. H. Liang, “Achieving illusion and invisibility of inhomogeneous cylinders and spheres,” J. Opt. 18(8), 085101 (2016).
[Crossref]

Y. Shi, W. Tang, L. Li, and C. H. Liang, “Three-dimensional complementary invisibility cloak with arbitrary shapes,” IEEE Antennas Wirel. Propag. Lett. 14, 1550–1553 (2015).
[Crossref]

Y. Shi, L. Zhang, W. Tang, L. Li, and C. H. Liang, “Design of a minimized complementary illusion cloak with arbitrary position,” Int. J. Antenn. Propag. 2015, 932495 (2015).

Y. Shi, W. Tang, and C. H. Liang, “A minimized invisibility complementary cloak with a composite shape,” IEEE Antennas Wirel. Propag. Lett. 13, 1800–1803 (2014).
[Crossref]

Smith, D. R.

D. Schurig, 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 314(5801), 977–980 (2006).
[Crossref] [PubMed]

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

Soric, J. C.

J. C. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alu, “Multiband and wideband bilayer mantle cloaks,” IEEE Trans. Antenn. Propag. 63(7), 3235–3240 (2015).
[Crossref]

Starr, A. F.

D. Schurig, 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 314(5801), 977–980 (2006).
[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.

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. 26(5), e73 (2014).

Tang, W.

Y. Shi, W. Tang, L. Li, and C. H. Liang, “Three-dimensional complementary invisibility cloak with arbitrary shapes,” IEEE Antennas Wirel. Propag. Lett. 14, 1550–1553 (2015).
[Crossref]

Y. Shi, L. Zhang, W. Tang, L. Li, and C. H. Liang, “Design of a minimized complementary illusion cloak with arbitrary position,” Int. J. Antenn. Propag. 2015, 932495 (2015).

Y. Shi, W. Tang, and C. H. Liang, “A minimized invisibility complementary cloak with a composite shape,” IEEE Antennas Wirel. Propag. Lett. 13, 1800–1803 (2014).
[Crossref]

Tarkhanyan, R.

R. Tarkhanyan and D. Niarchos, “Coexisting of thermal and electric cloaking effects in bi-layer nanoporous composite,” International Congress on Advanced Electromagnetic Materials in Microwave and Optics (Oxford, 2015), pp. 304–306.
[Crossref]

Thangawng, A. L.

C. A. Rohde, T. P. Martin, M. D. Guild, C. N. Layman, C. J. Naify, M. Nicholas, A. L. Thangawng, D. C. Calvo, and G. J. Orris, “Experimental demonstration of underwater acoustic scattering cancellation,” Sci. Rep. 5(1), 13175 (2015).
[Crossref] [PubMed]

Thong, J. T.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensor: Simultaneous sensing and camflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Toscano, A.

J. C. Soric, A. Monti, A. Toscano, F. Bilotti, and A. Alu, “Multiband and wideband bilayer mantle cloaks,” IEEE Trans. Antenn. Propag. 63(7), 3235–3240 (2015).
[Crossref]

Vemuri, K. P.

K. P. Vemuri, F. M. Canbazoglu, and P. R. Bandaru, “Guiding conductive heat flux through thermal meatmaterials,” Appl. Phys. Lett. 105(19), 193904 (2014).
[Crossref]

Vincent, V. L. Y.

V. L. Y. Vincent, M. P. Mengüç, and T. A. Nieminen, “Discrete-dipole approximation with surface interaction: Computational toolbox for MATLAB,” J. Quant. Spectrosc. Ra. 112(11), 1711–1725 (2011).
[Crossref]

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]

Weng, C. N.

T. Chen, C. N. Weng, and J. S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93(11), 685 (2008).
[Crossref]

Willis, J. R.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8(10), 248 (2006).
[Crossref]

Wilson, P. S.

M. D. Guild, A. J. Hicks, M. R. Haberman, A. Alù, and P. S. Wilson, “Acoustic scattering cancellation of irregular objects surrounded by spherical layers in the resonant regime,” J. Appl. Phys. 118(16), 016623 (2015).
[Crossref]

Wu, L.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensor: Simultaneous sensing and camflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Xiang, N.

N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015).
[Crossref]

Yan, M.

W. Yan, M. Yan, Z. Ruan, and M. Liu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[Crossref]

Yan, W.

W. Yan, M. Yan, Z. Ruan, and M. Liu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10(4), 043040 (2008).
[Crossref]

Yang, F.

F. Yang, Z. L. Mei, W. X. Jiang, and T. J. Cui, “Electromagnetic illusion with isotropic and homogeneous materials through scattering manipulation,” J. Opt. 17(10), 105610 (2015).
[Crossref]

Yang, T.

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensor: Simultaneous sensing and camflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Zhang, L.

Y. Shi and L. Zhang, “Cloaking design for arbitrarily shape objects based on characteristic mode method,” Opt. Express 25(26), 32263–32279 (2017).
[Crossref]

L. Zhang, Y. Shi, and C. H. Liang, “Achieving illusion and invisibility of inhomogeneous cylinders and spheres,” J. Opt. 18(8), 085101 (2016).
[Crossref]

L. Zhang, Y. Shi, and C. H. Liang, “Optimal illusion and invisibility of multilayered anisotropic cylinders and spheres,” Opt. Express 24(20), 23333–23352 (2016).
[Crossref] [PubMed]

Y. Shi, L. Zhang, W. Tang, L. Li, and C. H. Liang, “Design of a minimized complementary illusion cloak with arbitrary position,” Int. J. Antenn. Propag. 2015, 932495 (2015).

Zhang, S.

W. X. Jiang, C. W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusion using wave dynamics in meatmaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

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]

Zhao, J.

N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015).
[Crossref]

Zhou, J.

C. W. Lan, K. Bi, Z. H. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

Adv. Funct. Mater. (1)

W. X. Jiang, C. W. Qiu, T. C. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusion using wave dynamics in meatmaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Adv. Mater. (1)

T. Yang, X. Bai, D. Gao, L. Wu, B. Li, J. T. Thong, and C. W. Qiu, “Invisible sensor: Simultaneous sensing and camflaging in multiphysical fields,” Adv. Mater. 27(47), 7752–7758 (2015).
[Crossref] [PubMed]

Appl. Phys. Express (1)

N. Xiang, Q. Cheng, H. B. Chen, J. Zhao, W. X. Jiang, H. F. Ma, and T. J. Cui, “Bifunctional metasurface for electromagnetic cloaking and illusion,” Appl. Phys. Express 8(9), 092601 (2015).
[Crossref]

Appl. Phys. Lett. (4)

K. P. Vemuri, F. M. Canbazoglu, and P. R. Bandaru, “Guiding conductive heat flux through thermal meatmaterials,” Appl. Phys. Lett. 105(19), 193904 (2014).
[Crossref]

T. Chen, C. N. Weng, and J. S. Chen, “Cloak for curvilinearly anisotropic media in conduction,” Appl. Phys. Lett. 93(11), 685 (2008).
[Crossref]

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).
[Crossref]

C. W. Lan, K. Bi, Z. H. Gao, B. Li, and J. Zhou, “Achieving bifunctional cloak via combination of passive and active schemes,” Appl. Phys. Lett. 109(20), 201903 (2016).
[Crossref]

Astrophys. J. (1)

E. Purcell and C. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astrophys. J. 186(2), 705–714 (1973).
[Crossref]

IEEE Antennas Wirel. Propag. Lett. (2)

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Int. J. Antenn. Propag. (1)

Y. Shi, L. Zhang, W. Tang, L. Li, and C. H. Liang, “Design of a minimized complementary illusion cloak with arbitrary position,” Int. J. Antenn. Propag. 2015, 932495 (2015).

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram for static thermal problem.
Fig. 2
Fig. 2 Comparison of potential and temperature distributions between the original object and the coated object. (a) potential distribution of original object. (b) potential distribution of coated object with optimized coating. (c) temperature distribution of original object. (b) temperature distribution of coated object with optimized coating.
Fig. 3
Fig. 3 Variation of the optimization function with material parameters of the coating. (a) Electric optimization function. (b) Thermal optimization function.
Fig. 4
Fig. 4 Potential and temperature deformation parameters on the reference line. (a) Potential deformation. (b) Temperature deformation.
Fig. 5
Fig. 5 Variation of the optimized function with material parameters of the coating. (a) Electric optimization function. (b) Thermal optimization function.
Fig. 6
Fig. 6 Comparison of temperature and potential distributions on the reference line between the illusion object, coated object with initial design, and coated object with optimized design. (a) Temperature distribution (b) Potential distribution.
Fig. 7
Fig. 7 The cubic cloak for the cubic object.
Fig. 8
Fig. 8 Variation of the optimized function with material parameters of the coating. (a) Electric optimization function. (b) Thermal optimization function.
Fig. 9
Fig. 9 Potential and temperature deformations on the observation line in xoy and xoz planes for different rotation angles. (a) Potential deformation in xoy plane. (b) Temperature deformation in xoy plane. (c) Potential deformation in xoz plane. (d) Temperature deformation in xoz plane.
Fig. 10
Fig. 10 The cloak design for the spherical object. (a) Variation of the electric optimized function with material parameters of the coating. (b) Variation of the thermal optimized function with material parameters of the coating. (c) Potential deformation on the reference line. (d) Temperature deformation on the reference line.

Equations (37)

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2 T= q ˙ v κ 0
2 ϕ= ρ ε 0
f= 1 4πυ V ζ( r ) | r r | d v
f={ T for thermal ϕ for electric , ζ={ q ˙ v for thermal ρ for electric , υ={ κ 0 for thermal ε 0 for electric
q =0
q =κT
( κ 0 T)=[ ( κ 0 +κ)T ]
Q =( κ 0 +κ)T
T s = 1 4π κ 0 V ( r r ) Q ( r ) | r r | 3 d v
T= T s + T 0 = T 0 + 1 4π κ 0 V ( r r ) Q ( r ) | r r | 3 d v
T( r j ) 1 4π κ 0 V j ( r r ) Q ( r ) | r r | 3 d v = T 0 ( r j )+ 1 4π κ 0 l=1 lj N ( r j r l ) Q ( r l ) | r j r l | 3 Δ V l = T 0 ( r j )+ 1 4π κ 0 l=1 lj N | r j r l |cos θ jl | r j r l | 3 Q( r l )Δ V l
T( r j ) 1 4π κ 0 V j ( r r ) Q ( r ) | r r | 3 d v = T 0 ( r j )+ l=1 lj N G T ( r j , r l ) p l H
G T ( r j , r l )= 1 4π κ 0 1 | r j r l | 3
p j H = α j H { T( r j ) 1 4π κ 0 V j ( r r ) Q ( r ) | r r | 3 d v }
A ¯ H p ¯ H = T ¯ 0
A ij H ={ 1 4π κ 0 | r i r j | 3 ij 1/ α j T i=j
A ¯ E p ¯ E = ϕ ¯ 0
A ij E ={ 1 4π ε 0 | r i r j | 3 ij 1/ α j E i=j
α l S = 3 d 3 4π m l m 0 m l +2 m 0 S=H,E
m={ κ S=H ε S=E
U S = j=1 N 1 4π m 0 r 3 p j S (S=H,E)
U S ={ T S=H ϕ S=E
A ¯ S q ¯ k S = λ k S q ¯ k S (S=H,E and k=1,,N)
( q ¯ k S ) T A ¯ k S q ¯ k S =1
p ¯ S = k=1 N ( q ¯ k S ) T U ¯ 0 S λ k S q ¯ k S
U ¯ 0 S ={ T ¯ 0 S=H ϕ ¯ 0 S=E
U S = 1 4π m 0 r 3 λ k S W k=1 N [ ( q ¯ k S ) T U ¯ 0 S ] q ¯ k S
A ¯ Q S p ¯ Q S = U ¯ 0 S (S=H,E;Q=coated,illusion)
Trace{ [ A ¯ coated S ] 1 }=Trace{ [ A ¯ illusion S ] 1 }
j=1 N α j,coated S = j=1 N α j,illusion S
N 1 α orignal S + N 2 α coating S =N α illusion S
ε 2 / ε 0 κ 2 / κ 0 = 2N η e E 2 N 1 η 1 E + N 2 2N η e H 2 N 1 η 1 H + N 2 N η e H + N 1 η 1 H + N 2 N η e E + N 1 η 1 E + N 2
η 1 E = ε 1 ε 0 ε 1 +2 ε 0 , η e E = ε e ε 0 ε e +2 ε 0 , η 1 H = κ 1 κ 0 κ 1 +2 κ 0 , η e H = κ e κ 0 κ e +2 κ 0
ε 2 / ε 0 κ 2 / κ 0 = C 1 ε 1 +2 ε 0 C 2 ε 1 + ε 0 C 2 κ 1 + κ 0 C 1 κ 1 +2 κ 0
C 1 = (η2) (η+1) C 2 = (η+1) (2η1) ,η= N 2 N 1
De=| U coated S U Illusion S |
δ= 1 L L Dedl

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