Abstract

Thermal radiation is a universal property for all objects with temperatures above 0K. Every object with a specific shape and emissivity has its own thermal radiation signature; such signature allows the object to be detected and recognized which can be an undesirable situation. In this paper, we apply transformation optics theory to a thermal radiation problem to develop an electromagnetic illusion by controlling the thermal radiation signature of a given object. Starting from the fluctuation dissipation theorem where thermally fluctuating sources are related to the radiative losses, we demonstrate that it is possible for objects residing in two spaces, virtual and physical, to have the same thermal radiation signature if the complex permittivities and permeabilities satisfy the standard space transformations. We emphasize the invariance of the fluctuation electrodynamics physics under transformation, and show how this result allows the mimicking in thermal radiation. We illustrate the concept using the illusion paradigm in the two-dimensional space and a numerical calculation validates all predictions. Finally, we discuss limitations and extensions of the proposed technique.

© 2017 Optical Society of America

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References

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    [Crossref]

2017 (1)

A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017).
[Crossref] [PubMed]

2016 (9)

C. Khandekar, W. Jin, O. D. Miller, A. Pick, and A. W. Rodriguez, “Giant frequency-selective near-field energy transfer in active\ passive structures,” Phys. Rev. B 94(11), 115402 (2016).
[Crossref]

R. Zhao, Y. Luo, and J. B. Pendry, “Transformation optics applied to van der Waals interactions,” Sci. Bull. 61(1), 59–67 (2016).
[Crossref]

C. García-Meca and C. Barceló, “Nontensorial Transformation Optics,” Phys. Rev. Appl. 5(6), 064008 (2016).
[Crossref]

K. Chen and S. Fan, “Nonequilibrium Casimir Force with a Nonzero Chemical Potential for Photons,” Phys. Rev. Lett. 117(26), 267401 (2016).
[Crossref] [PubMed]

M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt. 18(4), 044002 (2016).
[Crossref]

T. Han and C.-W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
[Crossref]

C. Henkel, “Nanoscale Thermal Transfer – An Invitation to Fluctuation Electrodynamics,” Z. Für Naturforschung A 72, 99–108 (2016).

J. Zhang, M. Wubs, P. Ginzburg, G. Wurtz, and A. V. Zayats, “Transformation quantum optics: designing spontaneous emission using coordinate transformations,” J. Opt. 18(4), 044029 (2016).
[Crossref]

M. Morshed Behbahani, E. Amooghorban, and A. Mahdifar, “Spontaneous emission and the operation of invisibility cloaks,” Phys. Rev. A 94(1), 013854 (2016).
[Crossref]

2015 (2)

D. L. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
[Crossref]

K. Chen, P. Santhanam, S. Sandhu, L. Zhu, and S. Fan, “Heat-flux control and solid-state cooling by regulating chemical potential of photons in near-field electromagnetic heat transfer,” Phys. Rev. B 91(13), 134301 (2015).
[Crossref]

2014 (2)

2013 (2)

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal Emission and Large Broadband Negative Differential Thermal Emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

R. Zhao, Y. Luo, A. I. Fernández-Domínguez, and J. B. Pendry, “Description of van der Waals Interactions Using Transformation Optics,” Phys. Rev. Lett. 111(3), 033602 (2013).
[Crossref] [PubMed]

2012 (3)

M. Selvanayagam and G. V. Eleftheriades, “An Active Electromagnetic Cloak Using the Equivalence Principle,” IEEE Antennas Wirel. Propag. Lett. 11, 1226–1229 (2012).
[Crossref]

S. Wijewardane and D. Y. Goswami, “A review on surface control of thermal radiation by paints and coatings for new energy applications,” Renew. Sustain. Energy Rev. 16(4), 1863–1873 (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,” JOSA B 28(8), 1994–2000 (2011).
[Crossref]

B.-I. Popa and S. A. Cummer, “Complex coordinates in transformation optics,” Phys. Rev. A 84(6), 063837 (2011).
[Crossref]

J. Guan, W. Li, W. Wang, and Z. Fu, “General boundary mapping method and its application in designing an arbitrarily shaped perfect electric conductor reshaper,” Opt. Express 19(20), 19740–19751 (2011).
[Crossref] [PubMed]

2010 (1)

H. H. Zheng, J. J. Xiao, Y. Lai, and C. T. Chan, “Exterior optical cloaking and illusions by using active sources: A boundary element perspective,” Phys. Rev. B 81(19), 195116 (2010).
[Crossref]

2009 (7)

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active Exterior Cloaking for the 2D Laplace and Helmholtz Equations,” Phys. Rev. Lett. 103(7), 073901 (2009).
[Crossref] [PubMed]

G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Cloak/anti-cloak interactions,” Opt. Express 17(5), 3101–3114 (2009).
[Crossref] [PubMed]

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[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]

U. Leonhardt and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 69–152 (2009).
[Crossref]

S. A. Cummer, N. Kundtz, and B.-I. Popa, “Electromagnetic surface and line sources under coordinate transformations,” Phys. Rev. A 80(3), 033820 (2009).
[Crossref]

G. Dupont, S. Guenneau, S. Enoch, G. Demesy, A. Nicolet, F. Zolla, and A. Diatta, “Revolution analysis of three-dimensional arbitrary cloaks,” Opt. Express 17(25), 22603–22608 (2009).
[Crossref] [PubMed]

2008 (7)

2006 (4)

2005 (1)

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[Crossref]

2001 (1)

K. K. Gupta, A. Nishkam, and N. Kasturiya, “Camouflage in the Non-Visible Region,” J. Ind. Text. 31(1), 27–42 (2001).
[Crossref]

1999 (1)

J. B. Pendry, “Radiative exchange of heat between nanostructures,” J. Phys. Condens. Matter 11(35), 6621–6633 (1999).
[Crossref]

1996 (1)

S. M. Burkinshaw, G. Hallas, and A. D. Towns, “Infrared camouflage,” Rev. Prog. Color. Relat. Top. 26(1), 47–53 (1996).
[Crossref]

1982 (1)

W. Eckhardt, “First and second fluctuation-dissipation-theorem in electromagnetic fluctuation theory,” Opt. Commun. 41(5), 305–309 (1982).
[Crossref]

1971 (1)

D. Polder and M. Van Hove, “Theory of Radiative Heat Transfer between Closely Spaced Bodies,” Phys. Rev. B 4(10), 3303–3314 (1971).
[Crossref]

1968 (1)

R. Graham and H. Haken, “Quantum theory of light propagation in a fluctuating laser-active medium,” Z. Für Phys. Hadrons Nucl. 213(5), 420–450 (1968).
[Crossref]

1966 (1)

R. Kubo, “The fluctuation-dissipation theorem,” Rep. Prog. Phys. 29(1), 255–284 (1966).
[Crossref]

1956 (1)

J. Weber, “Fluctuation Dissipation Theorem,” Phys. Rev. 101(6), 1620–1626 (1956).
[Crossref]

1951 (1)

H. B. Callen and T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83(1), 34–40 (1951).
[Crossref]

Allen, J.

Alu, A.

R. Fleury and A. Alu, “Cloaking and Invisibility: a Review (Invited Review),” Prog. Electromagnetics Res. 147, 171–202 (2014).
[Crossref]

Alù, A.

D. L. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
[Crossref]

G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Cloak/anti-cloak interactions,” Opt. Express 17(5), 3101–3114 (2009).
[Crossref] [PubMed]

Alwakil, A.

A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017).
[Crossref] [PubMed]

Amooghorban, E.

M. Morshed Behbahani, E. Amooghorban, and A. Mahdifar, “Spontaneous emission and the operation of invisibility cloaks,” Phys. Rev. A 94(1), 013854 (2016).
[Crossref]

Amra, C.

Barceló, C.

C. García-Meca and C. Barceló, “Nontensorial Transformation Optics,” Phys. Rev. Appl. 5(6), 064008 (2016).
[Crossref]

Bellieud, M.

A. Alwakil, M. Zerrad, M. Bellieud, and C. Amra, “Inverse heat mimicking of given objects,” Sci. Rep. 7, 43288 (2017).
[Crossref] [PubMed]

Blanchard, R.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal Emission and Large Broadband Negative Differential Thermal Emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

Burkinshaw, S. M.

S. M. Burkinshaw, G. Hallas, and A. D. Towns, “Infrared camouflage,” Rev. Prog. Color. Relat. Top. 26(1), 47–53 (1996).
[Crossref]

Callen, H. B.

H. B. Callen and T. A. Welton, “Irreversibility and Generalized Noise,” Phys. Rev. 83(1), 34–40 (1951).
[Crossref]

Capasso, F.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal Emission and Large Broadband Negative Differential Thermal Emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

Carminati, R.

K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
[Crossref]

Castaldi, G.

Chan, C. T.

H. H. Zheng, J. J. Xiao, Y. Lai, and C. T. Chan, “Exterior optical cloaking and illusions by using active sources: A boundary element perspective,” Phys. Rev. B 81(19), 195116 (2010).
[Crossref]

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]

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[Crossref] [PubMed]

H. Chen, X. Luo, H. Ma, and C. T. Chan, “The Anti-Cloak,” Opt. Express 16(19), 14603–14608 (2008).
[Crossref] [PubMed]

Chen, H.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[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, X. Luo, H. Ma, and C. T. Chan, “The Anti-Cloak,” Opt. Express 16(19), 14603–14608 (2008).
[Crossref] [PubMed]

T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: Enhancement of scattering with complementary media,” Opt. Express 16(22), 18545–18550 (2008).
[Crossref] [PubMed]

Chen, K.

K. Chen and S. Fan, “Nonequilibrium Casimir Force with a Nonzero Chemical Potential for Photons,” Phys. Rev. Lett. 117(26), 267401 (2016).
[Crossref] [PubMed]

K. Chen, P. Santhanam, S. Sandhu, L. Zhu, and S. Fan, “Heat-flux control and solid-state cooling by regulating chemical potential of photons in near-field electromagnetic heat transfer,” Phys. Rev. B 91(13), 134301 (2015).
[Crossref]

Cheng, Q.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 Pt 2), 066607 (2008).
[PubMed]

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W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 Pt 2), 066607 (2008).
[PubMed]

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W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 Pt 2), 066607 (2008).
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M. Selvanayagam and G. V. Eleftheriades, “An Active Electromagnetic Cloak Using the Equivalence Principle,” IEEE Antennas Wirel. Propag. Lett. 11, 1226–1229 (2012).
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K. Chen, P. Santhanam, S. Sandhu, L. Zhu, and S. Fan, “Heat-flux control and solid-state cooling by regulating chemical potential of photons in near-field electromagnetic heat transfer,” Phys. Rev. B 91(13), 134301 (2015).
[Crossref]

Fernández-Domínguez, A. I.

R. Zhao, Y. Luo, A. I. Fernández-Domínguez, and J. B. Pendry, “Description of van der Waals Interactions Using Transformation Optics,” Phys. Rev. Lett. 111(3), 033602 (2013).
[Crossref] [PubMed]

Fleury, R.

D. L. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
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M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal Emission and Large Broadband Negative Differential Thermal Emittance,” Phys. Rev. X 3(4), 041004 (2013).
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Ginzburg, P.

J. Zhang, M. Wubs, P. Ginzburg, G. Wurtz, and A. V. Zayats, “Transformation quantum optics: designing spontaneous emission using coordinate transformations,” J. Opt. 18(4), 044029 (2016).
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Guenneau, S.

Gupta, K. K.

K. K. Gupta, A. Nishkam, and N. Kasturiya, “Camouflage in the Non-Visible Region,” J. Ind. Text. 31(1), 27–42 (2001).
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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).
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T. Han and C.-W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
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X. Zang and C. Jiang, “Overlapped optics, illusion optics, and an external cloak based on shifting media,” JOSA B 28(8), 1994–2000 (2011).
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W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 Pt 2), 066607 (2008).
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C. Khandekar, W. Jin, O. D. Miller, A. Pick, and A. W. Rodriguez, “Giant frequency-selective near-field energy transfer in active\ passive structures,” Phys. Rev. B 94(11), 115402 (2016).
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K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
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K. K. Gupta, A. Nishkam, and N. Kasturiya, “Camouflage in the Non-Visible Region,” J. Ind. Text. 31(1), 27–42 (2001).
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Kats, M. A.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal Emission and Large Broadband Negative Differential Thermal Emittance,” Phys. Rev. X 3(4), 041004 (2013).
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C. Khandekar, W. Jin, O. D. Miller, A. Pick, and A. W. Rodriguez, “Giant frequency-selective near-field energy transfer in active\ passive structures,” Phys. Rev. B 94(11), 115402 (2016).
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Ko, C.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal Emission and Large Broadband Negative Differential Thermal Emittance,” Phys. Rev. X 3(4), 041004 (2013).
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S. A. Cummer, N. Kundtz, and B.-I. Popa, “Electromagnetic surface and line sources under coordinate transformations,” Phys. Rev. A 80(3), 033820 (2009).
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N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, “Optical source transformations,” Opt. Express 16(26), 21215–21222 (2008).
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Lai, Y.

H. H. Zheng, J. J. Xiao, Y. Lai, and C. T. Chan, “Exterior optical cloaking and illusions by using active sources: A boundary element perspective,” Phys. Rev. B 81(19), 195116 (2010).
[Crossref]

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[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).
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Lee, E. H.

M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt. 18(4), 044002 (2016).
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U. Leonhardt and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 69–152 (2009).
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Li, F.

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W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 Pt 2), 066607 (2008).
[PubMed]

Liu, R.

W. X. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. J. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped objects,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(6 Pt 2), 066607 (2008).
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M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt. 18(4), 044002 (2016).
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Luo, Y.

R. Zhao, Y. Luo, and J. B. Pendry, “Transformation optics applied to van der Waals interactions,” Sci. Bull. 61(1), 59–67 (2016).
[Crossref]

R. Zhao, Y. Luo, A. I. Fernández-Domínguez, and J. B. Pendry, “Description of van der Waals Interactions Using Transformation Optics,” Phys. Rev. Lett. 111(3), 033602 (2013).
[Crossref] [PubMed]

Ma, H.

Ma, Y.

M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt. 18(4), 044002 (2016).
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M. Morshed Behbahani, E. Amooghorban, and A. Mahdifar, “Spontaneous emission and the operation of invisibility cloaks,” Phys. Rev. A 94(1), 013854 (2016).
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K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
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Miller, D. A. B.

Miller, O. D.

C. Khandekar, W. Jin, O. D. Miller, A. Pick, and A. W. Rodriguez, “Giant frequency-selective near-field energy transfer in active\ passive structures,” Phys. Rev. B 94(11), 115402 (2016).
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F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active Exterior Cloaking for the 2D Laplace and Helmholtz Equations,” Phys. Rev. Lett. 103(7), 073901 (2009).
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M. Morshed Behbahani, E. Amooghorban, and A. Mahdifar, “Spontaneous emission and the operation of invisibility cloaks,” Phys. Rev. A 94(1), 013854 (2016).
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K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati, and J.-J. Greffet, “Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field,” Surf. Sci. Rep. 57(3-4), 59–112 (2005).
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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).
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Nicolet, A.

Nishkam, A.

K. K. Gupta, A. Nishkam, and N. Kasturiya, “Camouflage in the Non-Visible Region,” J. Ind. Text. 31(1), 27–42 (2001).
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Onofrei, D.

F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active Exterior Cloaking for the 2D Laplace and Helmholtz Equations,” Phys. Rev. Lett. 103(7), 073901 (2009).
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R. Zhao, Y. Luo, and J. B. Pendry, “Transformation optics applied to van der Waals interactions,” Sci. Bull. 61(1), 59–67 (2016).
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R. Zhao, Y. Luo, A. I. Fernández-Domínguez, and J. B. Pendry, “Description of van der Waals Interactions Using Transformation Optics,” Phys. Rev. Lett. 111(3), 033602 (2013).
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J. B. Pendry, “Radiative exchange of heat between nanostructures,” J. Phys. Condens. Matter 11(35), 6621–6633 (1999).
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Philbin, T. G.

U. Leonhardt and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 69–152 (2009).
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C. Khandekar, W. Jin, O. D. Miller, A. Pick, and A. W. Rodriguez, “Giant frequency-selective near-field energy transfer in active\ passive structures,” Phys. Rev. B 94(11), 115402 (2016).
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D. Polder and M. Van Hove, “Theory of Radiative Heat Transfer between Closely Spaced Bodies,” Phys. Rev. B 4(10), 3303–3314 (1971).
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B.-I. Popa and S. A. Cummer, “Complex coordinates in transformation optics,” Phys. Rev. A 84(6), 063837 (2011).
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S. A. Cummer, N. Kundtz, and B.-I. Popa, “Electromagnetic surface and line sources under coordinate transformations,” Phys. Rev. A 80(3), 033820 (2009).
[Crossref]

Qiu, C.-W.

T. Han and C.-W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
[Crossref]

Ramanathan, S.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal Emission and Large Broadband Negative Differential Thermal Emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

Raza, M.

M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt. 18(4), 044002 (2016).
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Roberts, D. A.

Rodriguez, A. W.

C. Khandekar, W. Jin, O. D. Miller, A. Pick, and A. W. Rodriguez, “Giant frequency-selective near-field energy transfer in active\ passive structures,” Phys. Rev. B 94(11), 115402 (2016).
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K. Chen, P. Santhanam, S. Sandhu, L. Zhu, and S. Fan, “Heat-flux control and solid-state cooling by regulating chemical potential of photons in near-field electromagnetic heat transfer,” Phys. Rev. B 91(13), 134301 (2015).
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Santhanam, P.

K. Chen, P. Santhanam, S. Sandhu, L. Zhu, and S. Fan, “Heat-flux control and solid-state cooling by regulating chemical potential of photons in near-field electromagnetic heat transfer,” Phys. Rev. B 91(13), 134301 (2015).
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Schurig, D.

Selvanayagam, M.

M. Selvanayagam and G. V. Eleftheriades, “An Active Electromagnetic Cloak Using the Equivalence Principle,” IEEE Antennas Wirel. Propag. Lett. 11, 1226–1229 (2012).
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D. L. Sounas, R. Fleury, and A. Alù, “Unidirectional Cloaking Based on Metasurfaces with Balanced Loss and Gain,” Phys. Rev. Appl. 4(1), 014005 (2015).
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S. M. Burkinshaw, G. Hallas, and A. D. Towns, “Infrared camouflage,” Rev. Prog. Color. Relat. Top. 26(1), 47–53 (1996).
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D. Polder and M. Van Hove, “Theory of Radiative Heat Transfer between Closely Spaced Bodies,” Phys. Rev. B 4(10), 3303–3314 (1971).
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F. G. Vasquez, G. W. Milton, and D. Onofrei, “Active Exterior Cloaking for the 2D Laplace and Helmholtz Equations,” Phys. Rev. Lett. 103(7), 073901 (2009).
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Wubs, M.

J. Zhang, M. Wubs, P. Ginzburg, G. Wurtz, and A. V. Zayats, “Transformation quantum optics: designing spontaneous emission using coordinate transformations,” J. Opt. 18(4), 044029 (2016).
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Wurtz, G.

J. Zhang, M. Wubs, P. Ginzburg, G. Wurtz, and A. V. Zayats, “Transformation quantum optics: designing spontaneous emission using coordinate transformations,” J. Opt. 18(4), 044029 (2016).
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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]

Xiao, J. J.

H. H. Zheng, J. J. Xiao, Y. Lai, and C. T. Chan, “Exterior optical cloaking and illusions by using active sources: A boundary element perspective,” Phys. Rev. B 81(19), 195116 (2010).
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Yang, T.

Zang, X.

X. Zang and C. Jiang, “Overlapped optics, illusion optics, and an external cloak based on shifting media,” JOSA B 28(8), 1994–2000 (2011).
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J. Zhang, M. Wubs, P. Ginzburg, G. Wurtz, and A. V. Zayats, “Transformation quantum optics: designing spontaneous emission using coordinate transformations,” J. Opt. 18(4), 044029 (2016).
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Zerrad, M.

Zhang, J.

J. Zhang, M. Wubs, P. Ginzburg, G. Wurtz, and A. V. Zayats, “Transformation quantum optics: designing spontaneous emission using coordinate transformations,” J. Opt. 18(4), 044029 (2016).
[Crossref]

Zhang, S.

M. A. Kats, R. Blanchard, S. Zhang, P. Genevet, C. Ko, S. Ramanathan, and F. Capasso, “Vanadium Dioxide as a Natural Disordered Metamaterial: Perfect Thermal Emission and Large Broadband Negative Differential Thermal Emittance,” Phys. Rev. X 3(4), 041004 (2013).
[Crossref]

Zhang, Z.-Q.

Y. Lai, H. Chen, Z.-Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett. 102(9), 093901 (2009).
[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]

Zhao, R.

R. Zhao, Y. Luo, and J. B. Pendry, “Transformation optics applied to van der Waals interactions,” Sci. Bull. 61(1), 59–67 (2016).
[Crossref]

R. Zhao, Y. Luo, A. I. Fernández-Domínguez, and J. B. Pendry, “Description of van der Waals Interactions Using Transformation Optics,” Phys. Rev. Lett. 111(3), 033602 (2013).
[Crossref] [PubMed]

Zheng, H. H.

H. H. Zheng, J. J. Xiao, Y. Lai, and C. T. Chan, “Exterior optical cloaking and illusions by using active sources: A boundary element perspective,” Phys. Rev. B 81(19), 195116 (2010).
[Crossref]

Zhu, L.

K. Chen, P. Santhanam, S. Sandhu, L. Zhu, and S. Fan, “Heat-flux control and solid-state cooling by regulating chemical potential of photons in near-field electromagnetic heat transfer,” Phys. Rev. B 91(13), 134301 (2015).
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IEEE Antennas Wirel. Propag. Lett. (1)

M. Selvanayagam and G. V. Eleftheriades, “An Active Electromagnetic Cloak Using the Equivalence Principle,” IEEE Antennas Wirel. Propag. Lett. 11, 1226–1229 (2012).
[Crossref]

J. Ind. Text. (1)

K. K. Gupta, A. Nishkam, and N. Kasturiya, “Camouflage in the Non-Visible Region,” J. Ind. Text. 31(1), 27–42 (2001).
[Crossref]

J. Opt. (3)

J. Zhang, M. Wubs, P. Ginzburg, G. Wurtz, and A. V. Zayats, “Transformation quantum optics: designing spontaneous emission using coordinate transformations,” J. Opt. 18(4), 044029 (2016).
[Crossref]

M. Raza, Y. Liu, E. H. Lee, and Y. Ma, “Transformation thermodynamics and heat cloaking: a review,” J. Opt. 18(4), 044002 (2016).
[Crossref]

T. Han and C.-W. Qiu, “Transformation Laplacian metamaterials: recent advances in manipulating thermal and dc fields,” J. Opt. 18(4), 044003 (2016).
[Crossref]

J. Phys. Condens. Matter (1)

J. B. Pendry, “Radiative exchange of heat between nanostructures,” J. Phys. Condens. Matter 11(35), 6621–6633 (1999).
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JOSA B (1)

X. Zang and C. Jiang, “Overlapped optics, illusion optics, and an external cloak based on shifting media,” JOSA B 28(8), 1994–2000 (2011).
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Opt. Commun. (1)

W. Eckhardt, “First and second fluctuation-dissipation-theorem in electromagnetic fluctuation theory,” Opt. Commun. 41(5), 305–309 (1982).
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Opt. Express (11)

C. Li and F. Li, “Two-dimensional electromagnetic cloaks with arbitrary geometries,” Opt. Express 16(17), 13414–13420 (2008).
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H. Chen, X. Luo, H. Ma, and C. T. Chan, “The Anti-Cloak,” Opt. Express 16(19), 14603–14608 (2008).
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T. Yang, H. Chen, X. Luo, and H. Ma, “Superscatterer: Enhancement of scattering with complementary media,” Opt. Express 16(22), 18545–18550 (2008).
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N. Kundtz, D. A. Roberts, J. Allen, S. Cummer, and D. R. Smith, “Optical source transformations,” Opt. Express 16(26), 21215–21222 (2008).
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G. Castaldi, I. Gallina, V. Galdi, A. Alù, and N. Engheta, “Cloak/anti-cloak interactions,” Opt. Express 17(5), 3101–3114 (2009).
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G. Dupont, S. Guenneau, S. Enoch, G. Demesy, A. Nicolet, F. Zolla, and A. Diatta, “Revolution analysis of three-dimensional arbitrary cloaks,” Opt. Express 17(25), 22603–22608 (2009).
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J. Guan, W. Li, W. Wang, and Z. Fu, “General boundary mapping method and its application in designing an arbitrarily shaped perfect electric conductor reshaper,” Opt. Express 19(20), 19740–19751 (2011).
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S. Guenneau, C. Amra, and D. Veynante, “Transformation thermodynamics: cloaking and concentrating heat flux,” Opt. Express 20(7), 8207–8218 (2012).
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S. Guenneau, D. Petiteau, M. Zerrad, and C. Amra, “Bicephalous transformed media: concentrator versus rotator and cloak versus superscatterer,” Opt. Express 22(19), 23614–23619 (2014).
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D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
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D. A. B. Miller, “On perfect cloaking,” Opt. Express 14(25), 12457–12466 (2006).
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Figures (2)

Fig. 1
Fig. 1

Schematic of the TR illusion example discussed in section 4. The middle figure is for the TE/TM physical space (departure space) with a homogenous anisotropic lossy circular object with radius r0 [ ε obj mn = δ mn (3+i0.02)and μ obj mn = δ mn (1+i0.02 δ mz )] coated with an inhomogeneous anisotropic circular coat with radius rex. The left figure is for the TE virtual space with inhomogeneous anisotropic horizontal elliptical shaped object with semi-axes a and b embedded in a homogenous medium. The right figure is similar but for a vertical ellipse and for TM polarization. The region outside r ex is unity transformed for both polarizations. The areas of all spaces between the dotted external cylinder and the virtual or physical objects, are lossless and do not contribute to the thermal radiation. For numerical calculations, L was set to be 11.1λ with matched boundary conditions at the square frames.

Fig. 2
Fig. 2

Numerical calculation of normalized time averaged radiated poynting vector (log scale) at the virtual and physical spaces of TE and TM as depicted in Fig. 1, (a) TM physical (left) and virtual (right) (b) TE physical (left) and virtual (right). Colored surfaces, red arrows and white contours indicate the modulus (log scale), direction and isoclines of the poynting vector respectively. The left figures consider the circular radiating cylinder given in the middle part of Fig. 2. These left figures give the TR pattern of the cylinder coated to mimic the TR patterns of vertical (Fig. 2(a)) and horizontal (Fig. 2(b)) ellipses for TE and TM polarizations (see text). The right figures consider the vertical and horizontal coated ellipses of Fig. 1. These right figures give the TR pattern of the ellipses for each polarization and these patterns must be compared to those of the left figures. Normalization constants are: for TM, <S>0 = 5.7 × 10-33 W/m2, while for TE, <S>0 = 10-28 W/m2. We notice that the emitted power has the same distribution outside the transformation regions for both polarizations at the physical and virtual spaces. Slight differences between both spaces are attributed to numerical error of discretization.

Equations (36)

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ε m'n' = 1 | A _ _ | A m m' A n n' ε mn and µ m'n' = 1 | A _ _ | A m m' A n n' µ mn ,
J m' = 1 | A _ _ | A m m' J m and K m' = 1 | A _ _ | A m m' K m .
J m ( x 1 ; ω 1 ) J n* ( x 2 ; ω 2 ) = ω ε 0 π θ( ω 1 ,T )Im{ ε mn ( x 1 ; ω 1 ) }δ( x 1 x 2 )δ( ω 1 ω 2 ).
K m ( x 1 ; ω 1 ) K n* ( x 2 ; ω 2 ) = ω μ 0 π θ( ω 1 ,T )Im{ μ mn ( x 1 ; ω 1 ) }δ( x 1 x 2 )δ( ω 1 ω 2 ).
J m' ( x 1 ' ; ω 1 ) J n'* ( x 2 ' ; ω 2 ) = 1 | A _ _ | 2 A m m' A n n' J m ( x 1 ; ω 1 ) J n* ( x 2 ; ω 2 ) .
J m' ( x 1 ' ; ω 1 ) J n'* ( x 2 ' ; ω 2 ) = 1 | A _ _ | 2 A m m' A n n' ω ε 0 π θ( ω 1 ,T )Im{ ε mn ( x 1 ; ω 1 ) }δ( x 1 x 2 )δ( ω 1 ω 2 ).
δ( x 1 ' x 2 ' )= 1 | A _ _ | δ( x 1 x 2 ).
J m' ( x 1 ' ; ω 1 ) J n'* ( x 2 ' ; ω 2 ) = ω ε 0 π θ( ω 1 ,T )Im{ ε m'n' ( x 1 ' ; ω 1 ) }δ( x 1 ' x 2 ' )δ( ω 1 ω 2 ).
K m' ( x 1 ' ; ω 1 ) K n'* ( x 2 ' ; ω 2 ) = 1 | A _ _ | 2 A m m' A n n' K m ( x 1 ; ω 1 ) K n* ( x 2 ; ω 2 ) = ω μ 0 π θ( ω 1 ,T )Im{ μ m'n' ( x 1 ' ; ω 1 ) }δ( x 1 ' x 2 ' )δ( ω 1 ω 2 ).
r'= η( θ ) r 0 r and θ'=θ object transformation (0<r< r 0 ).
r={ r ex r 0 r ex η ( r' r ex )+ r ex ( η<r<r ex )and( η<r'<r ex ). r' ( r>r ex )and( r'>r ex ). θ'=θ.
J x' = 1 | A _ _ | A x x' J x + 1 | A _ _ | A y x' J y and J y' = 1 | A _ _ | A x y' J x + 1 | A _ _ | A y y' J y .
K z ' = K z | A _ _ | .
ε xx = ε yy =3+i0.02 , ε zz =3+i0.02 , μ xx = μ yy =1 and μ zz =1+i0.02
η( θ )= [ ( cos( θ ) b ) 2 + ( sin( θ ) a ) 2 ] 1 2 and ρ( θ )=η( θ± π 2 ).
ε mn =( ε _ _ T 0 0 ε zz ), μ mn =( μ _ _ T 0 0 μ zz ), J m =( J _ T J z ), K m =( K _ T K z ), E m =( E _ T E z ), H m =( H _ T H z ) ε m'n' =( ε _ _ T ' 0 0 ε zz ' ), μ m'n' =( μ _ _ T ' 0 0 μ zz ' ), J m' =( J _ T ' J z ' ), K m' =( K _ T ' K z ' ), E m' =( E _ T ' E z ' ) and H m' =( H _ T ' H z ' ).
× ε _ _ T 1 ×( H z z ) k 0 2 μ zz ( H z z )=× ε _ _ T 1 J _ T +iω ε 0 ( K z z ).
' × ε _ _ T '1 ' ×( H z ' z ) k 0 2 μ zz ( H z ' z )= ' × ε _ _ T '1 J _ T ' +iω ε 0 ( K z ' z ).
μ zz ' = μ zz | A _ _ | , K z ' = K z | A _ _ | , ε T m'n' = 1 | A _ _ | A m m' A n n' ε T mn , J T m' = 1 | A _ _ | A m m' J T m , E _ T ' = A _ _ τ E _ T and H z ' = H z .
× μ _ _ T 1 ×( E z z ) k 0 2 ε zz ( E z z )=× μ _ _ T 1 K _ T +iω ε 0 ( J z z ).
' × μ _ _ T '1 ' ×( E z ' z ) k 0 2 ε zz ' ( E z ' z )= ' × μ _ _ T '1 K _ T ' +iω μ 0 ( J z ' z ).
ε zz ' = ε zz | B _ _ | , μ T m'n' = 1 | B _ _ | B m m' B n n' μ T mn , K T m' = 1 | B _ _ | B m m' K T m , J z ' = J z | B _ _ | , H _ T ' = B _ _ τ H _ T and E z ' = E z .
S _ =4× 1 2 Re{ E _ × H _ * }.
H z ( r _ )= G zz HH ( r _ , r _ 1 ) K z ( r _ 1 ) d 2 r _ 1 + G zx HE ( r _ , r _ 2 ) J T x ( r _ 2 ) d 2 r _ 2 + G zy HE ( r _ , r _ 3 ) J T y ( r _ 3 ) d 2 r _ 3 .
E _ n ( r _ )= G nz EH ( r _ , r _ 4 ) K z ( r _ 4 ) d 2 r _ 4 + G nx EE ( r _ , r _ 5 ) J T x ( r _ 5 ) d 2 r _ 5 + G ny EE ( r _ , r _ 6 ) J T y ( r _ 6 ) d 2 r _ 6 .
S _ TM =2 x Re{ E y H z * }2 y Re{ E x H z * }= x S x TM + y S y TM .
E y H z * = ω μ 0 π θ( ω,T ) d 2 r _ 1 G yz EH ( r _ , r _ 1 )Im{ μ zz ( r _ 1 ) } G zz HH* ( r _ , r _ 1 ) + ω ε 0 π θ( ω,T )s d 2 r _ 2 n=x,y m=x,y G yn EE ( r _ , r _ 2 )Im{ ε mn ( r _ 2 ) } G zm HE* ( r _ , r _ 2 ) .
E x H z * = ω μ 0 π θ( ω,T ) d 2 r _ 1 G xz EH ( r _ , r _ 1 )Im{ μ zz ( r _ 1 ) } G zz HH* ( r _ , r _ 1 ) + ω ε 0 π θ( ω,T ) d 2 r _ 2 n=x,y m=x,y G xn EE ( r _ , r _ 2 )Im{ ε mn ( r _ 2 ) } G zm HE* ( r _ , r _ 2 ) .
E z ( r _ )= G zz EE ( r _ , r _ 1 ) J z ( r _ 1 ) d 2 r _ 1 + G zx EH ( r _ , r _ 2 ) K T x ( r _ 2 ) d 2 r _ 2 + G zy EH ( r _ , r _ 3 ) K T y ( r _ 3 ) d 2 r _ 3 .
H _ n ( r _ )= G nz HE ( r _ , r _ 4 ) J z ( r _ 4 ) d 2 r _ 4 + G nx HH ( r _ , r _ 5 ) K T x ( r _ 5 ) d 2 r _ 5 + G zy HH ( r _ , r _ 6 ) K T y ( r _ 6 ) d 2 r _ 6 .
S _ TE =2 x Re{ E z H y * }+2 y Re{ E z H x * }= x S x TE + y S y TE .
E z H y * = ω ε 0 π θ( ω,T ) d 2 r _ 1 G zz EE ( r _ , r _ 1 )Im{ ε zz ( r _ 1 ) } G yz HE* ( r _ , r _ 1 ) + ω μ 0 π θ( ω,T ) d 2 r _ 2 n=x,y m=x,y G zn EH ( r _ , r _ 2 )Im{ μ mn ( r _ 2 ) } G ym HH* ( r _ , r _ 2 ) .
E z H x * = ω ε 0 π θ( ω,T ) d 2 r _ 1 G zz EE ( r _ , r _ 1 )Im{ ε zz ( r _ 1 ) } G xz HE* ( r _ , r _ 1 ) + ω μ 0 π θ( ω,T ) d 2 r _ 2 n=x,y m=x,y G zn EH ( r _ , r _ 2 )Im{ μ mn ( r _ 2 ) } G xm HH* ( r _ , r _ 2 ) .
( c _ _ u+ γ _ )+au=f.
c _ _ = ε _ _ T | ε _ _ T | , γ _ = 1 | ε _ _ T | ( ε xy J T x + ε xx J T y ε yy J T x + ε xy J T y ), a= k 0 2 μ zz and f=iω ε 0 K z .
c _ _ = μ _ _ T | μ _ _ T | , γ _ = 1 | μ _ _ T | ( μ xy K T x μ xx K T y μ yy K T x μ xy K T y ), a= k 0 2 ε zz and f=iω μ 0 J z .

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