Abstract

The discrete coordinate transformation (DCT), as a unique technique to control the electromagnetic waves, has been applied for creating all-dielectric devices recently. To extend the applicability of this technique, we propose the concept of multiple discrete coordinate transformation, which serves to deal with more complicated geometries in the transformation domain. As an example, an all-dielectric absorber is created by compressing a pyramidal absorber to a third of its original thickness using the multiple DCT technique. The Finite-Difference Time-Domain (FDTD) method based numerical simulations demonstrate the broadband performance of the transformation absorber from 2 GHz to 20 GHz.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  7. N. Engheta, “Thin absorbing screens using metamaterial surfaces,” in Antennas and Propagation Society International Symposium, IEEE (2002), pp. 392–395.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. J. B. Pendry, A. Holden, D. Robbins, W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47(11), 2075–2084 (1999).
    [CrossRef]
  16. J. Li, J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
    [CrossRef] [PubMed]
  17. D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
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  20. J. Valentine, J. Li, T. Zentgraf, G. Bartal, X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [CrossRef] [PubMed]
  21. H. F. Ma, T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
    [CrossRef] [PubMed]
  22. W. Tang, C. Argyropoulos, E. Kallos, W. Song, Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58(12), 3795–3804 (2010).
    [CrossRef]
  23. Z. Mei, J. Bai, T. J. Cui, “Experimental verification of a broadband planar focusing antenna based on transformation optics,” New J. Phys. 13, 063028 (2011).
    [CrossRef]
  24. N. Kundtz, D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
    [CrossRef]
  25. H. F. Ma, T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
    [CrossRef] [PubMed]
  26. Y. Luo, D. Y. Lei, S. A. Maier, J. B. Pendry, “Broadband light harvesting nanostructures robust to edge bluntness,” Phys. Rev. Lett. 108(2), 023901 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2012 (1)

Y. Luo, D. Y. Lei, S. A. Maier, J. B. Pendry, “Broadband light harvesting nanostructures robust to edge bluntness,” Phys. Rev. Lett. 108(2), 023901 (2012).
[CrossRef] [PubMed]

2011 (2)

Z. Mei, J. Bai, T. J. Cui, “Experimental verification of a broadband planar focusing antenna based on transformation optics,” New J. Phys. 13, 063028 (2011).
[CrossRef]

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
[CrossRef]

2010 (5)

Q. Cheng, T. J. Cui, W. X. Jiang, B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

N. Kundtz, D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[CrossRef]

H. F. Ma, T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef] [PubMed]

H. F. Ma, T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[CrossRef] [PubMed]

W. Tang, C. Argyropoulos, E. Kallos, W. Song, Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58(12), 3795–3804 (2010).
[CrossRef]

2009 (4)

D. Roberts, N. Kundtz, D. R. Smith, “Optical lens compression via transformation optics,” Opt. Express 17(19), 16535–16542 (2009).
[CrossRef] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

E. E. Narimanov, A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

2008 (2)

J. Li, J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

2006 (3)

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

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. Holden, D. Robbins, W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1997 (1)

C. Holloway, R. DeLyser, R. German, P. McKenna, M. Kanda, “Comparison of electromagnetic absorber used in anechoic and semi-anechoic chambers for emissions and immunity testing of digital devices,” IEEE Trans. Electromagn. Compat. 39(1), 33–47 (1997).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

1991 (1)

S. Kim, S. Jo, K. Gueon, K. Choi, J. Kim, K. Churn, “Complex permeability and permittivity and microwave absorption of ferrite-rubber composite at x-band frequencies,” IEEE Trans. Magnetics 27(6), 5462–5464 (1991).
[CrossRef]

1988 (1)

B. T. Dewitt, W. D. Burnside, “Electromagnetic scattering by pyramidal and wedge absorber,” IEEE Trans. Antennas Propag. 36(7), 971–984 (1988).
[CrossRef]

1973 (1)

W. Emerson, “Electromagnetic wave absorbers and anechoic chambers through the years,” IEEE Trans. Antennas Propag. 21, 484–490 (1973).
[CrossRef]

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–12 (1949).
[CrossRef]

Argyropoulos, C.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
[CrossRef]

W. Tang, C. Argyropoulos, E. Kallos, W. Song, Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58(12), 3795–3804 (2010).
[CrossRef]

Bai, J.

Z. Mei, J. Bai, T. J. Cui, “Experimental verification of a broadband planar focusing antenna based on transformation optics,” New J. Phys. 13, 063028 (2011).
[CrossRef]

Bao, D.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
[CrossRef]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

Burnside, W. D.

B. T. Dewitt, W. D. Burnside, “Electromagnetic scattering by pyramidal and wedge absorber,” IEEE Trans. Antennas Propag. 36(7), 971–984 (1988).
[CrossRef]

Cai, B. G.

Q. Cheng, T. J. Cui, W. X. Jiang, B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

Cheng, Q.

Q. Cheng, T. J. Cui, W. X. Jiang, B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

Chin, J. Y.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Choi, K.

S. Kim, S. Jo, K. Gueon, K. Choi, J. Kim, K. Churn, “Complex permeability and permittivity and microwave absorption of ferrite-rubber composite at x-band frequencies,” IEEE Trans. Magnetics 27(6), 5462–5464 (1991).
[CrossRef]

Churn, K.

S. Kim, S. Jo, K. Gueon, K. Choi, J. Kim, K. Churn, “Complex permeability and permittivity and microwave absorption of ferrite-rubber composite at x-band frequencies,” IEEE Trans. Magnetics 27(6), 5462–5464 (1991).
[CrossRef]

Cui, T. J.

Z. Mei, J. Bai, T. J. Cui, “Experimental verification of a broadband planar focusing antenna based on transformation optics,” New J. Phys. 13, 063028 (2011).
[CrossRef]

H. F. Ma, T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef] [PubMed]

Q. Cheng, T. J. Cui, W. X. Jiang, B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

H. F. Ma, T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[CrossRef] [PubMed]

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

T. J. Cui, D. R. Smith, R. Liu, Metamaterials: Theory, Design and Applications (Springer, 2010).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

DeLyser, R.

C. Holloway, R. DeLyser, R. German, P. McKenna, M. Kanda, “Comparison of electromagnetic absorber used in anechoic and semi-anechoic chambers for emissions and immunity testing of digital devices,” IEEE Trans. Electromagn. Compat. 39(1), 33–47 (1997).
[CrossRef]

Dewitt, B. T.

B. T. Dewitt, W. D. Burnside, “Electromagnetic scattering by pyramidal and wedge absorber,” IEEE Trans. Antennas Propag. 36(7), 971–984 (1988).
[CrossRef]

Emerson, W.

W. Emerson, “Electromagnetic wave absorbers and anechoic chambers through the years,” IEEE Trans. Antennas Propag. 21, 484–490 (1973).
[CrossRef]

Engheta, N.

N. Engheta, “Thin absorbing screens using metamaterial surfaces,” in Antennas and Propagation Society International Symposium, IEEE (2002), pp. 392–395.
[CrossRef]

German, R.

C. Holloway, R. DeLyser, R. German, P. McKenna, M. Kanda, “Comparison of electromagnetic absorber used in anechoic and semi-anechoic chambers for emissions and immunity testing of digital devices,” IEEE Trans. Electromagn. Compat. 39(1), 33–47 (1997).
[CrossRef]

Gueon, K.

S. Kim, S. Jo, K. Gueon, K. Choi, J. Kim, K. Churn, “Complex permeability and permittivity and microwave absorption of ferrite-rubber composite at x-band frequencies,” IEEE Trans. Magnetics 27(6), 5462–5464 (1991).
[CrossRef]

Hao, Y.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
[CrossRef]

W. Tang, C. Argyropoulos, E. Kallos, W. Song, Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58(12), 3795–3804 (2010).
[CrossRef]

Holden, A.

J. B. Pendry, A. Holden, D. Robbins, W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Holloway, C.

C. Holloway, R. DeLyser, R. German, P. McKenna, M. Kanda, “Comparison of electromagnetic absorber used in anechoic and semi-anechoic chambers for emissions and immunity testing of digital devices,” IEEE Trans. Electromagn. Compat. 39(1), 33–47 (1997).
[CrossRef]

Ji, C.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

Jiang, W. X.

Q. Cheng, T. J. Cui, W. X. Jiang, B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

Jo, S.

S. Kim, S. Jo, K. Gueon, K. Choi, J. Kim, K. Churn, “Complex permeability and permittivity and microwave absorption of ferrite-rubber composite at x-band frequencies,” IEEE Trans. Magnetics 27(6), 5462–5464 (1991).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Kallos, E.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
[CrossRef]

W. Tang, C. Argyropoulos, E. Kallos, W. Song, Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58(12), 3795–3804 (2010).
[CrossRef]

Kanda, M.

C. Holloway, R. DeLyser, R. German, P. McKenna, M. Kanda, “Comparison of electromagnetic absorber used in anechoic and semi-anechoic chambers for emissions and immunity testing of digital devices,” IEEE Trans. Electromagn. Compat. 39(1), 33–47 (1997).
[CrossRef]

Kildishev, A. V.

E. E. Narimanov, A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Kim, J.

S. Kim, S. Jo, K. Gueon, K. Choi, J. Kim, K. Churn, “Complex permeability and permittivity and microwave absorption of ferrite-rubber composite at x-band frequencies,” IEEE Trans. Magnetics 27(6), 5462–5464 (1991).
[CrossRef]

Kim, S.

S. Kim, S. Jo, K. Gueon, K. Choi, J. Kim, K. Churn, “Complex permeability and permittivity and microwave absorption of ferrite-rubber composite at x-band frequencies,” IEEE Trans. Magnetics 27(6), 5462–5464 (1991).
[CrossRef]

Kundtz, N.

Landy, N. I.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Lei, D. Y.

Y. Luo, D. Y. Lei, S. A. Maier, J. B. Pendry, “Broadband light harvesting nanostructures robust to edge bluntness,” Phys. Rev. Lett. 108(2), 023901 (2012).
[CrossRef] [PubMed]

Leonhardt, U.

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

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

J. Li, J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

Liu, R.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

T. J. Cui, D. R. Smith, R. Liu, Metamaterials: Theory, Design and Applications (Springer, 2010).
[CrossRef]

Luo, Y.

Y. Luo, D. Y. Lei, S. A. Maier, J. B. Pendry, “Broadband light harvesting nanostructures robust to edge bluntness,” Phys. Rev. Lett. 108(2), 023901 (2012).
[CrossRef] [PubMed]

Ma, H. F.

H. F. Ma, T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[CrossRef] [PubMed]

H. F. Ma, T. J. Cui, “Three-dimensional broadband ground-plane cloak made of metamaterials,” Nat. Commun. 1, 21 (2010).
[CrossRef] [PubMed]

Maier, S. A.

Y. Luo, D. Y. Lei, S. A. Maier, J. B. Pendry, “Broadband light harvesting nanostructures robust to edge bluntness,” Phys. Rev. Lett. 108(2), 023901 (2012).
[CrossRef] [PubMed]

McKenna, P.

C. Holloway, R. DeLyser, R. German, P. McKenna, M. Kanda, “Comparison of electromagnetic absorber used in anechoic and semi-anechoic chambers for emissions and immunity testing of digital devices,” IEEE Trans. Electromagn. Compat. 39(1), 33–47 (1997).
[CrossRef]

Mei, Z.

Z. Mei, J. Bai, T. J. Cui, “Experimental verification of a broadband planar focusing antenna based on transformation optics,” New J. Phys. 13, 063028 (2011).
[CrossRef]

Mock, J. J.

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Narimanov, E. E.

E. E. Narimanov, A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Padilla, W. J.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Pendry, J. B.

Y. Luo, D. Y. Lei, S. A. Maier, J. B. Pendry, “Broadband light harvesting nanostructures robust to edge bluntness,” Phys. Rev. Lett. 108(2), 023901 (2012).
[CrossRef] [PubMed]

J. Li, J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

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

J. B. Pendry, A. Holden, D. Robbins, W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Piao, Y.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
[CrossRef]

Rajab, K. Z.

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
[CrossRef]

Robbins, D.

J. B. Pendry, A. Holden, D. Robbins, W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Roberts, D.

Sajuyigbe, S.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Salisbury, W. W.

W. W. Salisbury, “Absorbent body for electromagnetic waves,” U.S. Patent No. 2.599.944, filed 1952.

Schurig, D.

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R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
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W. Tang, C. Argyropoulos, E. Kallos, W. Song, Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58(12), 3795–3804 (2010).
[CrossRef]

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D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
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J. Valentine, J. Li, T. Zentgraf, G. Bartal, X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
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W. Tang, C. Argyropoulos, E. Kallos, W. Song, Y. Hao, “Discrete coordinate transformation for designing all-dielectric flat antennas,” IEEE Trans. Antennas Propag. 58(12), 3795–3804 (2010).
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N. Kundtz, D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef] [PubMed]

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Z. Mei, J. Bai, T. J. Cui, “Experimental verification of a broadband planar focusing antenna based on transformation optics,” New J. Phys. 13, 063028 (2011).
[CrossRef]

D. Bao, K. Z. Rajab, Y. Hao, E. Kallos, W. Tang, C. Argyropoulos, Y. Piao, S. Yang, “All-dielectric invisibility cloaks made of BaTiO3-loaded polyurethane foam,” New J. Phys. 13, 103023 (2011).
[CrossRef]

Q. Cheng, T. J. Cui, W. X. Jiang, B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

Opt. Express (1)

Phys. Rev. Lett. (4)

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008).
[CrossRef] [PubMed]

Y. Luo, D. Y. Lei, S. A. Maier, J. B. Pendry, “Broadband light harvesting nanostructures robust to edge bluntness,” Phys. Rev. Lett. 108(2), 023901 (2012).
[CrossRef] [PubMed]

J. Li, J. B. Pendry, “Hiding under the carpet: A new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Proc. IRE (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–12 (1949).
[CrossRef]

Science (4)

R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, D. R. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
[CrossRef] [PubMed]

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

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

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef] [PubMed]

Other (4)

T. J. Cui, D. R. Smith, R. Liu, Metamaterials: Theory, Design and Applications (Springer, 2010).
[CrossRef]

N. Engheta, “Thin absorbing screens using metamaterial surfaces,” in Antennas and Propagation Society International Symposium, IEEE (2002), pp. 392–395.
[CrossRef]

W. W. Salisbury, “Absorbent body for electromagnetic waves,” U.S. Patent No. 2.599.944, filed 1952.

F. Trautnitz, “Emc absorbers through the years with respect to the new site vswr validation procedure in the frequency range from 1 to 18 ghz-a practical approach,” in Electromagnetic Compatibility International Symposium, IEEE (2007), pp. 1–6.

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Figures (10)

Fig. 1
Fig. 1

(Section view) (a) Some examples of the discrete coordinate transformation. The solid black line and the blue line (numbered 1) represent the physical space for a carpet cloak design. The solid black line and the green line (numbered 2) represent the virtual space for a planar reflector design. The solid black line and the brown line (numbered 3) represent the virtual space for a flattened convex lens design. The solid black line and the red line (numbered 4) represent the virtual space for a flattened Luneburg lens design. The east (E), south (S), west (W) and north (N) boundaries are marked. (b) When the north boundary of the virtual space changes from the brown line to the blue line and then to the red line, the discretising mesh becomes significantly distorted and local coordinates are no longer near-orthogonal. (c) An arbitrary dielectric object and its surroundings are compressed by the multiple DCT technique and an all-dielectric solution is expected in the physical space.

Fig. 2
Fig. 2

Schematic showing of the multiple transformation (section view). (a) The original virtual space to be compressed. (b) The transit physical space. (c) The transit virtual space. (d) The target physical space. The arrowed red lines and the arrowed dashed red lines illustrate the propagation of the incident waves along the horizontal axis and the vertical axis, respectively.

Fig. 3
Fig. 3

(a) A space to be compressed is discretised into K layers. (b–e) The two-step DCT is applied to compress the 1st layer. (f–i) The compressed 1st layer is added to the 2nd layer and another round of the two-step DCT carries on.

Fig. 4
Fig. 4

Geometry of a 3 × 3 microwave pyramidal absorber unit from the TDK corporation (left), and its dimensions (right).

Fig. 5
Fig. 5

(Section view.) The space containing the pyramid in Fig. 4 is discretised into 10 layers, and the multiple DCT technique is applied to compress the space. Positions of the top right points in each layer of the absorber are noted in the figure.

Fig. 6
Fig. 6

An illustration of the multiple DCT procedure applied to compress the pyramidal absorber. (a) The base and Layer 0 are filled in the virtual space outlined by the dashed black line. (b) The transformation space is compressed from the bottom. The space outlined by the dashed black line and the solid red line is the transit physical space. (c) The transit physical space in (b) is rotated by 180° and the left half and the right half are exchanged. (d) The transit virtual space outlined by the dashed black line and the solid red line is compressed from the top. (e) The physical space after compression. (f) The physical space in (e) is rotated by 180° and the left half and the right half are exchanged. Quasi-orthogonal grids are generated and shown in the right part of (a)–(f). (g) The target physical space of the virtual space in (a). The total height is reduced by 20 mm after transformation. The target physical space in (g) is filled with spatially-dispersive media. After that, Layer 1 in Fig. 5 is added above and the same procedure from (a) to (g) will be repeated.

Fig. 7
Fig. 7

Relative permittivity distribution of the transformation absorber. (a) The real part and (b) the imaginary part of permittivity are plotted in logarithmic scale.

Fig. 8
Fig. 8

Simulation setup to test (a) the pyramidal absorber and (b) the transformation absorber.

Fig. 9
Fig. 9

Reflection from the conducting wall when the pyramidal absorber and the compressed absorber are applied respectively. The incidence is from (a) ϕ = 90°, (b) ϕ = 45° and (c) ϕ = 27°.

Fig. 10
Fig. 10

Distribution of the electric field inside (a) the pyramidal absorber, (b) the compressed all-dielectric absorber and (c) the compressed absorber with matched impedance (when the relative permittivity distribution and the relative permeability distribution are identical) respectively when the incidence is from ϕ = 27°. (d) Reflections when the compressed absorber with matched impedance is applied. The incidence is from ϕ = 90°, ϕ = 45° and ϕ = 27° respectively.

Equations (13)

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ε ¯ ¯ = J ε ¯ ¯ J T det ( J ) , μ ¯ ¯ = J μ ¯ ¯ J T det ( J ) .
ε ( x i , j , y i , j ) ε ( i , j ) = ε [ X m ( j ) M ( i 1 + 0.5 ) , Y m ( i ) N ( j 1 + 0.5 ) ] , μ ( x i , j , y i , j ) μ ( i , j ) = μ [ X m ( j ) M ( i 1 + 0.5 ) , Y m ( i ) N ( j 1 + 0.5 ) ] , i = 1 , 2 , , M , j = 1 , 2 , , N ,
ε z ε z z = ε det ( J ) 1 ,
μ ¯ ¯ = μ det ( J ) ( ( x x ) 2 + ( x y ) 2 x x y x + x y y y y x x x + x y y y ( y x ) 2 + ( y y ) 2 ) .
x y 0 , y x 0 , x y 0 , y x 0 .
μ ¯ ¯ = μ 0 det ( J ) ( ( x x ) 2 0 0 ( y y ) 2 ) .
n 2 ε z / ε 0 = 1 det ( J ) = 1 x x y y Δ x Δ y Δ x Δ y ,
ε ( i 1 , j 1 ) = Δ x 0 ( i 1 , j 1 ) Δ y 0 ( i 1 , j 1 ) Δ x 1 ( i 1 , j 1 ) Δ y 1 ( i 1 , j 1 ) ε ( i 1 , j 1 ) , μ ( i 1 , j 1 ) = μ 0 , i 1 = 1 , 2 , , M 1 , j 1 = 1 , 2 , , N 1 ,
ε ( i 1 , j 1 ) = { ε ( | M 1 2 | + i 1 , j 1 ) , i 1 < | M 1 2 | ε ( i 1 | M 1 2 | , j 1 ) , i 1 | M 1 2 | , μ ( i 1 , j 1 ) = μ 0 .
ε ( i 2 , j 2 ) = Δ x 2 ( i 2 , j 2 ) Δ y 2 ( i 2 , j 2 ) Δ x 3 ( i 2 , j 2 ) Δ y 3 ( i 2 , j 2 ) ε ( i 2 , j 2 ) , μ ( i 2 , j 2 ) = μ 0 , i 2 = 1 , 2 , , M 2 , j 2 = 1 , 2 , , N 2 ,
α = H H Δ H .
ε 2 = { ε , H K Y 2 H K ε 1 , 0 < Y < H K , μ 2 = μ 0 ,
ε k + 1 = { ε , k H K Y ( k + 1 ) H K ε k , ( k 1 ) H K < Y < k H K , μ k + 1 = μ 0 , k = 1 , 2 , , K .

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