Abstract

A dispersive full-wave finite-difference time-domain model is used to study the performance of point mapped and line-segment mapped complementary invisibility cloaking devices. We have used the permittivity and the permeability tensors for conventional elliptic and bipolar cylindrical invisibility cloaks obtained from an effective medium approach in general relativity. In the case of a line-segment mapped cloak we also employ the mapping of the σ-axis in bipolar cylindrical coordinates. In these cloaks, we employ the complementary media both horizontally and vertically. Cloaks with horizontally or vertically arranged complementary media mapped to a point show good performance of cloaking in any case. On the other hand, cloaks with horizontally arranged complementary media mapped to a line-segment, do not show cloaking performance. However, for cloaks with vertically arranged complementary media mapped to a line-segment, cloaking works very well in any cases. These results show improved cloaking performance over the conventional cloaks with perfect electrical conductor mapped to a line-segment. On the other hand, realistic cloaking materials with loss still show cloaking but attenuated backscattering waves exist.

© 2013 Optical Society of America

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
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  4. P. H. Tichit, S. N. Burokur, and A. De Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18, 767–772 (2010).
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  5. K. Zhang, Q. Wu, F. Y. Meng, and L. W. Li, “Arbitrary waveguide connector based on embedded optical transformation,” Opt. Express 18, 17273–17279 (2010).
    [CrossRef]
  6. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef]
  7. S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [CrossRef]
  8. D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [CrossRef]
  9. Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133–11141 (2007).
    [CrossRef]
  10. B. Zhang, H. Chen, and B. I. Wu, “Limitations of high-order transformation and incident angle on simplified invisibility cloaks,” Opt. Express 16, 14655–14660 (2008).
    [CrossRef]
  11. Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
    [CrossRef]
  12. Q. Wu, K. Zhang, F. Y. Meng, and L. W. Li, “Investigation of the far/near-field properties of the inhomogeneous and anisotropic invisible cloak covered PEC cylinder illuminated by the parallel electric-line-source,” Appl. Phys. A 95, 335–341 (2009).
    [CrossRef]
  13. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
    [CrossRef]
  14. D. Ahn, “Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity,” J. Mod. Opt. 58, 700–710 (2011).
    [CrossRef]
  15. Y. Lee and D. Ahn, “Dispersive finite-difference time-domain (FDTD) analysis of the elliptic cylindrical cloak,” J. Korean Phys. Soc. 60, 1349–1360 (2012).
    [CrossRef]
  16. Y. Y. Lee and D. Ahn, “Dispersive full-wave finite-difference time-domain analysis of the bipolar cylindrical cloak based on the effective medium approach,” J. Opt. Soc. Am. B 30, 140–148 (2013).
    [CrossRef]
  17. I. Tamm, “Electrodynamics of an anisotropic medium in the special theory of relativity,” J. Russ. Phys. Chem. Soc 56, 248 (1924).
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    [CrossRef]
  19. A. Lakhtakia and T. G. Mackay, “Towards gravitationally assisted negative refraction of light by vacuum,” J. Phys. A 37, L505–L510 (2004).
    [CrossRef]
  20. T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
    [CrossRef]
  21. T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009).
    [CrossRef]
  22. M. W. McCall, “On negative refraction in classical vacuum,” J. Mod. Opt. 54, 119–128 (2007).
    [CrossRef]
  23. M. W. McCall, “Classical gravity does not refract negatively,” Phys. Rev. Lett. 98, 91102 (2007).
    [CrossRef]
  24. Y. Lai, H. Chen, Z. Q. Zhang, and C. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 93901 (2009).
    [CrossRef]
  25. J. Yang, M. Huang, C. Yang, and J. Yu, “Reciprocal invisibility cloak based on complementary media,” Eur. Phys. J. D 61, 731–736 (2011).
    [CrossRef]
  26. J. S. Mei, Q. Wu, and K. Zhang, “Complementary cloak based on conventional cloak with axial symmetrical cloaked region,” Appl. Phys. A 108, 1001–1005 (2012).
    [CrossRef]
  27. B. Kanté, D. Germain, and A. De Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
    [CrossRef]
  28. R. Liu, C. Ji, J. Mock, J. Chin, T. Cui, and D. Smith, “Broadband ground-plane cloak,” Science 323, 366–369 (2009).
    [CrossRef]
  29. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [CrossRef]
  30. C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antenna Propag. 57, 1432–1441 (2009).
  31. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 1995).
  32. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).
  33. D. M. Sullivan, “A simplified PML for use with the FDTD method,” IEEE Microw. Guided Wave Lett. 6, 97 (1996).
    [CrossRef]
  34. Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2009).
  35. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14, 302–307 (1966).

2013 (1)

2012 (2)

Y. Lee and D. Ahn, “Dispersive finite-difference time-domain (FDTD) analysis of the elliptic cylindrical cloak,” J. Korean Phys. Soc. 60, 1349–1360 (2012).
[CrossRef]

J. S. Mei, Q. Wu, and K. Zhang, “Complementary cloak based on conventional cloak with axial symmetrical cloaked region,” Appl. Phys. A 108, 1001–1005 (2012).
[CrossRef]

2011 (2)

J. Yang, M. Huang, C. Yang, and J. Yu, “Reciprocal invisibility cloak based on complementary media,” Eur. Phys. J. D 61, 731–736 (2011).
[CrossRef]

D. Ahn, “Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity,” J. Mod. Opt. 58, 700–710 (2011).
[CrossRef]

2010 (2)

2009 (7)

Q. Wu, K. Zhang, F. Y. Meng, and L. W. Li, “Investigation of the far/near-field properties of the inhomogeneous and anisotropic invisible cloak covered PEC cylinder illuminated by the parallel electric-line-source,” Appl. Phys. A 95, 335–341 (2009).
[CrossRef]

Y. Lai, H. Chen, Z. Q. Zhang, and C. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 93901 (2009).
[CrossRef]

B. Kanté, D. Germain, and A. De Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[CrossRef]

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

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

C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antenna Propag. 57, 1432–1441 (2009).

T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009).
[CrossRef]

2008 (4)

2007 (3)

Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133–11141 (2007).
[CrossRef]

M. W. McCall, “On negative refraction in classical vacuum,” J. Mod. Opt. 54, 119–128 (2007).
[CrossRef]

M. W. McCall, “Classical gravity does not refract negatively,” Phys. Rev. Lett. 98, 91102 (2007).
[CrossRef]

2006 (5)

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

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

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

2005 (1)

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

2004 (1)

A. Lakhtakia and T. G. Mackay, “Towards gravitationally assisted negative refraction of light by vacuum,” J. Phys. A 37, L505–L510 (2004).
[CrossRef]

1996 (1)

D. M. Sullivan, “A simplified PML for use with the FDTD method,” IEEE Microw. Guided Wave Lett. 6, 97 (1996).
[CrossRef]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14, 302–307 (1966).

1960 (1)

J. Plebanski, “Electromagnetic waves in gravitational fields,” Phys. Rev. 118, 1396–1408 (1960).
[CrossRef]

1924 (1)

I. Tamm, “Electrodynamics of an anisotropic medium in the special theory of relativity,” J. Russ. Phys. Chem. Soc 56, 248 (1924).

Ahn, D.

Y. Y. Lee and D. Ahn, “Dispersive full-wave finite-difference time-domain analysis of the bipolar cylindrical cloak based on the effective medium approach,” J. Opt. Soc. Am. B 30, 140–148 (2013).
[CrossRef]

Y. Lee and D. Ahn, “Dispersive finite-difference time-domain (FDTD) analysis of the elliptic cylindrical cloak,” J. Korean Phys. Soc. 60, 1349–1360 (2012).
[CrossRef]

D. Ahn, “Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity,” J. Mod. Opt. 58, 700–710 (2011).
[CrossRef]

Argyropoulos, C.

C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antenna Propag. 57, 1432–1441 (2009).

Bartal, G.

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

Burokur, S. N.

Chan, C.

Y. Lai, H. Chen, Z. Q. Zhang, and C. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 93901 (2009).
[CrossRef]

Chen, H.

Y. Lai, H. Chen, Z. Q. Zhang, and C. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 93901 (2009).
[CrossRef]

B. Zhang, H. Chen, and B. I. Wu, “Limitations of high-order transformation and incident angle on simplified invisibility cloaks,” Opt. Express 16, 14655–14660 (2008).
[CrossRef]

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

Chin, J.

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

Cui, J.

Cui, T.

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

Cummer, S. A.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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

De Lustrac, A.

P. H. Tichit, S. N. Burokur, and A. De Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18, 767–772 (2010).
[CrossRef]

B. Kanté, D. Germain, and A. De Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[CrossRef]

Du, C.

Feng, Y.

Germain, D.

B. Kanté, D. Germain, and A. De Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 1995).

Hao, Y.

C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antenna Propag. 57, 1432–1441 (2009).

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2009).

Huang, M.

J. Yang, M. Huang, C. Yang, and J. Yu, “Reciprocal invisibility cloak based on complementary media,” Eur. Phys. J. D 61, 731–736 (2011).
[CrossRef]

Huang, Y.

Ji, C.

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

Jiang, T.

Justice, B.

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

Kanté, B.

B. Kanté, D. Germain, and A. De Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B 80, 201104 (2009).
[CrossRef]

Lai, Y.

Y. Lai, H. Chen, Z. Q. Zhang, and C. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 93901 (2009).
[CrossRef]

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009).
[CrossRef]

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

A. Lakhtakia and T. G. Mackay, “Towards gravitationally assisted negative refraction of light by vacuum,” J. Phys. A 37, L505–L510 (2004).
[CrossRef]

Lee, Y.

Y. Lee and D. Ahn, “Dispersive finite-difference time-domain (FDTD) analysis of the elliptic cylindrical cloak,” J. Korean Phys. Soc. 60, 1349–1360 (2012).
[CrossRef]

Lee, Y. Y.

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

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

Li, J.

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

Li, L. W.

K. Zhang, Q. Wu, F. Y. Meng, and L. W. Li, “Arbitrary waveguide connector based on embedded optical transformation,” Opt. Express 18, 17273–17279 (2010).
[CrossRef]

Q. Wu, K. Zhang, F. Y. Meng, and L. W. Li, “Investigation of the far/near-field properties of the inhomogeneous and anisotropic invisible cloak covered PEC cylinder illuminated by the parallel electric-line-source,” Appl. Phys. A 95, 335–341 (2009).
[CrossRef]

Lin, L.

Liu, R.

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

Luo, X.

Luo, Y.

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

Ma, J.

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009).
[CrossRef]

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

A. Lakhtakia and T. G. Mackay, “Towards gravitationally assisted negative refraction of light by vacuum,” J. Phys. A 37, L505–L510 (2004).
[CrossRef]

McCall, M. W.

M. W. McCall, “On negative refraction in classical vacuum,” J. Mod. Opt. 54, 119–128 (2007).
[CrossRef]

M. W. McCall, “Classical gravity does not refract negatively,” Phys. Rev. Lett. 98, 91102 (2007).
[CrossRef]

Mei, J. S.

J. S. Mei, Q. Wu, and K. Zhang, “Complementary cloak based on conventional cloak with axial symmetrical cloaked region,” Appl. Phys. A 108, 1001–1005 (2012).
[CrossRef]

Meng, F. Y.

K. Zhang, Q. Wu, F. Y. Meng, and L. W. Li, “Arbitrary waveguide connector based on embedded optical transformation,” Opt. Express 18, 17273–17279 (2010).
[CrossRef]

Q. Wu, K. Zhang, F. Y. Meng, and L. W. Li, “Investigation of the far/near-field properties of the inhomogeneous and anisotropic invisible cloak covered PEC cylinder illuminated by the parallel electric-line-source,” Appl. Phys. A 95, 335–341 (2009).
[CrossRef]

Mittra, R.

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials: Theory and Applications (Artech House, 2009).

Mock, J.

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

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

Pendry, J.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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

Pendry, J. B.

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

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

Plebanski, J.

J. Plebanski, “Electromagnetic waves in gravitational fields,” Phys. Rev. 118, 1396–1408 (1960).
[CrossRef]

Popa, B. I.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

Schurig, D.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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

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

Setiawan, S.

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

Smith, D.

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

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

Smith, D. R.

S. A. Cummer, B. I. Popa, D. Schurig, D. R. Smith, and J. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
[CrossRef]

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

Starr, A.

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

Sullivan, D. M.

D. M. Sullivan, “A simplified PML for use with the FDTD method,” IEEE Microw. Guided Wave Lett. 6, 97 (1996).
[CrossRef]

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 1995).

Tamm, I.

I. Tamm, “Electrodynamics of an anisotropic medium in the special theory of relativity,” J. Russ. Phys. Chem. Soc 56, 248 (1924).

Tichit, P. H.

Valentine, J.

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

Wang, C.

Wang, W.

Wu, B. I.

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

B. Zhang, H. Chen, and B. I. Wu, “Limitations of high-order transformation and incident angle on simplified invisibility cloaks,” Opt. Express 16, 14655–14660 (2008).
[CrossRef]

Wu, Q.

J. S. Mei, Q. Wu, and K. Zhang, “Complementary cloak based on conventional cloak with axial symmetrical cloaked region,” Appl. Phys. A 108, 1001–1005 (2012).
[CrossRef]

K. Zhang, Q. Wu, F. Y. Meng, and L. W. Li, “Arbitrary waveguide connector based on embedded optical transformation,” Opt. Express 18, 17273–17279 (2010).
[CrossRef]

Q. Wu, K. Zhang, F. Y. Meng, and L. W. Li, “Investigation of the far/near-field properties of the inhomogeneous and anisotropic invisible cloak covered PEC cylinder illuminated by the parallel electric-line-source,” Appl. Phys. A 95, 335–341 (2009).
[CrossRef]

Xi, S.

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

Yang, C.

J. Yang, M. Huang, C. Yang, and J. Yu, “Reciprocal invisibility cloak based on complementary media,” Eur. Phys. J. D 61, 731–736 (2011).
[CrossRef]

Yang, J.

J. Yang, M. Huang, C. Yang, and J. Yu, “Reciprocal invisibility cloak based on complementary media,” Eur. Phys. J. D 61, 731–736 (2011).
[CrossRef]

Yee, K.

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14, 302–307 (1966).

Yu, J.

J. Yang, M. Huang, C. Yang, and J. Yu, “Reciprocal invisibility cloak based on complementary media,” Eur. Phys. J. D 61, 731–736 (2011).
[CrossRef]

Zentgraf, T.

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

Zhang, B.

Zhang, J.

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

Zhang, K.

J. S. Mei, Q. Wu, and K. Zhang, “Complementary cloak based on conventional cloak with axial symmetrical cloaked region,” Appl. Phys. A 108, 1001–1005 (2012).
[CrossRef]

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[CrossRef]

Q. Wu, K. Zhang, F. Y. Meng, and L. W. Li, “Investigation of the far/near-field properties of the inhomogeneous and anisotropic invisible cloak covered PEC cylinder illuminated by the parallel electric-line-source,” Appl. Phys. A 95, 335–341 (2009).
[CrossRef]

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[CrossRef]

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Y. Lai, H. Chen, Z. Q. Zhang, and C. Chan, “Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell,” Phys. Rev. Lett. 102, 93901 (2009).
[CrossRef]

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C. Argyropoulos, Y. Zhao, and Y. Hao, “A radially-dependent dispersive finite-difference time-domain method for the evaluation of electromagnetic cloaks,” IEEE Trans. Antenna Propag. 57, 1432–1441 (2009).

Appl. Phys. A (2)

Q. Wu, K. Zhang, F. Y. Meng, and L. W. Li, “Investigation of the far/near-field properties of the inhomogeneous and anisotropic invisible cloak covered PEC cylinder illuminated by the parallel electric-line-source,” Appl. Phys. A 95, 335–341 (2009).
[CrossRef]

J. S. Mei, Q. Wu, and K. Zhang, “Complementary cloak based on conventional cloak with axial symmetrical cloaked region,” Appl. Phys. A 108, 1001–1005 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Luo, J. Zhang, H. Chen, S. Xi, and B. I. Wu, “Cylindrical cloak with axial permittivity/permeability spatially invariant,” Appl. Phys. Lett. 93, 033504 (2008).
[CrossRef]

Eur. Phys. J. D (1)

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Figures (10)

Fig. 1.
Fig. 1.

Spatial distribution of constitutive parameters (a) εzz of the elliptic cylindrical cloak with the half-length of the major axis of ellipses K1=0.1 and K2=0.3, and the semi-focal distance a=0.001m while εuu and εvv are constants, 0.17 and 5.8, respectively. (The relation between Ki and Ui is Ui=Re{arccosh(Ki/a)}) (b) εzz of the elliptic cylindrical cloak with K1=0.1, K2=0.3, and a=0.09m while εuu and εvv are constants, 0.75 and 1.3, respectively. (c) εzz of the bipolar cylindrical cloak with σ1=0.75π, σ2=0.5π, and a=0.3m while εσσ and εττ are constants, 0.5 and 2.0, respectively.

Fig. 2.
Fig. 2.

(a) Elliptic cylindrical cloak with horizontally located complementary media that consist of free space and its complementary medium with (εr,μr)=(1,1). (b) The σ-mapped bipolar cylindrical cloak with horizontally located complementary media that consist of free space and its complementary medium with (εr,μr)=(1,1).

Fig. 3.
Fig. 3.

Ez(V/m) field distributions when an ideal elliptic cylindrical cloak with complementary media is exposed to TE illumination with different incident axes: (a) x direction and (b) y direction. Hz(A/m) field distributions when an ideal elliptic cylindrical cloak with complementary media is exposed to TM illumination with different incident axes: (c) x direction and (d) y direction. In these cases the semi-focal distance a is 0.001 m and the complementary media are arranged horizontally.

Fig. 4.
Fig. 4.

Ez(V/m) field distributions when an ideal elliptic cylindrical cloak with complementary media is exposed to TE illumination with different incident axes: (a) x direction and (b) y direction. Hz(A/m) field distributions when an ideal elliptic cylindrical cloak with complementary media is exposed to TM illumination with different incident axes: (c) x direction and (d) y direction. In these cases the semi-focal distance a is 0.001 m and the complementary media are arranged vertically.

Fig. 5.
Fig. 5.

Ez(V/m) field distributions when an ideal elliptic cylindrical cloak with complementary media is exposed to TE illumination with different incident axes: (a) x direction and (b) y direction. Hz(A/m) field distributions when an ideal elliptic cylindrical cloak with complementary media is exposed to TM illumination with different incident axes: (c) x direction and (d) y direction. In these cases the semi-focal distance a is 0.09 m and the complementary media are arranged horizontally.

Fig. 6.
Fig. 6.

Ez(V/m) field distributions when an ideal elliptic cylindrical cloak with complementary media is exposed to TE illumination with different incident axes: (a) x direction and (b) y direction. Hz(A/m) field distributions when an ideal elliptic cylindrical cloak with complementary media is exposed to TM illumination with different incident axes: (c) x direction and (d) y direction. In these cases the semi-focal distance a is 0.09 m and the complementary media are arranged vertically.

Fig. 7.
Fig. 7.

Ez(V/m) field distributions when an ideal elliptic cylindrical cloak with complementary media including an object and an antiobject is exposed to TE illumination with different incident axes: (a) x direction and (b) y direction. Hz(A/m) field distributions when an ideal elliptic cylindrical cloak with complementary media including an object and an antiobject is exposed to TM illumination with different incident axes: (c) x direction and (d) y direction. In these cases the semi-focal distance a is 0.09 m and the complementary media are arranged vertically.

Fig. 8.
Fig. 8.

Ez(V/m) field distributions when an ideal σ-mapped bipolar cylindrical cloak with complementary media is exposed to TE illumination with different incident axes: (a) x direction and (b) y direction. Hz(A/m) field distributions when an ideal σ-mapped bipolar cylindrical cloak with complementary media is exposed to TM illumination with different incident axes: (c) x direction and (d) y direction. In these cases the semi-focal distance a is 0.3 m and the complementary media are arranged vertically.

Fig. 9.
Fig. 9.

Ez(V/m) field distributions when an ideal σ-mapped bipolar cylindrical cloak with complementary media including an object and an antiobject is exposed to TE illumination with different incident axes: (a) x direction and (b) y direction. Hz(A/m) field distributions when an ideal σ-mapped bipolar cylindrical cloak with complementary media including an object and an antiobject is exposed to TM illumination with different incident axes: (c) x direction and (d) y direction. In these cases the semi-focal distance a is 0.3 m and the complementary media are arranged vertically.

Fig. 10.
Fig. 10.

Ez(V/m) field distributions when a practical elliptic cylindrical cloak with complementary media including an object and an antiobject is exposed to TE illumination with different incident axes: (a) x direction and (b) y direction. Hz(A/m) field distributions when a practical elliptic cylindrical cloak with complementary media including an object and an antiobject is exposed to TM illumination with different incident axes: (c) x direction and (d) y direction. In these cases the semi-focal distance a is 0.09 m and the complementary media are arranged vertically. These structures’ loss is tan(δ)=0.1.

Equations (4)

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u=U1+uU2U1U2,v=v,z=z.
εji=μji=diag((U2U1U2),(U2U2U1),(U2U2U1)sinh2u+sin2vsinh2u+sin2v).
σ=σ2σ1σ2π(σπ)+σ1,σ[σ2,π],σ=σ2σ1σ2π(σπ)+2πσ1,σ(π,2πσ2],τ=τ,z=z.
εji=μji=diag(σ2σ1σ2π,σ2πσ2σ1,σ2πσ2σ1(cosσcoshτ)2(cosσcoshτ)2).

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