Abstract

The increasing interest in invisible cloaks has been prompted in part by the availability of powerful computational resources which permit numerical studies of such a phenomenon. These are usually carried out with commercial software. We report here a full time domain simulation of cloaking structures with the Transmission Line Modeling (TLM) method. We first develop a new condensed TLM node to model metamaterials in two dimensional situations; various results are then presented, with special emphasis on what is not easily achievable using commercial software.

©2008 Optical Society of America

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References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [Crossref] [PubMed]
  2. H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
    [Crossref] [PubMed]
  3. F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
    [Crossref] [PubMed]
  4. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [Crossref] [PubMed]
  5. S. A. Cummer, B-I. Popa, D. Schurig, D. R. Smith, and J. B. Pendry, “Full-wave simulations of electromagnetic cloaking structures,” Phys. Rev. E 74, 036621 (2006).
    [Crossref]
  6. C. Christopoulos, The Transmission-Line Modeling method, The Institute of Electrical and Electronic Engineers (New York and Oxford University Press, Oxford, 1995).
    [Crossref]
  7. C. Blanchard, J. A. Portí, J. A. Morente, A. Salinas, and E. A. Navarro, “Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method,” J. Appl. Phys. 102, 064101 (2007).
    [Crossref]
  8. J. A. Portí and J. A. Morente, “A three-dimensional symmetrical condensed TLM node for acoustics,” J. Sound Vibr. 241, 207–222 (2001).
    [Crossref]
  9. P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microw. Theory Tech. 53, 1496–1505 (2005).
    [Crossref]
  10. J. P. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM-Part 2: Materials with anisotropic properties,” IEEE Trans. Antennas Propag. 47, 1535–1542 (1999).
    [Crossref]
  11. L. de Menezes and W. J. R. Hoefer, “Modeling of general constitutive relationships using SCN TLM,” IEEE Trans. Microw. Theory Tech. 44, 854–861 (1996).
    [Crossref]
  12. Y. Huang, Y. Feng, and T. Jiang, “Electromagnetic cloaking by layered structure of homogeneous isotropic materials,” Opt. Express 15, 11133 (2007).
    [Crossref] [PubMed]
  13. O. Wiener, “Zur theorie der refraktionskonstanten,” Berichteüber die Verhandlungen der Königlich-Sächsischen Gesellsschaft der Wissenschaften zu Leipzig, 256–277 (1910).
  14. S. Xi, H. Chen, B-I. Wu, B. Zhang, Y. Luo, J. Huangfu, D. Wang, and J. A. Kong, “Effects of different transformations on the performance of a nonideal cylindrical cloak,” Submitted to PIERS.
  15. P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Elec. Eng. 118, 1203–1208 (2007).
    [Crossref]
  16. P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microw. Theory Tech. 35, 370–377 (1987).
    [Crossref]
  17. J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, and M. Rodríguez-Sola, “A generalized dynamic symmetrical condensed TLM node for the modeling of time-varying electromagnetic media,” IEEE Trans. Antennas Propag. 54, 2–11 (2006).
    [Crossref]
  18. J. A. Portí, J. A. Morente, A. Salinas, M. Rodríguez-Sola, and C. Blanchard, “On the circuit description of TLM nodes,” Int. J. Electron. 93, 479–491 (2006).
    [Crossref]
  19. J. A. Portí, J. A. Morente, and M. C. Carrión, “Simple derivation of scattering matrix for TLM nodes,” Electron. Lett. 34, 1763–1764 (1998).
    [Crossref]
  20. R. Luebbers, D. Ryan, and J. Beggs, “A two-dimensional time-domain near-zone to Far-zone transformation,” IEEE Trans. Antennas Propag. 40, 848–851 (1992).
    [Crossref]
  21. C. Balanis, Advanced Enginnering Electromagnetics, John Wiley & Sons (1989).
  22. B. Zhang, H. Chen, B-I. Wu, Y. Luo, L. Ran, and J. A. Kong, “Response of a cylindrical invisibility cloak to electromagnetic waves,” Phys. Rev. B 76, 121101 (2007).
    [Crossref]
  23. M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
    [Crossref]

2007 (7)

C. Blanchard, J. A. Portí, J. A. Morente, A. Salinas, and E. A. Navarro, “Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method,” J. Appl. Phys. 102, 064101 (2007).
[Crossref]

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Elec. Eng. 118, 1203–1208 (2007).
[Crossref]

B. Zhang, H. Chen, B-I. Wu, Y. Luo, L. Ran, and J. A. Kong, “Response of a cylindrical invisibility cloak to electromagnetic waves,” Phys. Rev. B 76, 121101 (2007).
[Crossref]

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[Crossref]

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
[Crossref] [PubMed]

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

2006 (5)

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

J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, and M. Rodríguez-Sola, “A generalized dynamic symmetrical condensed TLM node for the modeling of time-varying electromagnetic media,” IEEE Trans. Antennas Propag. 54, 2–11 (2006).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, M. Rodríguez-Sola, and C. Blanchard, “On the circuit description of TLM nodes,” Int. J. Electron. 93, 479–491 (2006).
[Crossref]

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

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

2005 (1)

P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microw. Theory Tech. 53, 1496–1505 (2005).
[Crossref]

2001 (1)

J. A. Portí and J. A. Morente, “A three-dimensional symmetrical condensed TLM node for acoustics,” J. Sound Vibr. 241, 207–222 (2001).
[Crossref]

1999 (1)

J. P. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM-Part 2: Materials with anisotropic properties,” IEEE Trans. Antennas Propag. 47, 1535–1542 (1999).
[Crossref]

1998 (1)

J. A. Portí, J. A. Morente, and M. C. Carrión, “Simple derivation of scattering matrix for TLM nodes,” Electron. Lett. 34, 1763–1764 (1998).
[Crossref]

1996 (1)

L. de Menezes and W. J. R. Hoefer, “Modeling of general constitutive relationships using SCN TLM,” IEEE Trans. Microw. Theory Tech. 44, 854–861 (1996).
[Crossref]

1992 (1)

R. Luebbers, D. Ryan, and J. Beggs, “A two-dimensional time-domain near-zone to Far-zone transformation,” IEEE Trans. Antennas Propag. 40, 848–851 (1992).
[Crossref]

1987 (1)

P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microw. Theory Tech. 35, 370–377 (1987).
[Crossref]

Balanis, C.

C. Balanis, Advanced Enginnering Electromagnetics, John Wiley & Sons (1989).

Beggs, J.

R. Luebbers, D. Ryan, and J. Beggs, “A two-dimensional time-domain near-zone to Far-zone transformation,” IEEE Trans. Antennas Propag. 40, 848–851 (1992).
[Crossref]

Beurle, R. L.

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Elec. Eng. 118, 1203–1208 (2007).
[Crossref]

Blanchard, C.

C. Blanchard, J. A. Portí, J. A. Morente, A. Salinas, and E. A. Navarro, “Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method,” J. Appl. Phys. 102, 064101 (2007).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, M. Rodríguez-Sola, and C. Blanchard, “On the circuit description of TLM nodes,” Int. J. Electron. 93, 479–491 (2006).
[Crossref]

Carrión, M. C.

J. A. Portí, J. A. Morente, and M. C. Carrión, “Simple derivation of scattering matrix for TLM nodes,” Electron. Lett. 34, 1763–1764 (1998).
[Crossref]

Chen, H.

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

B. Zhang, H. Chen, B-I. Wu, Y. Luo, L. Ran, and J. A. Kong, “Response of a cylindrical invisibility cloak to electromagnetic waves,” Phys. Rev. B 76, 121101 (2007).
[Crossref]

S. Xi, H. Chen, B-I. Wu, B. Zhang, Y. Luo, J. Huangfu, D. Wang, and J. A. Kong, “Effects of different transformations on the performance of a nonideal cylindrical cloak,” Submitted to PIERS.

Christopoulos, C.

J. P. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM-Part 2: Materials with anisotropic properties,” IEEE Trans. Antennas Propag. 47, 1535–1542 (1999).
[Crossref]

C. Christopoulos, The Transmission-Line Modeling method, The Institute of Electrical and Electronic Engineers (New York and Oxford University Press, Oxford, 1995).
[Crossref]

Cummer, S. A.

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

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

de Menezes, L.

L. de Menezes and W. J. R. Hoefer, “Modeling of general constitutive relationships using SCN TLM,” IEEE Trans. Microw. Theory Tech. 44, 854–861 (1996).
[Crossref]

Du, H.

P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microw. Theory Tech. 53, 1496–1505 (2005).
[Crossref]

Feng, Y.

Guenneau, S.

Hoefer, W. J. R.

P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microw. Theory Tech. 53, 1496–1505 (2005).
[Crossref]

L. de Menezes and W. J. R. Hoefer, “Modeling of general constitutive relationships using SCN TLM,” IEEE Trans. Microw. Theory Tech. 44, 854–861 (1996).
[Crossref]

Huang, Y.

Huangfu, J.

S. Xi, H. Chen, B-I. Wu, B. Zhang, Y. Luo, J. Huangfu, D. Wang, and J. A. Kong, “Effects of different transformations on the performance of a nonideal cylindrical cloak,” Submitted to PIERS.

Jiang, T.

Johns, P. B.

P. B. Johns and R. L. Beurle, “Numerical solution of 2-dimensional scattering problems using a transmission-line matrix,” Proc. Inst. Elec. Eng. 118, 1203–1208 (2007).
[Crossref]

P. B. Johns, “A symmetrical condensed node for the TLM method,” IEEE Trans. Microw. Theory Tech. 35, 370–377 (1987).
[Crossref]

Justice, B. J.

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

Kong, J. A.

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

B. Zhang, H. Chen, B-I. Wu, Y. Luo, L. Ran, and J. A. Kong, “Response of a cylindrical invisibility cloak to electromagnetic waves,” Phys. Rev. B 76, 121101 (2007).
[Crossref]

S. Xi, H. Chen, B-I. Wu, B. Zhang, Y. Luo, J. Huangfu, D. Wang, and J. A. Kong, “Effects of different transformations on the performance of a nonideal cylindrical cloak,” Submitted to PIERS.

Luebbers, R.

R. Luebbers, D. Ryan, and J. Beggs, “A two-dimensional time-domain near-zone to Far-zone transformation,” IEEE Trans. Antennas Propag. 40, 848–851 (1992).
[Crossref]

Luo, Y.

B. Zhang, H. Chen, B-I. Wu, Y. Luo, L. Ran, and J. A. Kong, “Response of a cylindrical invisibility cloak to electromagnetic waves,” Phys. Rev. B 76, 121101 (2007).
[Crossref]

S. Xi, H. Chen, B-I. Wu, B. Zhang, Y. Luo, J. Huangfu, D. Wang, and J. A. Kong, “Effects of different transformations on the performance of a nonideal cylindrical cloak,” Submitted to PIERS.

Mock, J. J.

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

Morente, J. A.

C. Blanchard, J. A. Portí, J. A. Morente, A. Salinas, and E. A. Navarro, “Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method,” J. Appl. Phys. 102, 064101 (2007).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, and M. Rodríguez-Sola, “A generalized dynamic symmetrical condensed TLM node for the modeling of time-varying electromagnetic media,” IEEE Trans. Antennas Propag. 54, 2–11 (2006).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, M. Rodríguez-Sola, and C. Blanchard, “On the circuit description of TLM nodes,” Int. J. Electron. 93, 479–491 (2006).
[Crossref]

J. A. Portí and J. A. Morente, “A three-dimensional symmetrical condensed TLM node for acoustics,” J. Sound Vibr. 241, 207–222 (2001).
[Crossref]

J. A. Portí, J. A. Morente, and M. C. Carrión, “Simple derivation of scattering matrix for TLM nodes,” Electron. Lett. 34, 1763–1764 (1998).
[Crossref]

Navarro, E. A.

C. Blanchard, J. A. Portí, J. A. Morente, A. Salinas, and E. A. Navarro, “Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method,” J. Appl. Phys. 102, 064101 (2007).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, and M. Rodríguez-Sola, “A generalized dynamic symmetrical condensed TLM node for the modeling of time-varying electromagnetic media,” IEEE Trans. Antennas Propag. 54, 2–11 (2006).
[Crossref]

Nicolet, A.

Paul, J. P.

J. P. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM-Part 2: Materials with anisotropic properties,” IEEE Trans. Antennas Propag. 47, 1535–1542 (1999).
[Crossref]

Pendry, J. B.

F. Zolla, S. Guenneau, A. Nicolet, and J. B. Pendry, “Electromagnetic analysis of cylindrical invisibility cloaks and the mirage effect,” Opt. Lett. 32, 1069–1071 (2007).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and 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, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

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

Popa, B-I.

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

Portí, J. A.

C. Blanchard, J. A. Portí, J. A. Morente, A. Salinas, and E. A. Navarro, “Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method,” J. Appl. Phys. 102, 064101 (2007).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, M. Rodríguez-Sola, and C. Blanchard, “On the circuit description of TLM nodes,” Int. J. Electron. 93, 479–491 (2006).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, and M. Rodríguez-Sola, “A generalized dynamic symmetrical condensed TLM node for the modeling of time-varying electromagnetic media,” IEEE Trans. Antennas Propag. 54, 2–11 (2006).
[Crossref]

J. A. Portí and J. A. Morente, “A three-dimensional symmetrical condensed TLM node for acoustics,” J. Sound Vibr. 241, 207–222 (2001).
[Crossref]

J. A. Portí, J. A. Morente, and M. C. Carrión, “Simple derivation of scattering matrix for TLM nodes,” Electron. Lett. 34, 1763–1764 (1998).
[Crossref]

Qiu, M.

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[Crossref]

Ran, L.

B. Zhang, H. Chen, B-I. Wu, Y. Luo, L. Ran, and J. A. Kong, “Response of a cylindrical invisibility cloak to electromagnetic waves,” Phys. Rev. B 76, 121101 (2007).
[Crossref]

Rodríguez-Sola, M.

J. A. Portí, J. A. Morente, A. Salinas, M. Rodríguez-Sola, and C. Blanchard, “On the circuit description of TLM nodes,” Int. J. Electron. 93, 479–491 (2006).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, and M. Rodríguez-Sola, “A generalized dynamic symmetrical condensed TLM node for the modeling of time-varying electromagnetic media,” IEEE Trans. Antennas Propag. 54, 2–11 (2006).
[Crossref]

Ruan, Z.

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[Crossref]

Ryan, D.

R. Luebbers, D. Ryan, and J. Beggs, “A two-dimensional time-domain near-zone to Far-zone transformation,” IEEE Trans. Antennas Propag. 40, 848–851 (1992).
[Crossref]

Salinas, A.

C. Blanchard, J. A. Portí, J. A. Morente, A. Salinas, and E. A. Navarro, “Determination of the effective permittivity of dielectric mixtures with the transmission line matrix method,” J. Appl. Phys. 102, 064101 (2007).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, and M. Rodríguez-Sola, “A generalized dynamic symmetrical condensed TLM node for the modeling of time-varying electromagnetic media,” IEEE Trans. Antennas Propag. 54, 2–11 (2006).
[Crossref]

J. A. Portí, J. A. Morente, A. Salinas, M. Rodríguez-Sola, and C. Blanchard, “On the circuit description of TLM nodes,” Int. J. Electron. 93, 479–491 (2006).
[Crossref]

Schurig, D.

S. A. Cummer, B-I. Popa, D. Schurig, D. R. Smith, and J. B. 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] [PubMed]

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

Smith, D. R.

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

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

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

So, P. P. M.

P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2-D shunt and 3-D SCN TLM networks,” IEEE Trans. Microw. Theory Tech. 53, 1496–1505 (2005).
[Crossref]

Starr, A. F.

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

Thomas, D. W. P.

J. P. Paul, C. Christopoulos, and D. W. P. Thomas, “Generalized material models in TLM-Part 2: Materials with anisotropic properties,” IEEE Trans. Antennas Propag. 47, 1535–1542 (1999).
[Crossref]

Wang, D.

S. Xi, H. Chen, B-I. Wu, B. Zhang, Y. Luo, J. Huangfu, D. Wang, and J. A. Kong, “Effects of different transformations on the performance of a nonideal cylindrical cloak,” Submitted to PIERS.

Wiener, O.

O. Wiener, “Zur theorie der refraktionskonstanten,” Berichteüber die Verhandlungen der Königlich-Sächsischen Gesellsschaft der Wissenschaften zu Leipzig, 256–277 (1910).

Wu, B. I.

H. Chen, B. I. Wu, B. Zhang, and J. A. Kong, “Electromagnetic wave interactions with a metamaterial cloak,” Phys. Rev. Lett. 99, 063903 (2007).
[Crossref] [PubMed]

Wu, B-I.

B. Zhang, H. Chen, B-I. Wu, Y. Luo, L. Ran, and J. A. Kong, “Response of a cylindrical invisibility cloak to electromagnetic waves,” Phys. Rev. B 76, 121101 (2007).
[Crossref]

S. Xi, H. Chen, B-I. Wu, B. Zhang, Y. Luo, J. Huangfu, D. Wang, and J. A. Kong, “Effects of different transformations on the performance of a nonideal cylindrical cloak,” Submitted to PIERS.

Xi, S.

S. Xi, H. Chen, B-I. Wu, B. Zhang, Y. Luo, J. Huangfu, D. Wang, and J. A. Kong, “Effects of different transformations on the performance of a nonideal cylindrical cloak,” Submitted to PIERS.

Yan, M.

M. Yan, Z. Ruan, and M. Qiu, “Cylindrical invisibility cloak with simplified material parameters is inherently visible,” Phys. Rev. Lett. 99, 233901 (2007).
[Crossref]

Zhang, B.

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[Crossref]

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Figures (5)

Fig. 1.
Fig. 1.

(Color online) Representation of the 2-dimensional TLM shunt node without stubs.

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Fig. 2.
Fig. 2.

(Color online) Representation of (a) the classical 2D condensed shunt node with stubs, and (b) the modified 2D condensed shunt node allowing the simulation of metamaterials.

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Fig. 3.
Fig. 3.

(a). (Color online) Far field pattern for unprotected cylinder and two different cloakings. (b) Total and scattered amplitude field plot at the vicinity of the coated cylinder for μ and ε sampled at the inner boundary of each layer.

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Fig. 4.
Fig. 4.

(Color Online) (a) Far field pattern for reduced parameters. (b) Far field pattern for nonlinear transformation.

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Fig. 5.
Fig. 5.

(Color online) Two-dimensional scattering width, σ2D/λ, versus frequency of a conducting cylinder and cloaked cylinder at 2 GHZ.

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Equations (15)

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4 Y 0 Δ t 2 + Y y Y 0 Δ t 2 = ε y Δ x Δ z Δ y ⇒ Y y = 2 ε y Δ t Y 0 Δ x Δ z Δ y − 4 ,
2 Z 0 Δ t 2 + Z x Z 0 Δ t 2 = μ x Δ y Δ z Δ x ⇒ Z x = μ x Δ t Z 0 Δ y Δ z Δ x − 4 ,
2 Z 0 Δ t 2 + Z y Z 0 Δ t 2 = μ z Δ x Δ y Δ z ⇒ Z z = μ z Δ t Z 0 Δ x Δ z Δ z − 4 ,
L = Z y Z 0 Δ t 2
C eq = − 1 L ω 2 = − Y y Y 0 ω 2 2 Δ t .
4 Y 0 Δ t 2 − Y y Y 0 ω 2 2 Δ t = ε y Δ x Δ y Δ y ⇒ Y y = − Δ t 2 ω 2 4 [ 2 ε y Δ t Y 0 Δ x Δ z Δ y − 4 ] .
2 Z 0 Δ t 2 − Z x Z 0 ω 2 2 Δ t = μ x Δ y Δ z Δ x ⇒ Z x = − Δ t 2 ω 2 4 [ μ x Δ t Z 0 Δ y Δ z Δ x − 4 ] .
2 Z 0 Δ t 2 − Z z Z 0 ω 2 2 Δ t = μ z Δ x Δ y Δ z ⇒ Z z = − Δ t 2 ω 2 4 [ μ z Δ t Z 0 Δ x Δ y Δ z − 4 ] ,
ε r = μ r = r − R 1 r ,
ε θ = μ θ = r r − R 1 ,
ε y = μ y = ( R 2 R 2 − R 1 ) 2 r − R 1 r .
μ θ = μ A + μ B 2
1 μ r = 1 2 μ A + 1 2 μ B ,
μ A = μ θ + μ θ ( μ θ − μ r )
μ B = μ θ − μ θ ( μ θ − μ r ) .

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