Time domain simulation of electromagnetic
cloaking structures with TLM method

doi:10.1364/OE.16.006461

Time domain simulation of electromagnetic cloaking structures with TLM method

Cedric Blanchard, Jorge A. Portí, Bae-Ian Wu, Juan A. Morente, Alfonso Salinas, and Jin Au Kong »View Author Affiliations

Optics Express, Vol. 16, Issue 9, pp. 6461-6470 (2008)
http://dx.doi.org/10.1364/OE.16.006461

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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.

OCIS Codes
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(160.3918) Materials : Metamaterials
(230.3205) Optical devices : Invisibility cloaks

ToC Category:
Metamaterials

History
Original Manuscript: March 13, 2008
Revised Manuscript: April 17, 2008
Manuscript Accepted: April 18, 2008
Published: April 22, 2008

Citation
Cedric Blanchard, Jorge A. Portí, Bae-Ian Wu, Juan A. Morente, Alfonso Salinas, and Jin Au Kong, "Time domain simulation of electromagnetic cloaking structures with TLM method," Opt. Express 16, 6461-6470 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6461

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References

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006). [CrossRef] [PubMed]
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]
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]
C. Christopoulos, The Transmission-Line Modeling method, The Institute of Electrical and Electronic Engineers (New York and Oxford University Press, Oxford, 1995). [CrossRef]
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 and J. A. Morente, "A three-dimensional symmetrical condensed TLM node for acoustics," J. Sound Vibr. 241, 207-222 (2001). [CrossRef]
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. Microwave Theory Tech. 53, 1496-1505 (2005). [CrossRef]
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]
L. de Menezes and W. J. R. Hoefer, "Modeling of general constitutive relationships using SCN TLM," IEEE Trans. Microwave Theory Tech. 44, 854-861 (1996). [CrossRef]
Y. Huang, Y. Feng, and T. Jiang, "Electromagnetic cloaking by layered structure of homogeneous isotropic materials," Opt. Express 15, 11133 (2007). [CrossRef] [PubMed]
O. Wiener, "Zur theorie der refraktionskonstanten," Berichteüber die Verhandlungen der Königlich-Sächsischen Gesellsschaft der Wissenschaften zu Leipzig, 256-277 (1910).
S. Xi, H. Chen, B-I. Wu, B. Zhang, Y. Luo, J. Huangfu, D. Wang, J. A. Kong, "Effects of different transformations on the performance of a nonideal cylindrical cloak," Submitted to PIERS.
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. Microwave Theory Tech. 35, 370-377 (1987). [CrossRef]
J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, 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, C. Blanchard, "On the circuit description of TLM nodes," Int. J. Electron. 93, 479-491 (2006). [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]
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]
C. Balanis, Advanced Enginnering Electromagnetics, John Wiley & Sons (1989).
B. Zhang, H. Chen, B-I. Wu, Y. Luo, L. Ran, 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]

Beggs, J.
Beurle, R. L.
Blanchard, C.
Carrión, M. C.
Chen, H.
Christopoulos, C.
Cummer, S. A.
de Menezes, L.
Du, H.
Feng, Y.
Guenneau, S.
Hoefer, W. J. R.
Huang, Y.
Huangfu, J.
Jiang, T.
Johns, P. B.
Justice, B. J.
Kong, J. A.
Luebbers, R.
Luo, Y.
Mock, J. J.
Morente, J. A.
Navarro, E. A.
Nicolet, A.
Paul, J. P.
Pendry, J. B.
Popa, B-I.
Portí, J. A.
Qiu, M.
Ran, L.
Rodríguez-Sola, M.
Ruan, Z.
Ryan, D.
Salinas, A.
Schurig, D.
Smith, D. R.
So, P. P. M.
Starr, A. F.
Thomas, D. W. P.
Wang, D.
Wu, B. I.
Wu, B-I.
Xi, S.
Yan, M.
Zhang, B.
Zolla, F.

Electron. Lett.

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]

IEEE Trans. Antennas Propag.

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]
J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, 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. 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]

IEEE Trans. Microwave Theory Tech.

L. de Menezes and W. J. R. Hoefer, "Modeling of general constitutive relationships using SCN TLM," IEEE Trans. Microwave Theory Tech. 44, 854-861 (1996). [CrossRef]
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. Microwave Theory Tech. 53, 1496-1505 (2005). [CrossRef]
P. B. Johns, "A symmetrical condensed node for the TLM method," IEEE Trans. Microwave Theory Tech. 35, 370-377 (1987). [CrossRef]

Int. J. Electron.

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

J. Appl. Phys.

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. Sound Vibr.

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

Opt. Express

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

Opt. Lett.

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]

Phys. Rev. B

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

Phys. Rev. E

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]

Phys. Rev. Lett.

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

PIERS

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

Proc. Inst. Elec. Eng.

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]

Science

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]

Other

C. Christopoulos, The Transmission-Line Modeling method, The Institute of Electrical and Electronic Engineers (New York and Oxford University Press, Oxford, 1995). [CrossRef]
O. Wiener, "Zur theorie der refraktionskonstanten," Berichteüber die Verhandlungen der Königlich-Sächsischen Gesellsschaft der Wissenschaften zu Leipzig, 256-277 (1910).
C. Balanis, Advanced Enginnering Electromagnetics, John Wiley & Sons (1989).

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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. Microwave 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. Microwave 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, 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. Microwave Theory Tech. 35, 370-377 (1987). [CrossRef]

[17] J. A. Portí, J. A. Morente, A. Salinas, E. A. Navarro, 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, 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, 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]

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