Abstract

A surface integral equation (SIE) formulation is applied to the analysis of electromagnetic problems involving three-dimensional (3D) piecewise homogenized left-handed metamaterials (LHM). The resulting integral equations are discretized by the well-known method of moments (MoM) and solved via an iterative process. The unknowns are defined only on the interfaces between different media, avoiding the discretization of volumes and surrounding space, which entails a drastic reduction in the number of unknowns arising in the numerical discretization of the equations. Besides, the SIE-MoM formulation inherently includes the radiation condition at infinity, so it is not necessary to artificially include termination absorbing boundary conditions. Some 3D numerical examples are presented to confirm the validity and versatility of this approach on dealing with LHM, also providing some intuitive verifications of the singular properties of these amazing materials.

© 2010 OSA

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Soviet Physics USPEKI 10(4), 509–514 (1968).
    [CrossRef]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [CrossRef] [PubMed]
  3. N. Engheta and R. W. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).
    [CrossRef]
  4. C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed materials,” Prog. Electromagn. Res. 35, 315–334 (2002).
    [CrossRef]
  5. P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036605 (2004).
    [CrossRef] [PubMed]
  6. Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, “Numerical simulations of negative-index refraction in wedge-shaped metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016607 (2005).
    [CrossRef] [PubMed]
  7. R. S. Schechtera and S. T. Chun, “Large finite-difference time domain simulations of a left-handed metamaterial lens with wires and resonators,” Appl. Phys. Lett. 91(15), 154102 (2007).
    [CrossRef]
  8. Ö. Ergül, T. Malas, C. Yavuz, A. Ünal, and L. Gürel, “Computational Analysis of complicated metamaterial structures using MLFMA and nested preconditioners,” in Proceedings of European Conference on Antennas and Propagation (EuCAP), Edinburgh, UK, 11–16 Nov. 2007.
  9. F. Olyslager, L. Meert, and K. Cools, “The fast multipole method in electromagnetics applied to the simulation of metamateriales,” J. Comput. Appl. Math. 215(2), 528–537 (2008).
    [CrossRef]
  10. P. Yla-Oijala, Ö. Ergül, L. Gürel, and M. Taskinen, “Efficient surface integral equation methods for the analysis of complex metamaterial structures,” in Proceedings of European Conference on Antennas and Propagation (EuCAP), Berlin, Germany, 23–27 Mar. 2009.
  11. L. Gürel, Ö. Ergül, A. Ünal, and T. Malas, “Fast and accurate analysis of metamaterial structures using the multilevel fast multipole algorithm,” Prog. Electromagn. Res. 95, 179–198 (2009).
    [CrossRef]
  12. M. Lapine and S. Tretyakov, “Contemporary notes on metamaterials,” IET Microw. Ant. Propag. 1, 3–11 (2007).
    [CrossRef]
  13. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
    [CrossRef]
  14. X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
    [CrossRef] [PubMed]
  15. D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23(3), 391–403 (2006).
    [CrossRef]
  16. C. Caloz, C. C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90(11), 5483 (2001).
    [CrossRef]
  17. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001).
    [CrossRef] [PubMed]
  18. R. W. Ziolkowski, “Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs,” Opt. Express 11(7), 662–681 (2003).
    [CrossRef] [PubMed]
  19. P. F. Loschialpo, D. L. Smith, D. W. Forester, and F. J. Rachford, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 67, 025602 (2003).
  20. C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
    [CrossRef]
  21. P. Kolinko and D. R. Smith, “Numerical study of electromagnetic waves interacting with negative index materials,” Opt. Express 11(7), 640–648 (2003).
    [CrossRef] [PubMed]
  22. B. J. Justice, J. J. Mock, L. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14(19), 8694–8705 (2006).
    [CrossRef] [PubMed]
  23. R. F. Harrington, Field Computation by Moment Method. (NY: IEEE Press, 1993).
  24. L. Landesa, J. M. Taboada, J. L. Rodriguez, F. Obelleiro, J. M. Bertolo, J. C. Mouriño, and A. Gomez, “Analysis of 0.5 Billion Unknowns Using a Parallel FMM-FFT Solver,” in Proceedings of IEEE Antennas and Propagation Society International Symposium, Charleston, SC, USA, 1–5 Jun. 2009.
  25. J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
    [CrossRef]
  26. M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
    [CrossRef]
  27. A. J. Poggio, and E. K. Miller, Computer Techniques for Electromagnetics (Elmsford, NY: Permagon, 1973), Chap. 4.
  28. S. M. Rao and D. R. Wilton, “E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies,” Electromag. 10(4), 407–421 (1990).
    [CrossRef]
  29. P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag. 53(3), 1168–1173 (2005).
    [CrossRef]
  30. P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci. 40(6), RS6002 (2005).
    [CrossRef]
  31. P. Ylä-Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. 52, 81–108 (2005).
    [CrossRef]
  32. Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag. 57(1), 176–187 (2009).
    [CrossRef]
  33. S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. 30(3), 409–418 (1982).
    [CrossRef]
  34. D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag. 32(3), 276–281 (1984).
    [CrossRef]
  35. R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett. 14(1), 9–14 (1997).
    [CrossRef]
  36. R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag. 41(10), 1448–1455 (1993).
    [CrossRef]
  37. P. Yla-Oijala and M. Taskinen; “Calculation of CFIE impedance matrix elements with RWG and, ” IEEE Trans. Antenn. Propag. 51(8), 1837–1846 (2003).
    [CrossRef]
  38. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]

2010

M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
[CrossRef]

2009

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag. 57(1), 176–187 (2009).
[CrossRef]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

L. Gürel, Ö. Ergül, A. Ünal, and T. Malas, “Fast and accurate analysis of metamaterial structures using the multilevel fast multipole algorithm,” Prog. Electromagn. Res. 95, 179–198 (2009).
[CrossRef]

2008

F. Olyslager, L. Meert, and K. Cools, “The fast multipole method in electromagnetics applied to the simulation of metamateriales,” J. Comput. Appl. Math. 215(2), 528–537 (2008).
[CrossRef]

2007

R. S. Schechtera and S. T. Chun, “Large finite-difference time domain simulations of a left-handed metamaterial lens with wires and resonators,” Appl. Phys. Lett. 91(15), 154102 (2007).
[CrossRef]

M. Lapine and S. Tretyakov, “Contemporary notes on metamaterials,” IET Microw. Ant. Propag. 1, 3–11 (2007).
[CrossRef]

2006

2005

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag. 53(3), 1168–1173 (2005).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci. 40(6), RS6002 (2005).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. 52, 81–108 (2005).
[CrossRef]

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, “Numerical simulations of negative-index refraction in wedge-shaped metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016607 (2005).
[CrossRef] [PubMed]

N. Engheta and R. W. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).
[CrossRef]

2004

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036605 (2004).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

2003

P. Yla-Oijala and M. Taskinen; “Calculation of CFIE impedance matrix elements with RWG and, ” IEEE Trans. Antenn. Propag. 51(8), 1837–1846 (2003).
[CrossRef]

P. Kolinko and D. R. Smith, “Numerical study of electromagnetic waves interacting with negative index materials,” Opt. Express 11(7), 640–648 (2003).
[CrossRef] [PubMed]

R. W. Ziolkowski, “Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs,” Opt. Express 11(7), 662–681 (2003).
[CrossRef] [PubMed]

P. F. Loschialpo, D. L. Smith, D. W. Forester, and F. J. Rachford, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 67, 025602 (2003).

2002

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed materials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

C. Caloz, C. C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90(11), 5483 (2001).
[CrossRef]

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001).
[CrossRef] [PubMed]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1997

R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett. 14(1), 9–14 (1997).
[CrossRef]

1993

R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag. 41(10), 1448–1455 (1993).
[CrossRef]

1990

S. M. Rao and D. R. Wilton, “E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies,” Electromag. 10(4), 407–421 (1990).
[CrossRef]

1984

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag. 32(3), 276–281 (1984).
[CrossRef]

1982

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. 30(3), 409–418 (1982).
[CrossRef]

1968

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Soviet Physics USPEKI 10(4), 509–514 (1968).
[CrossRef]

Al-Bundak, O. M.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag. 32(3), 276–281 (1984).
[CrossRef]

Araujo, M. G.

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

Araújo, M. G.

M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
[CrossRef]

Bertolo, J. M.

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

Bértolo, J. M.

M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
[CrossRef]

Butler, C. M.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag. 32(3), 276–281 (1984).
[CrossRef]

Caloz, C.

C. Caloz, C. C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90(11), 5483 (2001).
[CrossRef]

Cao, W.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, “Numerical simulations of negative-index refraction in wedge-shaped metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016607 (2005).
[CrossRef] [PubMed]

Chang, C. C.

C. Caloz, C. C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90(11), 5483 (2001).
[CrossRef]

Chen, X.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Chun, S. T.

R. S. Schechtera and S. T. Chun, “Large finite-difference time domain simulations of a left-handed metamaterial lens with wires and resonators,” Appl. Phys. Lett. 91(15), 154102 (2007).
[CrossRef]

Cools, K.

F. Olyslager, L. Meert, and K. Cools, “The fast multipole method in electromagnetics applied to the simulation of metamateriales,” J. Comput. Appl. Math. 215(2), 528–537 (2008).
[CrossRef]

Degiron, A.

Dong, Z. G.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, “Numerical simulations of negative-index refraction in wedge-shaped metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016607 (2005).
[CrossRef] [PubMed]

Engheta, N.

N. Engheta and R. W. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).
[CrossRef]

Ergül, Ö.

L. Gürel, Ö. Ergül, A. Ünal, and T. Malas, “Fast and accurate analysis of metamaterial structures using the multilevel fast multipole algorithm,” Prog. Electromagn. Res. 95, 179–198 (2009).
[CrossRef]

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag. 57(1), 176–187 (2009).
[CrossRef]

Forester, D. W.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036605 (2004).
[CrossRef] [PubMed]

P. F. Loschialpo, D. L. Smith, D. W. Forester, and F. J. Rachford, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 67, 025602 (2003).

Glisson, A. W.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag. 32(3), 276–281 (1984).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. 30(3), 409–418 (1982).
[CrossRef]

Gomez, A.

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

Graglia, R. D.

R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag. 41(10), 1448–1455 (1993).
[CrossRef]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Grzegorczyk, T. M.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed materials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

Guo, L.

Gürel, L.

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag. 57(1), 176–187 (2009).
[CrossRef]

L. Gürel, Ö. Ergül, A. Ünal, and T. Malas, “Fast and accurate analysis of metamaterial structures using the multilevel fast multipole algorithm,” Prog. Electromagn. Res. 95, 179–198 (2009).
[CrossRef]

Heyman, E.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001).
[CrossRef] [PubMed]

Hodges, R. E.

R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett. 14(1), 9–14 (1997).
[CrossRef]

Itoh, T.

C. Caloz, C. C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90(11), 5483 (2001).
[CrossRef]

Järvenpää, S.

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci. 40(6), RS6002 (2005).
[CrossRef]

Justice, B. J.

Kolinko, P.

Kong, J. A.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed materials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

Landesa, L.

M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
[CrossRef]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

Lapine, M.

M. Lapine and S. Tretyakov, “Contemporary notes on metamaterials,” IET Microw. Ant. Propag. 1, 3–11 (2007).
[CrossRef]

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Liu, H.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, “Numerical simulations of negative-index refraction in wedge-shaped metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016607 (2005).
[CrossRef] [PubMed]

Loschialpo, P. F.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036605 (2004).
[CrossRef] [PubMed]

P. F. Loschialpo, D. L. Smith, D. W. Forester, and F. J. Rachford, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 67, 025602 (2003).

Malas, T.

L. Gürel, Ö. Ergül, A. Ünal, and T. Malas, “Fast and accurate analysis of metamaterial structures using the multilevel fast multipole algorithm,” Prog. Electromagn. Res. 95, 179–198 (2009).
[CrossRef]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Meert, L.

F. Olyslager, L. Meert, and K. Cools, “The fast multipole method in electromagnetics applied to the simulation of metamateriales,” J. Comput. Appl. Math. 215(2), 528–537 (2008).
[CrossRef]

Mock, J. J.

Monzon, C.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036605 (2004).
[CrossRef] [PubMed]

Moss, C. D.

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed materials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

Mouriño, J. C.

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

Nielsen, J. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Obelleiro, F.

M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
[CrossRef]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

Olyslager, F.

F. Olyslager, L. Meert, and K. Cools, “The fast multipole method in electromagnetics applied to the simulation of metamateriales,” J. Comput. Appl. Math. 215(2), 528–537 (2008).
[CrossRef]

Pacheco, J.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Pendry, J. B.

D. R. Smith and J. B. Pendry, “Homogenization of metamaterials by field averaging,” J. Opt. Soc. Am. B 23(3), 391–403 (2006).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Rachford, F. J.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036605 (2004).
[CrossRef] [PubMed]

P. F. Loschialpo, D. L. Smith, D. W. Forester, and F. J. Rachford, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 67, 025602 (2003).

Rahmat-Samii, Y.

R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett. 14(1), 9–14 (1997).
[CrossRef]

Rao, S. M.

S. M. Rao and D. R. Wilton, “E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies,” Electromag. 10(4), 407–421 (1990).
[CrossRef]

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag. 32(3), 276–281 (1984).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. 30(3), 409–418 (1982).
[CrossRef]

Rivero, J.

M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
[CrossRef]

Rodriguez, J. L.

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

Rodríguez, J. L.

M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
[CrossRef]

Sarvas, J.

P. Ylä-Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. 52, 81–108 (2005).
[CrossRef]

Schaubert, D. H.

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag. 32(3), 276–281 (1984).
[CrossRef]

Schechtera, R. S.

R. S. Schechtera and S. T. Chun, “Large finite-difference time domain simulations of a left-handed metamaterial lens with wires and resonators,” Appl. Phys. Lett. 91(15), 154102 (2007).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Schurig, D.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Smith, D. L.

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036605 (2004).
[CrossRef] [PubMed]

P. F. Loschialpo, D. L. Smith, D. W. Forester, and F. J. Rachford, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 67, 025602 (2003).

Smith, D. R.

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Taboada, J. M.

M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
[CrossRef]

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

Tanielian, M. H.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Taskinen, M.

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag. 53(3), 1168–1173 (2005).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci. 40(6), RS6002 (2005).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. 52, 81–108 (2005).
[CrossRef]

P. Yla-Oijala and M. Taskinen; “Calculation of CFIE impedance matrix elements with RWG and, ” IEEE Trans. Antenn. Propag. 51(8), 1837–1846 (2003).
[CrossRef]

Thompson, M. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Tretyakov, S.

M. Lapine and S. Tretyakov, “Contemporary notes on metamaterials,” IET Microw. Ant. Propag. 1, 3–11 (2007).
[CrossRef]

Ünal, A.

L. Gürel, Ö. Ergül, A. Ünal, and T. Malas, “Fast and accurate analysis of metamaterial structures using the multilevel fast multipole algorithm,” Prog. Electromagn. Res. 95, 179–198 (2009).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Soviet Physics USPEKI 10(4), 509–514 (1968).
[CrossRef]

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Vier, D. C.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Wilton, D. R.

S. M. Rao and D. R. Wilton, “E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies,” Electromag. 10(4), 407–421 (1990).
[CrossRef]

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag. 32(3), 276–281 (1984).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. 30(3), 409–418 (1982).
[CrossRef]

Wu, B. I.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Yla-Oijala, P.

P. Yla-Oijala and M. Taskinen; “Calculation of CFIE impedance matrix elements with RWG and, ” IEEE Trans. Antenn. Propag. 51(8), 1837–1846 (2003).
[CrossRef]

Ylä-Oijala, P.

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag. 53(3), 1168–1173 (2005).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci. 40(6), RS6002 (2005).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. 52, 81–108 (2005).
[CrossRef]

Zhang, Y.

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed materials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

Zhu, J.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, “Numerical simulations of negative-index refraction in wedge-shaped metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016607 (2005).
[CrossRef] [PubMed]

Zhu, S. N.

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, “Numerical simulations of negative-index refraction in wedge-shaped metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016607 (2005).
[CrossRef] [PubMed]

Ziolkowski, R. W.

N. Engheta and R. W. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).
[CrossRef]

R. W. Ziolkowski, “Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs,” Opt. Express 11(7), 662–681 (2003).
[CrossRef] [PubMed]

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001).
[CrossRef] [PubMed]

Appl. Phys. Lett.

R. S. Schechtera and S. T. Chun, “Large finite-difference time domain simulations of a left-handed metamaterial lens with wires and resonators,” Appl. Phys. Lett. 91(15), 154102 (2007).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84(17), 3232–3234 (2004).
[CrossRef]

Electromag.

S. M. Rao and D. R. Wilton, “E-field, H-field, and combined field solution for arbitrarily shaped three-dimensional dielectric bodies,” Electromag. 10(4), 407–421 (1990).
[CrossRef]

IEEE Ant. Propag. Mag.

J. M. Taboada, L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mouriño, and A. Gomez, “High scalability FMM-FFT electromagnetic solver for supercomputer systems,” IEEE Ant. Propag. Mag. 51(6), 20–28 (2009).
[CrossRef]

IEEE Trans. Antenn. Propag.

P. Ylä-Oijala and M. Taskinen, “Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects,” IEEE Trans. Antenn. Propag. 53(3), 1168–1173 (2005).
[CrossRef]

R. D. Graglia, “On the numerical integration of the linear shape functions times the 3-D green’s function or its gradient on a plane triangle,” IEEE Trans. Antenn. Propag. 41(10), 1448–1455 (1993).
[CrossRef]

P. Yla-Oijala and M. Taskinen; “Calculation of CFIE impedance matrix elements with RWG and, ” IEEE Trans. Antenn. Propag. 51(8), 1837–1846 (2003).
[CrossRef]

Ö. Ergül and L. Gürel, “Comparison of integral-equation formulations for the fast and accurate solution of scattering problems involving dielectric objects with the multilevel fast multipole algorithm,” IEEE Trans. Antenn. Propag. 57(1), 176–187 (2009).
[CrossRef]

S. M. Rao, D. R. Wilton, and A. W. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antenn. Propag. 30(3), 409–418 (1982).
[CrossRef]

D. R. Wilton, S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, “Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains,” IEEE Trans. Antenn. Propag. 32(3), 276–281 (1984).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

N. Engheta and R. W. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microw. Theory Tech. 53(4), 1535–1556 (2005).
[CrossRef]

IET Microw. Ant. Propag.

M. Lapine and S. Tretyakov, “Contemporary notes on metamaterials,” IET Microw. Ant. Propag. 1, 3–11 (2007).
[CrossRef]

J. Appl. Phys.

C. Caloz, C. C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90(11), 5483 (2001).
[CrossRef]

J. Comput. Appl. Math.

F. Olyslager, L. Meert, and K. Cools, “The fast multipole method in electromagnetics applied to the simulation of metamateriales,” J. Comput. Appl. Math. 215(2), 528–537 (2008).
[CrossRef]

J. Opt. Soc. Am. B

Microw. Opt. Technol. Lett.

R. E. Hodges and Y. Rahmat-Samii, “The evaluation of MFIE integrals with the use of vector triangle basis functions,” Microw. Opt. Technol. Lett. 14(1), 9–14 (1997).
[CrossRef]

Opt. Express

Phys. Rev. B

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(5), 056625 (2001).
[CrossRef] [PubMed]

P. F. Loschialpo, D. W. Forester, D. L. Smith, F. J. Rachford, and C. Monzon, “Optical properties of an ideal homogeneous causal left-handed material slab,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(3), 036605 (2004).
[CrossRef] [PubMed]

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, “Numerical simulations of negative-index refraction in wedge-shaped metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016607 (2005).
[CrossRef] [PubMed]

Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top.

P. F. Loschialpo, D. L. Smith, D. W. Forester, and F. J. Rachford, “Electromagnetic waves focused by a negative-index planar lens,” Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 67, 025602 (2003).

Phys. Rev. Lett.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Prog. Electromagn. Res.

M. G. Araújo, J. M. Taboada, F. Obelleiro, J. M. Bértolo, L. Landesa, J. Rivero, and J. L. Rodríguez, “Supercomputer aware approach for the solution of challenging electromagnetic problems,” Prog. Electromagn. Res. 101, 241–256 (2010).
[CrossRef]

C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left-handed materials,” Prog. Electromagn. Res. 35, 315–334 (2002).
[CrossRef]

L. Gürel, Ö. Ergül, A. Ünal, and T. Malas, “Fast and accurate analysis of metamaterial structures using the multilevel fast multipole algorithm,” Prog. Electromagn. Res. 95, 179–198 (2009).
[CrossRef]

P. Ylä-Oijala, M. Taskinen, and J. Sarvas, “Surface integral equation method for general integral equation method for general composite metallic and dielectric structures with junctions,” Prog. Electromagn. Res. 52, 81–108 (2005).
[CrossRef]

Radio Sci.

P. Ylä-Oijala, M. Taskinen, and S. Järvenpää, “Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods,” Radio Sci. 40(6), RS6002 (2005).
[CrossRef]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Soviet Physics USPEKI

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Soviet Physics USPEKI 10(4), 509–514 (1968).
[CrossRef]

Other

Ö. Ergül, T. Malas, C. Yavuz, A. Ünal, and L. Gürel, “Computational Analysis of complicated metamaterial structures using MLFMA and nested preconditioners,” in Proceedings of European Conference on Antennas and Propagation (EuCAP), Edinburgh, UK, 11–16 Nov. 2007.

P. Yla-Oijala, Ö. Ergül, L. Gürel, and M. Taskinen, “Efficient surface integral equation methods for the analysis of complex metamaterial structures,” in Proceedings of European Conference on Antennas and Propagation (EuCAP), Berlin, Germany, 23–27 Mar. 2009.

A. J. Poggio, and E. K. Miller, Computer Techniques for Electromagnetics (Elmsford, NY: Permagon, 1973), Chap. 4.

R. F. Harrington, Field Computation by Moment Method. (NY: IEEE Press, 1993).

L. Landesa, J. M. Taboada, J. L. Rodriguez, F. Obelleiro, J. M. Bertolo, J. C. Mouriño, and A. Gomez, “Analysis of 0.5 Billion Unknowns Using a Parallel FMM-FFT Solver,” in Proceedings of IEEE Antennas and Propagation Society International Symposium, Charleston, SC, USA, 1–5 Jun. 2009.

Supplementary Material (1)

» Media 1: AVI (1743 KB)     

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Figures (4)

Fig. 1
Fig. 1

(a) Horizontal cut of an incident flat Gaussian beam (from the right hand side) negatively refracted by an impedance matched 3D LHM prism with ε r = −1 and μ r = −1. (b) Positive (conventional) refraction from a RHM prism with ε r = 2.2 and μ r = 1.

Fig. 2
Fig. 2

Angular pattern of the refracted wave 20λ0 away from a prism. Red solid curve: prism made up of LHM with ε r = −1 and μ r = −1. Blue dashed curve: prism made up of RHM with ε r = 2.2 and μ r = 1. The dotted red and blue straight lines indicate the Snell-Descartes law reference in each case.

Fig. 3
Fig. 3

(Media 1) (1744K) of the electric-field intensity distribution illustrating the focusing effect and the reversal of the phase velocity of a strongly diverging Gaussian beam as it propagates inside a matched LHM slab with n = −1.

Fig. 4
Fig. 4

Electric-field intensity distribution illustrating the focusing effect of a plane-concave LHM lens with n = −1. The incident wave is an almost flat Gaussian beam impinging onto the flat surface from the right hand side.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

T-EFIE l : ( η l l ( J l ) K l ( M l ) ) tan + 1 2 n ^ l × M l = ( E l i n c ) t a n
T-MFIE l : ( K l ( J l ) + 1 η l l ( M l ) ) t a n 1 2 n ^ l × J l = ( H l i n c ) t a n .
N-EFIE l : n ^ l × ( η l l ( J l ) K l ( M l ) ) 1 2 M l = n ^ l × E l i n c
N-MFIE l : n ^ l × ( K l ( J l ) + 1 η l l ( M l ) ) + 1 2 J l = n ^ l × H l i n c
l ( X l ) = j k l [ S X l ( r ' ) G l ( r , r ' ) d S ' + 1 k l 2 S ' X l G l ( r , r ' ) d S ' ]
K l ( X l ) = S , P V X l ( r ' ) × G l ( r , r ' ) d S ' .
G l ( r , r ' ) = e j k l | r r ' | 4 π | r r ' |
J l ( r ' ) = n ^ l × H l ( r ' )
M l ( r ' ) = n ^ l × E l ( r ' )
J 1 = J 2 ; M 1 = M 2
l = 1 2 a l 1 η l T-EFIE l + l = 1 2 b l 1 η l N-MFIE l
l = 1 2 c l N-EFIE l + l = 1 2 d l η l T-MFIE l
{ [ ( a 1 1 + a 2 2 ) tan ( a 1 η 1 K 1 a 2 η 2 K 2 ) tan ( d 1 η 1 K 1 + d 2 η 2 K 2 ) tan ( d 1 1 + d 2 2 ) tan ] + [ n ^ × ( b 1 K 1 b 2 K 2 ) n ^ × ( b 1 η 1 1 b 2 η 2 2 ) n ^ × ( c 1 η 1 1 c 2 η 2 2 ) n ^ × ( c 1 K 1 c 2 K 2 ) ] + 1 2 [ ( b 1 + b 2 ) ( a 1 η 1 a 2 η 2 ) n ^ × ( d 2 η 2 d 1 η 1 ) n ^ × ( c 1 + c 2 ) ] } [ J M ] = [ a 1 ( E 1 i n c ) tan a 2 ( E 2 i n c ) tan + n ^ × ( b 1 H 1 i n c + b 2 H 2 i n c ) n ^ × ( c 1 E 1 i n c + c 2 E 2 i n c ) + d 1 ( H 1 i n c ) tan d 2 ( H 2 i n c ) tan ]
k l = ω μ l ε l ; η l = μ l ε l .

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