Abstract

We assess the performance of three unconditionally stable finite-difference time-domain (FDTD) methods for the modeling of doubly dispersive metamaterials: 1) locally one-dimensional FDTD; 2) locally one-dimensional FDTD with Strang splitting; and (3) alternating direction implicit FDTD. We use both double-negative media and zero-index media as benchmarks.

© 2009 IEEE

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  1. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of $\varepsilon $ and $\mu $," Sov. Phys. Usp. 10, 509-514 (1968).
  2. W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. AP-10, 82-95 (1962).
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).
  4. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
  5. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz, "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).
  6. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).
  7. R. W. Ziolkowski, "Propagation in and scattering from a matched metamaterial having a zero index of refraction," Phys. Rev. E 70, 046608 (2004).
  8. B. Donderici, F. L. Teixeira, "Mixed finite-element time-domain method for transient Maxwell equations in doubly dispersive media," IEEE Trans. Microw. Theory Tech. 56, 113-120 (2008).
  9. K. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
  10. A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  11. Y. Zhao, P. Belov, Y. Hao, "Accurate modeling of the optical properties of left-handed media using a finite-difference time-domain method," Phys. Rev. E 75, 037602 (2007).
  12. D. L. Sounas, N. V. Kantartzis, T. D. Tsiboukis, "Temporal characteristics of resonant surface polaritons in superlensing planar double-negative slabs: Development of analytical schemes and numerical models," Phys. Rev. E 76, 046606 (2007).
  13. A. Taflove, M. E. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations," IEEE Trans. Microw. Theory Tech. 23, 623-630 (1975).
  14. T. Namiki, "A new FDTD algorithm based on alternating-direction implicit method," IEEE Trans. Microw. Theory Tech. 47, 2003-2007 (1999).
  15. F. Zheng, Z. Chen, J. Zhang, "A finite-difference time-domain method without the Courant stability conditions," IEEE Microw. Guided Wave Lett. 9, 441-443 (1999).
  16. S. G. Garcia, T. W. Lee, S. C. Hagness, "On the accuracy of the ADI-FDTD method," IEEE Antennas Wireless Propag. Lett. 1, 31-34 (2002).
  17. S. Wang, F. L. Teixeira, "An efficient PML implementation for the ADI-FDTD method," IEEE Microw. Wireless Compon. Lett. 13, 72-74 (2003).
  18. S. Ju, H. Kim, H.-H. Kim, "A study of the numerical dispersion relation for the 2-D ADI-FDTD method," IEEE Microw. Wireless Compon. Lett. 13, 405-407 (2003).
  19. K.-Y. Jung, F. L. Teixeira, "Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures," IEEE Photon. Technol. Lett. 19, 586-588 (2007).
  20. J. Lee, B. Fornberg, "A split step approach for the 3-D Maxwell's equations," J. Comput. Appl. Math. 158, 484-505 (2003).
  21. J. Lee, B. Fornberg, "Some unconditionally stable time stepping methods for the 3-D Maxwell's equations," J. Comput. Appl. Math. 166, 497-523 (2004).
  22. V. E. do Nascimento, J. A. Cuminato, F. L. Teixeira, B.-H. V. Borges, "Unconditionally stable finite-difference time-domain method based on the locally-one-dimensional technique," Proc. XXII Simpósio Brasileiro de Telecomunicações (2005) pp. 288-291.
  23. V. E. do Nascimento, B.-H. V. Borges, F. L. Teixeira, "Split-field PML implementations for the unconditionally stable LOD-FDTD method," IEEE Microw. Wireless Comp. Lett. 16, 398-400 (2006).
  24. J. Shibayama, M. Muraki, J. Yamauchi, H. Nakano, "Efficient implict FDTD algorithm based on locally one-dimensional scheme," Electron. Lett. 41, 1046-1047 (2005).
  25. J. Shibayama, R. Takahashi, J. Yamauchi, H. Nakano, "Frequency-dependent LOD-FDTD implementations for dispersive media," Electron. Lett. 42, 1084-1085 (2006).
  26. J. Shibayama, R. Takahashi, J. Yamauchi, H. Nakano, "Frequency-dependent locally one-dimensional FDTD implementation with a combined dispersion model for the analysis of surface plasmon waveguides," IEEE Photon. Technol. Lett. 20, 824-826 (2008).
  27. W. Fu, E. L. Tan, "Development of split-step FDTD method with higher-order spatial accuracy," Electron. Lett. 40, 1252-1254 (2004).
  28. E. L. Tan, "Unconditionally stable LOD-FDTD method for 3-D Maxwell's equations," IEEE Microw. Wireless Compon. Lett. 17, 85-87 (2007).
  29. K.-Y. Jung, F. L. Teixeira, "An iterative unconditionally stable LOD-FDTD method," IEEE Microw. Wireless Compon. Lett. 18, 76-78 (2008).
  30. J. Shibayama, M. Muraki, R. Takahashi, J. Yamauchi, H. Nakano, "Performance evaluation of several implicit FDTD methods for optical waveguide analyses," J. Lightw. Technol. 24, 2465-2472 (2006).
  31. R. W. Ziolkowski, E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 1-15 (2001).
  32. D. Correia, J. M. Jin, "Theoretical analysis of left-handed metamaterials using FDTD-PML method," Proc. SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (2003) pp. 1033-1036.
  33. J. J. Chen, T. M. Grzegorczyk, B. I. Wu, J. A. Kong, "Limitation o FDTD in simulation of a perfect lens imaging system," Opt. Exp. 13, 10840-10845 (2005).
  34. Y. Zhao, P. Belov, Y. Hao, "Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries," Phys. Rev. E 75, 037602 (2007).
  35. K.-Y. Jung, F. L. Teixeira, R. M. Reano, "${\rm Au}/{\rm SiO}_{2}$ nanoring plasmon waveguides at optical communication band," J. Lightw. Technol. 25, 2757-2765 (2007).
  36. N. V. Kantartzis, T. D. Tsiboukis, "Rigorous ADI-FDTD analysis of left-handed materials in optimally-designed EMC applications," presented at the XII Int. Symp. Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering (2005).
  37. N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).
  38. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
  39. N. Engheta, R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microw. Theory Tech. 53, 1535-1556 (2005).
  40. R. W. Ziolkowski, "Metamaterial based source and scattering enhancements: From microwave to optical frequencies," Opto-Electron. Rev. 14, 167-177 (2006).
  41. M. Silveirinha, N. Engheta, "Tunneling of electromagnetic energy through subwavelength channels and bends using $\varepsilon $-near-zero materials," Phys. Rev. Lett. 97, 157403 (2006).
  42. D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 9-10 (2007).
  43. B. Donderici, F. L. Teixeira, "Symmetric source implementation for the ADI-FDTD method," IEEE Trans. Antennas Propag. 53, 1562-1565 (2005).
  44. S. Wang, F. L. Teixeira, J. Chen, "An iterative ADI-FDTD with reduced splitting error," IEEE Microw. Wireless Comp. Lett. 15, 92-94 (2005).
  45. K.-Y. Jung, F. L. Teixeira, S. G. Garcia, R. Lee, "On numerical artifacts of the complex envelope ADI-FDTD method," IEEE Trans. Antennas Propagat. 57, 491-498 (2009).
  46. X. Huang, L. Zhou, C. T. Chan, "Modulating image oscillations in focusing by a metamaterial lens: Time-dependent Green's function approach," Phys. Rev. B 74, 045123 (2006).

2009 (1)

K.-Y. Jung, F. L. Teixeira, S. G. Garcia, R. Lee, "On numerical artifacts of the complex envelope ADI-FDTD method," IEEE Trans. Antennas Propagat. 57, 491-498 (2009).

2008 (3)

B. Donderici, F. L. Teixeira, "Mixed finite-element time-domain method for transient Maxwell equations in doubly dispersive media," IEEE Trans. Microw. Theory Tech. 56, 113-120 (2008).

J. Shibayama, R. Takahashi, J. Yamauchi, H. Nakano, "Frequency-dependent locally one-dimensional FDTD implementation with a combined dispersion model for the analysis of surface plasmon waveguides," IEEE Photon. Technol. Lett. 20, 824-826 (2008).

K.-Y. Jung, F. L. Teixeira, "An iterative unconditionally stable LOD-FDTD method," IEEE Microw. Wireless Compon. Lett. 18, 76-78 (2008).

2007 (8)

E. L. Tan, "Unconditionally stable LOD-FDTD method for 3-D Maxwell's equations," IEEE Microw. Wireless Compon. Lett. 17, 85-87 (2007).

Y. Zhao, P. Belov, Y. Hao, "Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries," Phys. Rev. E 75, 037602 (2007).

K.-Y. Jung, F. L. Teixeira, R. M. Reano, "${\rm Au}/{\rm SiO}_{2}$ nanoring plasmon waveguides at optical communication band," J. Lightw. Technol. 25, 2757-2765 (2007).

N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).

K.-Y. Jung, F. L. Teixeira, "Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures," IEEE Photon. Technol. Lett. 19, 586-588 (2007).

Y. Zhao, P. Belov, Y. Hao, "Accurate modeling of the optical properties of left-handed media using a finite-difference time-domain method," Phys. Rev. E 75, 037602 (2007).

D. L. Sounas, N. V. Kantartzis, T. D. Tsiboukis, "Temporal characteristics of resonant surface polaritons in superlensing planar double-negative slabs: Development of analytical schemes and numerical models," Phys. Rev. E 76, 046606 (2007).

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 9-10 (2007).

2006 (6)

R. W. Ziolkowski, "Metamaterial based source and scattering enhancements: From microwave to optical frequencies," Opto-Electron. Rev. 14, 167-177 (2006).

M. Silveirinha, N. Engheta, "Tunneling of electromagnetic energy through subwavelength channels and bends using $\varepsilon $-near-zero materials," Phys. Rev. Lett. 97, 157403 (2006).

X. Huang, L. Zhou, C. T. Chan, "Modulating image oscillations in focusing by a metamaterial lens: Time-dependent Green's function approach," Phys. Rev. B 74, 045123 (2006).

V. E. do Nascimento, B.-H. V. Borges, F. L. Teixeira, "Split-field PML implementations for the unconditionally stable LOD-FDTD method," IEEE Microw. Wireless Comp. Lett. 16, 398-400 (2006).

J. Shibayama, R. Takahashi, J. Yamauchi, H. Nakano, "Frequency-dependent LOD-FDTD implementations for dispersive media," Electron. Lett. 42, 1084-1085 (2006).

J. Shibayama, M. Muraki, R. Takahashi, J. Yamauchi, H. Nakano, "Performance evaluation of several implicit FDTD methods for optical waveguide analyses," J. Lightw. Technol. 24, 2465-2472 (2006).

2005 (5)

J. J. Chen, T. M. Grzegorczyk, B. I. Wu, J. A. Kong, "Limitation o FDTD in simulation of a perfect lens imaging system," Opt. Exp. 13, 10840-10845 (2005).

J. Shibayama, M. Muraki, J. Yamauchi, H. Nakano, "Efficient implict FDTD algorithm based on locally one-dimensional scheme," Electron. Lett. 41, 1046-1047 (2005).

N. Engheta, R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microw. Theory Tech. 53, 1535-1556 (2005).

B. Donderici, F. L. Teixeira, "Symmetric source implementation for the ADI-FDTD method," IEEE Trans. Antennas Propag. 53, 1562-1565 (2005).

S. Wang, F. L. Teixeira, J. Chen, "An iterative ADI-FDTD with reduced splitting error," IEEE Microw. Wireless Comp. Lett. 15, 92-94 (2005).

2004 (3)

J. Lee, B. Fornberg, "Some unconditionally stable time stepping methods for the 3-D Maxwell's equations," J. Comput. Appl. Math. 166, 497-523 (2004).

W. Fu, E. L. Tan, "Development of split-step FDTD method with higher-order spatial accuracy," Electron. Lett. 40, 1252-1254 (2004).

R. W. Ziolkowski, "Propagation in and scattering from a matched metamaterial having a zero index of refraction," Phys. Rev. E 70, 046608 (2004).

2003 (3)

S. Wang, F. L. Teixeira, "An efficient PML implementation for the ADI-FDTD method," IEEE Microw. Wireless Compon. Lett. 13, 72-74 (2003).

S. Ju, H. Kim, H.-H. Kim, "A study of the numerical dispersion relation for the 2-D ADI-FDTD method," IEEE Microw. Wireless Compon. Lett. 13, 405-407 (2003).

J. Lee, B. Fornberg, "A split step approach for the 3-D Maxwell's equations," J. Comput. Appl. Math. 158, 484-505 (2003).

2002 (2)

S. G. Garcia, T. W. Lee, S. C. Hagness, "On the accuracy of the ADI-FDTD method," IEEE Antennas Wireless Propag. Lett. 1, 31-34 (2002).

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).

2001 (2)

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz, "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).

R. W. Ziolkowski, E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 1-15 (2001).

2000 (2)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).

1999 (3)

J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).

T. Namiki, "A new FDTD algorithm based on alternating-direction implicit method," IEEE Trans. Microw. Theory Tech. 47, 2003-2007 (1999).

F. Zheng, Z. Chen, J. Zhang, "A finite-difference time-domain method without the Courant stability conditions," IEEE Microw. Guided Wave Lett. 9, 441-443 (1999).

1975 (1)

A. Taflove, M. E. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations," IEEE Trans. Microw. Theory Tech. 23, 623-630 (1975).

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of $\varepsilon $ and $\mu $," Sov. Phys. Usp. 10, 509-514 (1968).

1966 (1)

K. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).

1962 (1)

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. AP-10, 82-95 (1962).

Appl. Phys. Lett. (1)

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, S. Schultz, "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial," Appl. Phys. Lett. 78, 489-491 (2001).

Electron. Lett. (3)

J. Shibayama, M. Muraki, J. Yamauchi, H. Nakano, "Efficient implict FDTD algorithm based on locally one-dimensional scheme," Electron. Lett. 41, 1046-1047 (2005).

J. Shibayama, R. Takahashi, J. Yamauchi, H. Nakano, "Frequency-dependent LOD-FDTD implementations for dispersive media," Electron. Lett. 42, 1084-1085 (2006).

W. Fu, E. L. Tan, "Development of split-step FDTD method with higher-order spatial accuracy," Electron. Lett. 40, 1252-1254 (2004).

Electron. Lett. (1)

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, D. H. Werner, "Zero index metamaterials with checkerboard structure," Electron. Lett. 43, 9-10 (2007).

IEEE Microw. Wireless Comp. Lett. (1)

V. E. do Nascimento, B.-H. V. Borges, F. L. Teixeira, "Split-field PML implementations for the unconditionally stable LOD-FDTD method," IEEE Microw. Wireless Comp. Lett. 16, 398-400 (2006).

IEEE Trans. Microw. Theory Tech. (1)

T. Namiki, "A new FDTD algorithm based on alternating-direction implicit method," IEEE Trans. Microw. Theory Tech. 47, 2003-2007 (1999).

IEEE Antennas Wireless Propag. Lett. (1)

S. G. Garcia, T. W. Lee, S. C. Hagness, "On the accuracy of the ADI-FDTD method," IEEE Antennas Wireless Propag. Lett. 1, 31-34 (2002).

IEEE Microw. Wireless Compon. Lett. (1)

E. L. Tan, "Unconditionally stable LOD-FDTD method for 3-D Maxwell's equations," IEEE Microw. Wireless Compon. Lett. 17, 85-87 (2007).

IEEE Microw. Guided Wave Lett. (1)

F. Zheng, Z. Chen, J. Zhang, "A finite-difference time-domain method without the Courant stability conditions," IEEE Microw. Guided Wave Lett. 9, 441-443 (1999).

IEEE Microw. Wireless Compon. Lett. (3)

K.-Y. Jung, F. L. Teixeira, "An iterative unconditionally stable LOD-FDTD method," IEEE Microw. Wireless Compon. Lett. 18, 76-78 (2008).

S. Wang, F. L. Teixeira, "An efficient PML implementation for the ADI-FDTD method," IEEE Microw. Wireless Compon. Lett. 13, 72-74 (2003).

S. Ju, H. Kim, H.-H. Kim, "A study of the numerical dispersion relation for the 2-D ADI-FDTD method," IEEE Microw. Wireless Compon. Lett. 13, 405-407 (2003).

IEEE Microw. Wireless Comp. Lett. (1)

S. Wang, F. L. Teixeira, J. Chen, "An iterative ADI-FDTD with reduced splitting error," IEEE Microw. Wireless Comp. Lett. 15, 92-94 (2005).

IEEE Photon. Technol. Lett. (2)

K.-Y. Jung, F. L. Teixeira, "Multispecies ADI-FDTD algorithm for nanoscale three-dimensional photonic metallic structures," IEEE Photon. Technol. Lett. 19, 586-588 (2007).

J. Shibayama, R. Takahashi, J. Yamauchi, H. Nakano, "Frequency-dependent locally one-dimensional FDTD implementation with a combined dispersion model for the analysis of surface plasmon waveguides," IEEE Photon. Technol. Lett. 20, 824-826 (2008).

IEEE Trans. Antennas Propag. (1)

B. Donderici, F. L. Teixeira, "Symmetric source implementation for the ADI-FDTD method," IEEE Trans. Antennas Propag. 53, 1562-1565 (2005).

IEEE Trans. Antennas Propag. (1)

K. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).

IEEE Trans. Antennas Propagat. (1)

K.-Y. Jung, F. L. Teixeira, S. G. Garcia, R. Lee, "On numerical artifacts of the complex envelope ADI-FDTD method," IEEE Trans. Antennas Propagat. 57, 491-498 (2009).

IEEE Trans. Magn. (1)

N. V. Kantartzis, D. L. Sounas, C. S. Antonopoulos, T. D. Tsiboukis, "A wideband ADI-FDTD algorithm for the design of double negative metamaterial-based waveguides and antenna substrates," IEEE Trans. Magn. 43, 1329-1332 (2007).

IEEE Trans. Microw. Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microw. Theory Tech. 47, 2075-2084 (1999).

IEEE Trans. Microw. Theory Tech. (3)

B. Donderici, F. L. Teixeira, "Mixed finite-element time-domain method for transient Maxwell equations in doubly dispersive media," IEEE Trans. Microw. Theory Tech. 56, 113-120 (2008).

A. Taflove, M. E. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations," IEEE Trans. Microw. Theory Tech. 23, 623-630 (1975).

N. Engheta, R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microw. Theory Tech. 53, 1535-1556 (2005).

IRE Trans. Antennas Propag. (1)

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. AP-10, 82-95 (1962).

J. Comput. Appl. Math. (1)

J. Lee, B. Fornberg, "Some unconditionally stable time stepping methods for the 3-D Maxwell's equations," J. Comput. Appl. Math. 166, 497-523 (2004).

J. Lightw. Technol. (2)

J. Shibayama, M. Muraki, R. Takahashi, J. Yamauchi, H. Nakano, "Performance evaluation of several implicit FDTD methods for optical waveguide analyses," J. Lightw. Technol. 24, 2465-2472 (2006).

K.-Y. Jung, F. L. Teixeira, R. M. Reano, "${\rm Au}/{\rm SiO}_{2}$ nanoring plasmon waveguides at optical communication band," J. Lightw. Technol. 25, 2757-2765 (2007).

J. Comput. Appl. Math. (1)

J. Lee, B. Fornberg, "A split step approach for the 3-D Maxwell's equations," J. Comput. Appl. Math. 158, 484-505 (2003).

Opt. Exp. (1)

J. J. Chen, T. M. Grzegorczyk, B. I. Wu, J. A. Kong, "Limitation o FDTD in simulation of a perfect lens imaging system," Opt. Exp. 13, 10840-10845 (2005).

Opto-Electron. Rev. (1)

R. W. Ziolkowski, "Metamaterial based source and scattering enhancements: From microwave to optical frequencies," Opto-Electron. Rev. 14, 167-177 (2006).

Phys. Rev. E (2)

R. W. Ziolkowski, E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 1-15 (2001).

Y. Zhao, P. Belov, Y. Hao, "Accurate modeling of the optical properties of left-handed media using a finite-difference time-domain method," Phys. Rev. E 75, 037602 (2007).

Phys. Rev. Lett. (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).

Phys. Rev. B (1)

X. Huang, L. Zhou, C. T. Chan, "Modulating image oscillations in focusing by a metamaterial lens: Time-dependent Green's function approach," Phys. Rev. B 74, 045123 (2006).

Phys. Rev. E (3)

R. W. Ziolkowski, "Propagation in and scattering from a matched metamaterial having a zero index of refraction," Phys. Rev. E 70, 046608 (2004).

D. L. Sounas, N. V. Kantartzis, T. D. Tsiboukis, "Temporal characteristics of resonant surface polaritons in superlensing planar double-negative slabs: Development of analytical schemes and numerical models," Phys. Rev. E 76, 046606 (2007).

Y. Zhao, P. Belov, Y. Hao, "Accurate modelling of left-handed metamaterials using a finite-difference time-domain method with spatial averaging at the boundaries," Phys. Rev. E 75, 037602 (2007).

Phys. Rev. Lett. (3)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, P. Vincent, "A metamaterial for directive emission," Phys. Rev. Lett. 89, 213902 (2002).

M. Silveirinha, N. Engheta, "Tunneling of electromagnetic energy through subwavelength channels and bends using $\varepsilon $-near-zero materials," Phys. Rev. Lett. 97, 157403 (2006).

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of $\varepsilon $ and $\mu $," Sov. Phys. Usp. 10, 509-514 (1968).

Other (4)

A. Taflove, S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

N. V. Kantartzis, T. D. Tsiboukis, "Rigorous ADI-FDTD analysis of left-handed materials in optimally-designed EMC applications," presented at the XII Int. Symp. Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering (2005).

D. Correia, J. M. Jin, "Theoretical analysis of left-handed metamaterials using FDTD-PML method," Proc. SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference (2003) pp. 1033-1036.

V. E. do Nascimento, J. A. Cuminato, F. L. Teixeira, B.-H. V. Borges, "Unconditionally stable finite-difference time-domain method based on the locally-one-dimensional technique," Proc. XXII Simpósio Brasileiro de Telecomunicações (2005) pp. 288-291.

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