Abstract

The ability of the Finite-Difference Time-Domain method to model a perfect lens made of a slab of homogeneous left-handed material (LHM) is investigated. It is shown that because of the frequency dispersive nature of the medium and the time discretization, an inherent mismatch in the constitutive parameters exists between the slab and its surrounding medium. This mismatch in the real part of the permittivity and permeability is found to have the same order of magnitude as the losses typically used in numerical simulations. Hence, when the LHM slab is lossless, this mismatch is shown to be the main factor contributing to the image resolution loss of the slab.

© 2005 Optical Society of America

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References

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  1. J. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  2. R.W. Ziolkowski and E. Heyman, "Wave Propagation in Media Having Negative Permittivity and Permeability," Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  3. S.A. Cummer, "Simulated causal subwavelength focusing by a negative refractive index slab," Appl. Phys. Lett. 82, 1503-1505 (2003).
    [CrossRef]
  4. L. Chen and S. He and L. Shen, "Finite-Size Effects of a Left-Handed Material Slab on the image Quality," Phys. Rev. Lett. 92, 107404 (2004).
    [CrossRef] [PubMed]
  5. M.W. Feise and J.B. Schneider and P.J. Bevelacqua, "Finite-Difference and Pseudospectral Time-Domain Methods Applied to Backward-Wave .Metamaterials," IEEE Trans. Antennas. Propag. 52, 2955-2962 (2004).
    [CrossRef]
  6. M.W. Feise and Y.S. Kivshar, "Sub-wavelength imaging with a left-handed material flat lens," Phys. Lett. A 334, 326-323 (2005).
    [CrossRef]
  7. A. Taflove, Computational Electrodynamics - The Finite-Difference Time-Domain Method, (Artech House, 1995).
  8. D.R. Smith and D. Schurig and M. Rosenbluth and S. Schultz, "Limitations on subdiffraction imaging with a negative index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
    [CrossRef]
  9. J. Lu and T. M. Grzegorczyk and B.-I. Wu and J. Pacheco and M. Chen and J. A. Kong, "Effect of poles on subwavelength focusing by an LHM slab," Microwave Opt. Technol. Lett. 45, 49 (2005).
    [CrossRef]
  10. J. A. Kong, Electromagnetic Wave Theory, (EMW, 2000).
  11. J. A. Kong, "Electromagnetic interactions with stratified negative isotropic media," Progress In Electromagnetic Research 35, 1-52 (2001).
    [CrossRef]

Appl. Phys. Lett. (2)

S.A. Cummer, "Simulated causal subwavelength focusing by a negative refractive index slab," Appl. Phys. Lett. 82, 1503-1505 (2003).
[CrossRef]

D.R. Smith and D. Schurig and M. Rosenbluth and S. Schultz, "Limitations on subdiffraction imaging with a negative index slab," Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

IEEE Trans. Antennas. Propag. (1)

M.W. Feise and J.B. Schneider and P.J. Bevelacqua, "Finite-Difference and Pseudospectral Time-Domain Methods Applied to Backward-Wave .Metamaterials," IEEE Trans. Antennas. Propag. 52, 2955-2962 (2004).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

J. Lu and T. M. Grzegorczyk and B.-I. Wu and J. Pacheco and M. Chen and J. A. Kong, "Effect of poles on subwavelength focusing by an LHM slab," Microwave Opt. Technol. Lett. 45, 49 (2005).
[CrossRef]

Phys. Lett. A (1)

M.W. Feise and Y.S. Kivshar, "Sub-wavelength imaging with a left-handed material flat lens," Phys. Lett. A 334, 326-323 (2005).
[CrossRef]

Phys. Rev. E (1)

R.W. Ziolkowski and E. Heyman, "Wave Propagation in Media Having Negative Permittivity and Permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

J. Pendry, "Negative Refraction Makes a Perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

L. Chen and S. He and L. Shen, "Finite-Size Effects of a Left-Handed Material Slab on the image Quality," Phys. Rev. Lett. 92, 107404 (2004).
[CrossRef] [PubMed]

Progress In Electromagnetic Research (1)

J. A. Kong, "Electromagnetic interactions with stratified negative isotropic media," Progress In Electromagnetic Research 35, 1-52 (2001).
[CrossRef]

Other (2)

A. Taflove, Computational Electrodynamics - The Finite-Difference Time-Domain Method, (Artech House, 1995).

J. A. Kong, Electromagnetic Wave Theory, (EMW, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Comparison of |Ey | at the image plane from the FDTD simulation and the analytical calculation for an LHM slab with a thickness of 0.2λ. The grid size used in the simulation is λ/100. The analytical calculation considers an LHM slab of μr = εr = -1.000297 in vacuum.

Fig. 2.
Fig. 2.

Comparison of Ey spectra at the image plane from the FDTD simulations and the analytical calculations for two slab configurations: one with a thickness of 0.2λ and the other with a thickness of 0.1λ. Both slabs are simulated with a same grid size of λ/100.

Fig. 3.
Fig. 3.

Comparison of time averaged Poynting power densities < Sz > at the image plane from the FDTD simulation and the analytical calculation for the two line source imaging. The LHM slab is the same as in Fig. 1. The line sources are separated by 0.2λ.

Fig. 4.
Fig. 4.

Comparison of Ey spectrum at the image plane from the FDTD simulations using different grid sizes. The time step size is calculated from Courant’s criterion based on the grid size of λ/200 and is adopted for the simulation using the grid size of λ/100 as well. The LHM slab is the same as in Fig. 1.

Equations (7)

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E ¯ · d l ¯ = t d s ¯ · B ¯ d s ¯ · M ¯
E y n + 1 2 ( I , K ) E y n + 1 2 ( I 1 , K ) = Δ x μ o Δ t [ H z n + 1 ( I , k + 1 2 )
H z n ( I , K + 1 2 ) ] Δ x 2 M z n + 1 2 ( I , K )
H z n + 1 ( I , K ) = H z n ( I , K ) Δ t 2 μ o M z n + 1 2 ( I , K ) Δ t Δ x μ o ( E y n + 1 2 ( I , K ) E y n - 1 2 ( I 1 , K ) )
× H ¯ = t ε 0 E ¯ + J ¯ e = t ε o ε r E ¯
J ¯ e t + Γ e J ¯ e = ε 0 ω pe 2 E ¯
ε r = 1 ω pe 2 4 sin ( ω o Δ t 2 ) ( Δ t ) 2

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