Abstract

When microwave emitted from a point source is focused on a target by using a left-handed metamaterial (LHM) flat lens, microwave backscattered from the target will be refocused by the LHM lens in the vicinity of the point source. Numerical simulations with two-dimensional (2D) finite-difference time-domain (FDTD) method demonstrate that, even for flat LHM lens of material losses to the order as that reported in some LHM microwave experiments and simulations, the refocusing of backscattered microwave will yield a sub-wavelength lateral resolution and remarkable enhancement of the backscattered microwave, which will benefit the detection and imaging of small target.

© 2007 Optical Society of America

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  1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 -79 (2001).
    [CrossRef] [PubMed]
  3. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp.  10, 509-514 (1968).
    [CrossRef]
  4. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
    [CrossRef] [PubMed]
  5. C. Caloz and T. Itoh, "Metamaterials for high-frequency electronics," Proc. IEEE 93, 1744-1751 (2005).
    [CrossRef]
  6. N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
    [CrossRef]
  7. J.B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  8. J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
    [CrossRef]
  9. S.A. Cummer, "Simulated causal subwavelength focusing by a negative refractive index slab," Appl. Phys. Lett. 82, 1503-1505 (2003).
    [CrossRef]
  10. X. S. Rao and C. K. Ong, "Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 0676011-3 (2003).
    [CrossRef]
  11. N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163, (2003).
    [CrossRef]
  12. M. W. Feise, and Y. S. Kivshar, "Sub-wavelength imaging with a left-handed material flat lens," Phys. Lett. A 334, 326-330 (2005).
    [CrossRef]
  13. A. N. Lagarkov and V. N. Kissel, "Near-perfect imaging in a focusing system based on a left-handed-material plate," Phys. Rev. Lett. 92, 774011-4 (2004).
    [CrossRef]
  14. A. Grbic and G. V. Eleftheriades, "Overcoming the diffraction limit with a planar left-handed transmission-line lens," Phys. Rev. Lett. 92, 1174031-4 (2004).
    [CrossRef]
  15. K. Aydin, I. Bulu, and E. Ozbay, "Focusing of electromagnetic waves by a left-handed metamaterial flat lens," Opt. Express 13, 8753-8759 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-22-8753
    [CrossRef] [PubMed]
  16. A. Grbic and G. V. Eleftheriades, "Practical limitations of subwavelength resolution using negative-refractive-index transmission- line lenses," IEEE Trans. Antennas Propagat. 53, 3201-3209 (2005).
    [CrossRef]
  17. X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, "Perfectly Matched Layer-Absorbing Boundary Condition for Left-Handed Materials," IEEE Microwave Wireless Compon. Lett. 14, 301-303 (2004).
    [CrossRef]
  18. R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811-1819 (2001).
    [CrossRef]
  19. A. Grbic and G. V. Eleftheriades, "An isotropic three- dimensional negative-refractive-index transmission-line metamaterial," J. Appl. Phys. 98, 431061-5 (2005).
    [CrossRef]
  20. T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 1211031-4 (2005).
    [CrossRef]

2005

C. Caloz and T. Itoh, "Metamaterials for high-frequency electronics," Proc. IEEE 93, 1744-1751 (2005).
[CrossRef]

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

M. W. Feise, and Y. S. Kivshar, "Sub-wavelength imaging with a left-handed material flat lens," Phys. Lett. A 334, 326-330 (2005).
[CrossRef]

A. Grbic and G. V. Eleftheriades, "Practical limitations of subwavelength resolution using negative-refractive-index transmission- line lenses," IEEE Trans. Antennas Propagat. 53, 3201-3209 (2005).
[CrossRef]

A. Grbic and G. V. Eleftheriades, "An isotropic three- dimensional negative-refractive-index transmission-line metamaterial," J. Appl. Phys. 98, 431061-5 (2005).
[CrossRef]

T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 1211031-4 (2005).
[CrossRef]

K. Aydin, I. Bulu, and E. Ozbay, "Focusing of electromagnetic waves by a left-handed metamaterial flat lens," Opt. Express 13, 8753-8759 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-22-8753
[CrossRef] [PubMed]

2004

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, "Perfectly Matched Layer-Absorbing Boundary Condition for Left-Handed Materials," IEEE Microwave Wireless Compon. Lett. 14, 301-303 (2004).
[CrossRef]

A. N. Lagarkov and V. N. Kissel, "Near-perfect imaging in a focusing system based on a left-handed-material plate," Phys. Rev. Lett. 92, 774011-4 (2004).
[CrossRef]

A. Grbic and G. V. Eleftheriades, "Overcoming the diffraction limit with a planar left-handed transmission-line lens," Phys. Rev. Lett. 92, 1174031-4 (2004).
[CrossRef]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

2003

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

X. S. Rao and C. K. Ong, "Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 0676011-3 (2003).
[CrossRef]

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163, (2003).
[CrossRef]

2002

J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
[CrossRef]

2001

R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

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

2000

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

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

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp.  10, 509-514 (1968).
[CrossRef]

Aydin, K.

Bulu, I.

Caloz, C.

C. Caloz and T. Itoh, "Metamaterials for high-frequency electronics," Proc. IEEE 93, 1744-1751 (2005).
[CrossRef]

Cummer, S.A.

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

Dong, X. T.

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, "Perfectly Matched Layer-Absorbing Boundary Condition for Left-Handed Materials," IEEE Microwave Wireless Compon. Lett. 14, 301-303 (2004).
[CrossRef]

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, "An isotropic three- dimensional negative-refractive-index transmission-line metamaterial," J. Appl. Phys. 98, 431061-5 (2005).
[CrossRef]

A. Grbic and G. V. Eleftheriades, "Practical limitations of subwavelength resolution using negative-refractive-index transmission- line lenses," IEEE Trans. Antennas Propagat. 53, 3201-3209 (2005).
[CrossRef]

A. Grbic and G. V. Eleftheriades, "Overcoming the diffraction limit with a planar left-handed transmission-line lens," Phys. Rev. Lett. 92, 1174031-4 (2004).
[CrossRef]

Engheta, N.

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

Fang, N.

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163, (2003).
[CrossRef]

Feise, M. W.

M. W. Feise, and Y. S. Kivshar, "Sub-wavelength imaging with a left-handed material flat lens," Phys. Lett. A 334, 326-330 (2005).
[CrossRef]

Gan, Y. B.

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, "Perfectly Matched Layer-Absorbing Boundary Condition for Left-Handed Materials," IEEE Microwave Wireless Compon. Lett. 14, 301-303 (2004).
[CrossRef]

Grbic, A.

A. Grbic and G. V. Eleftheriades, "An isotropic three- dimensional negative-refractive-index transmission-line metamaterial," J. Appl. Phys. 98, 431061-5 (2005).
[CrossRef]

A. Grbic and G. V. Eleftheriades, "Practical limitations of subwavelength resolution using negative-refractive-index transmission- line lenses," IEEE Trans. Antennas Propagat. 53, 3201-3209 (2005).
[CrossRef]

A. Grbic and G. V. Eleftheriades, "Overcoming the diffraction limit with a planar left-handed transmission-line lens," Phys. Rev. Lett. 92, 1174031-4 (2004).
[CrossRef]

Guo, B.

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, "Perfectly Matched Layer-Absorbing Boundary Condition for Left-Handed Materials," IEEE Microwave Wireless Compon. Lett. 14, 301-303 (2004).
[CrossRef]

Itoh, T.

C. Caloz and T. Itoh, "Metamaterials for high-frequency electronics," Proc. IEEE 93, 1744-1751 (2005).
[CrossRef]

Kissel, V. N.

A. N. Lagarkov and V. N. Kissel, "Near-perfect imaging in a focusing system based on a left-handed-material plate," Phys. Rev. Lett. 92, 774011-4 (2004).
[CrossRef]

Kivshar, Y. S.

M. W. Feise, and Y. S. Kivshar, "Sub-wavelength imaging with a left-handed material flat lens," Phys. Lett. A 334, 326-330 (2005).
[CrossRef]

Koschny, T.

T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 1211031-4 (2005).
[CrossRef]

Lagarkov, A. N.

A. N. Lagarkov and V. N. Kissel, "Near-perfect imaging in a focusing system based on a left-handed-material plate," Phys. Rev. Lett. 92, 774011-4 (2004).
[CrossRef]

Nemat-Nasser, S. C.

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

Ong, C. K.

X. S. Rao and C. K. Ong, "Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 0676011-3 (2003).
[CrossRef]

Ozbay, E.

Padilla, W. J.

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

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Pendry, J.B.

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

Platzman, P. M.

J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
[CrossRef]

Rao, X. S.

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, "Perfectly Matched Layer-Absorbing Boundary Condition for Left-Handed Materials," IEEE Microwave Wireless Compon. Lett. 14, 301-303 (2004).
[CrossRef]

X. S. Rao and C. K. Ong, "Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 0676011-3 (2003).
[CrossRef]

Ruppin, R.

R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

Schultz, S.

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

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

Shelby, R. A.

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

Shen, J. T.

J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
[CrossRef]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

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

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

Soukoulis, C. M.

T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 1211031-4 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp.  10, 509-514 (1968).
[CrossRef]

Vier, D. C.

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

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Yin, W. Y.

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, "Perfectly Matched Layer-Absorbing Boundary Condition for Left-Handed Materials," IEEE Microwave Wireless Compon. Lett. 14, 301-303 (2004).
[CrossRef]

Zhang, L.

T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 1211031-4 (2005).
[CrossRef]

Zhang, X.

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163, (2003).
[CrossRef]

Ziolkowski, R. W.

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

Appl. Phys. Lett.

J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
[CrossRef]

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

N. Fang and X. Zhang, "Imaging properties of a metamaterial superlens," Appl. Phys. Lett. 82, 161-163, (2003).
[CrossRef]

IEEE Microwave Wireless Compon. Lett.

X. T. Dong, X. S. Rao, Y. B. Gan, B. Guo, and W. Y. Yin, "Perfectly Matched Layer-Absorbing Boundary Condition for Left-Handed Materials," IEEE Microwave Wireless Compon. Lett. 14, 301-303 (2004).
[CrossRef]

IEEE Trans. Antennas Propagat.

A. Grbic and G. V. Eleftheriades, "Practical limitations of subwavelength resolution using negative-refractive-index transmission- line lenses," IEEE Trans. Antennas Propagat. 53, 3201-3209 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

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

J. Appl. Phys.

A. Grbic and G. V. Eleftheriades, "An isotropic three- dimensional negative-refractive-index transmission-line metamaterial," J. Appl. Phys. 98, 431061-5 (2005).
[CrossRef]

J. Phys.: Condens. Matter

R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

Opt. Express

Phys. Lett. A

M. W. Feise, and Y. S. Kivshar, "Sub-wavelength imaging with a left-handed material flat lens," Phys. Lett. A 334, 326-330 (2005).
[CrossRef]

Phys. Rev. B

T. Koschny, L. Zhang, and C. M. Soukoulis, "Isotropic three-dimensional left-handed metamaterials," Phys. Rev. B 71, 1211031-4 (2005).
[CrossRef]

Phys. Rev. E

X. S. Rao and C. K. Ong, "Subwavelength imaging by a left-handed material superlens," Phys. Rev. E 68, 0676011-3 (2003).
[CrossRef]

Phys. Rev. Lett.

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

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

A. N. Lagarkov and V. N. Kissel, "Near-perfect imaging in a focusing system based on a left-handed-material plate," Phys. Rev. Lett. 92, 774011-4 (2004).
[CrossRef]

A. Grbic and G. V. Eleftheriades, "Overcoming the diffraction limit with a planar left-handed transmission-line lens," Phys. Rev. Lett. 92, 1174031-4 (2004).
[CrossRef]

Proc. IEEE

C. Caloz and T. Itoh, "Metamaterials for high-frequency electronics," Proc. IEEE 93, 1744-1751 (2005).
[CrossRef]

Science

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and Negative Refractive Index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

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

Sov. Phys. Usp

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp.  10, 509-514 (1968).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Focusing and refocusing of microwave in target detection by using flat LHM lens.

Fig. 2.
Fig. 2.

Lateral beam profiles of focused and refocused microwave by using flat LHM lens.

Fig. 3.
Fig. 3.

Lateral beam profile of refocused microwave when two PEC cylinders are scanned.

Fig. 4.
Fig. 4.

(a) The focusing of microwave emitted by a line source and (b) the refocusing of microwave backscattered from the PEC cylinder of diameter φ = λ/6 at the focal point.

Fig. 5.
Fig. 5.

Distribution of electric field levels of incident and backscattered microwave along x-axis.

Fig. 6.
Fig. 6.

Distribution of backscattered microwave field levels for the detection of PEC cylinders of diameters of 1mm and 3mm, respectively.

Equations (2)

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ε r ( ω ) = 1 ω pe 2 ω 2 + 2 jδω ,
μ r ( ω ) = 1 ω pm 2 ω 2 + 2 jδω .

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