Abstract

A new compact structure is presented in this paper to localize electromagnetic energies using a thin grounded left-handed medium (LHM) slab. For a perfectly-matched LHM slab with negative permittivity -ε 0 and negative permeability -µ 0 backed with a conducting plane, we have shown rigorously that all electromagnetic fields excited by a current source, which is located in front of the slab at a distance of the slab thickness, are completely confined in a region between the source and the conducting plane, and the fields outside the region are zero. Hence, it is an ideal energy-localization system, and the electromagnetic energies can be localized in any small regions as required using such a system. However, it has been known that the perfectly matched LHM is unphysical and it does not exist in nature. Hence, we have further studied the lossy and retardation effects of the LHM slab on the energy localization. Most remarkably, electromagnetic waves remain strongly localized even when small losses are taken into account, as demonstrated by numerical simulations.

©2005 Optical Society of America

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References

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  1. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1997).
    [Crossref]
  3. M. W. Takeda, S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, “Localization of electromagnetic waves in three-dimensional photonic fractal cavities,” Phys. Rev. Lett. 92, 093902 (2004).
    [Crossref] [PubMed]
  4. T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang, and J. A. Kong, “Localization of electromagnetic energy using a LHM slab,” Phys. Rev. B 71, to be published, Jan. 2005.
    [Crossref]
  5. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509 (1968).
    [Crossref]
  6. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
    [Crossref] [PubMed]
  7. N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett 88, 207403 (2002).
    [Crossref] [PubMed]
  8. G. W.’t Hooft, “Comment on ‘Negative refraction makes a perfect lens’,” Phys. Rev. Lett. 87, 249701 (2001).
    [Crossref] [PubMed]
  9. J. M. Williams, “Some problems with negative refraction,” Phy. Rev. Lett. 87, 249703 (2001).
    [Crossref]
  10. G. Gomez-Santos, “Universal features of the time evolution of evanescent modes in a left-handed perfect lens,” Phys. Rev. Lett. 90, 077401 (2003).
    [Crossref] [PubMed]
  11. R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys: Condens. Matter. 13, 1811 (2001).
    [Crossref]
  12. D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on sub-diffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506 (2003).
    [Crossref]
  13. N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
    [Crossref]
  14. J. A. Kong, “Electromagnetic wave interaction with stratified negative isotropic media,” Progress in Electromagnetics Research, PIER 35, 1 (2002).
    [Crossref]
  15. X. S. Rao and C. K. Ong, “Amplification of evanescent wave s i n a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
    [Crossref]

2005 (1)

T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang, and J. A. Kong, “Localization of electromagnetic energy using a LHM slab,” Phys. Rev. B 71, to be published, Jan. 2005.
[Crossref]

2004 (1)

M. W. Takeda, S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, “Localization of electromagnetic waves in three-dimensional photonic fractal cavities,” Phys. Rev. Lett. 92, 093902 (2004).
[Crossref] [PubMed]

2003 (4)

G. Gomez-Santos, “Universal features of the time evolution of evanescent modes in a left-handed perfect lens,” Phys. Rev. Lett. 90, 077401 (2003).
[Crossref] [PubMed]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on sub-diffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506 (2003).
[Crossref]

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
[Crossref]

X. S. Rao and C. K. Ong, “Amplification of evanescent wave s i n a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
[Crossref]

2002 (2)

J. A. Kong, “Electromagnetic wave interaction with stratified negative isotropic media,” Progress in Electromagnetics Research, PIER 35, 1 (2002).
[Crossref]

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett 88, 207403 (2002).
[Crossref] [PubMed]

2001 (3)

G. W.’t Hooft, “Comment on ‘Negative refraction makes a perfect lens’,” Phys. Rev. Lett. 87, 249701 (2001).
[Crossref] [PubMed]

J. M. Williams, “Some problems with negative refraction,” Phy. Rev. Lett. 87, 249703 (2001).
[Crossref]

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

2000 (1)

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

1997 (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1997).
[Crossref]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

Cheng, Q.

T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang, and J. A. Kong, “Localization of electromagnetic energy using a LHM slab,” Phys. Rev. B 71, to be published, Jan. 2005.
[Crossref]

Cui, T. J.

T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang, and J. A. Kong, “Localization of electromagnetic energy using a LHM slab,” Phys. Rev. B 71, to be published, Jan. 2005.
[Crossref]

Fang, N.

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
[Crossref]

Garcia, N.

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett 88, 207403 (2002).
[Crossref] [PubMed]

Gomez-Santos, G.

G. Gomez-Santos, “Universal features of the time evolution of evanescent modes in a left-handed perfect lens,” Phys. Rev. Lett. 90, 077401 (2003).
[Crossref] [PubMed]

Honda, K.

M. W. Takeda, S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, “Localization of electromagnetic waves in three-dimensional photonic fractal cavities,” Phys. Rev. Lett. 92, 093902 (2004).
[Crossref] [PubMed]

Hooft, G. W.’t

G. W.’t Hooft, “Comment on ‘Negative refraction makes a perfect lens’,” Phys. Rev. Lett. 87, 249701 (2001).
[Crossref] [PubMed]

Jiang, Q.

T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang, and J. A. Kong, “Localization of electromagnetic energy using a LHM slab,” Phys. Rev. B 71, to be published, Jan. 2005.
[Crossref]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1997).
[Crossref]

Kirihara, S.

M. W. Takeda, S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, “Localization of electromagnetic waves in three-dimensional photonic fractal cavities,” Phys. Rev. Lett. 92, 093902 (2004).
[Crossref] [PubMed]

Kong, J. A.

T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang, and J. A. Kong, “Localization of electromagnetic energy using a LHM slab,” Phys. Rev. B 71, to be published, Jan. 2005.
[Crossref]

J. A. Kong, “Electromagnetic wave interaction with stratified negative isotropic media,” Progress in Electromagnetics Research, PIER 35, 1 (2002).
[Crossref]

Lu, W. B.

T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang, and J. A. Kong, “Localization of electromagnetic energy using a LHM slab,” Phys. Rev. B 71, to be published, Jan. 2005.
[Crossref]

Miyamoto, Y.

M. W. Takeda, S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, “Localization of electromagnetic waves in three-dimensional photonic fractal cavities,” Phys. Rev. Lett. 92, 093902 (2004).
[Crossref] [PubMed]

Nieto-Vesperinas, M.

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett 88, 207403 (2002).
[Crossref] [PubMed]

Ong, C. K.

X. S. Rao and C. K. Ong, “Amplification of evanescent wave s i n a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
[Crossref]

Pendry, J. B.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on sub-diffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506 (2003).
[Crossref]

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

Ramakrishna, S. A.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on sub-diffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506 (2003).
[Crossref]

Rao, X. S.

X. S. Rao and C. K. Ong, “Amplification of evanescent wave s i n a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
[Crossref]

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on sub-diffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506 (2003).
[Crossref]

Ruppin, R.

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

Sakoda, K.

M. W. Takeda, S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, “Localization of electromagnetic waves in three-dimensional photonic fractal cavities,” Phys. Rev. Lett. 92, 093902 (2004).
[Crossref] [PubMed]

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on sub-diffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506 (2003).
[Crossref]

Schurig, D.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on sub-diffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506 (2003).
[Crossref]

Smith, D. R.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on sub-diffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506 (2003).
[Crossref]

Takeda, M. W.

M. W. Takeda, S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, “Localization of electromagnetic waves in three-dimensional photonic fractal cavities,” Phys. Rev. Lett. 92, 093902 (2004).
[Crossref] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

Williams, J. M.

J. M. Williams, “Some problems with negative refraction,” Phy. Rev. Lett. 87, 249703 (2001).
[Crossref]

Zhang, X.

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
[Crossref]

Appl. Phys. Lett. (2)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on sub-diffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506 (2003).
[Crossref]

N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Appl. Phys. Lett. 82, 161 (2003).
[Crossref]

J. Phys: Condens. Matter. (1)

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

Phy. Rev. Lett. (1)

J. M. Williams, “Some problems with negative refraction,” Phy. Rev. Lett. 87, 249703 (2001).
[Crossref]

Phys. Rev. B (2)

X. S. Rao and C. K. Ong, “Amplification of evanescent wave s i n a lossy left-handed material slab,” Phys. Rev. B 68, 113103 (2003).
[Crossref]

T. J. Cui, Q. Cheng, W. B. Lu, Q. Jiang, and J. A. Kong, “Localization of electromagnetic energy using a LHM slab,” Phys. Rev. B 71, to be published, Jan. 2005.
[Crossref]

Phys. Rev. Lett (1)

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett 88, 207403 (2002).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

G. W.’t Hooft, “Comment on ‘Negative refraction makes a perfect lens’,” Phys. Rev. Lett. 87, 249701 (2001).
[Crossref] [PubMed]

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

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1997).
[Crossref]

M. W. Takeda, S. Kirihara, Y. Miyamoto, K. Sakoda, and K. Honda, “Localization of electromagnetic waves in three-dimensional photonic fractal cavities,” Phys. Rev. Lett. 92, 093902 (2004).
[Crossref] [PubMed]

G. Gomez-Santos, “Universal features of the time evolution of evanescent modes in a left-handed perfect lens,” Phys. Rev. Lett. 90, 077401 (2003).
[Crossref] [PubMed]

Progress in Electromagnetics Research, PIER (1)

J. A. Kong, “Electromagnetic wave interaction with stratified negative isotropic media,” Progress in Electromagnetics Research, PIER 35, 1 (2002).
[Crossref]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509 (1968).
[Crossref]

Other (1)

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).

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Figures (5)

Fig. 1.
Fig. 1. A compact energy-localization system, in which a linear source I is located in front of a grounded LHM slab at a distance of d 1, the thickness of the slab.
Fig. 2.
Fig. 2. Electric field distributions along the line y=0, where the source is located at z=0, the slab interfaces are d 1=15 mm and d 2=2d 1=30 mm, δε =δµ =0, and f=10 GHz. (a) The propagating components (Left). (b) The evanescent components (Right).
Fig. 3.
Fig. 3. Electric field distributions for a thin LHM slab, where d 1=1.5 mm, d 2=2d 1=3 mm, δε =δµ =0, and f=10 GHz. (a) The propagating components along the line y=0 (Left). (b) The total electric field on the yoz plane when γε =γµ =10-3 (Right).
Fig. 4.
Fig. 4. Electric field distributions for a thin LHM slab, where d 1=1.5 mm, d 2=2d 1=3 mm, δε =δµ =10-2, γε =γµ =10-2, and f=10 GHz. (a) The propagating components (Left). (b) The evanescent components (Right).
Fig. 5.
Fig. 5. Electric field distributions along the line y=0, where the source is located at z=0, the slab interfaces are located at z=d 1-δd and z=d 2=2d 1, and the PEC plane is placed at z=d 2. Here, d 1=1.5 mm, d 2=3 mm, δε =δµ =0, γε =γµ =10-3, f=10 GHz, and δd =0.01 mm and 0.1mm, respectively. (a) The propagating components (Left). (b) The evanescent components (Right).

Equations (6)

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

E 0 x = ω μ 0 I 4 π d k y k 0 z ( 1 + R ) e i k 0 z z e i k y y , z 0 ,
E 0 x = ω μ 0 I 4 π d k y k 0 z ( e i k 0 z z + R e i k 0 z z ) e i k y y , 0 z < d 1 ,
E 1 x = ω μ 0 I 4 π d k y ( E 1 + e i k 1 z z + E 1 e i k 1 z z ) e i k y y , d 1 z < 2 d 1 ,
R = R 01 e i 2 ( k 0 z + k 1 z ) d 1 e i 2 ( k 0 z d 1 + 2 k 1 z d 1 ) e i 2 k 1 z d 1 R 01 e i 4 k 1 z d 1 ,
E 1 + = 1 2 k 0 z [ ( 1 + p 10 ) e i ( k 0 z k 1 z ) d 1 + ( 1 p 10 ) R e i ( k 0 z + k 1 z ) d 1 ]
E 1 = 1 2 k 0 z [ ( 1 p 10 ) e i ( k 0 z + k 1 z ) d 1 + ( 1 + p 10 ) R e i ( k 0 z k 1 z ) d 1 ]

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