Abstract

We show that a planar waveguide excited by a three-dimensional linear electric dipole exhibits unusual physical properties if it is filled with two equal-thickness layers, where one layer is air and the other layer is a specialized left-handed material (LHM) with the relative permittivity -1/(1 + δ) + ε and permeability -(1 + δ) + μ (δ, γε and γμ are all small parameters). In such a LHM waveguide, extremely high power densities are generated and transmitted under the excitation of the electric dipole no matter whether the LHM layer is lossless or lossy. We also show that a dominant mode always exists in the waveguide, which is not restricted by the guidance condition and the waveguide geometry. The guidance condition only determines the existence of higher guided modes. Numerical experiments verify the above conclusions.

© 2005 Optical Society of America

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References

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  1. V. G. Veselago,"The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77 (2001).
    [CrossRef] [PubMed]
  4. A. Grbic and G. V. Eleftheriades, "Overcoming the diffraction limit. with a planar left-handed transmission-line lens," Phys. Rev. Lett. 92, 117403 (2004).
    [CrossRef] [PubMed]
  5. Q. Cheng and T. J. Cui, "High power generation and transmission through a left-handed material," Phys. Rev. B, 72, 113112, 2005.
    [CrossRef]
  6. W. C. Chew, Waves and Fields in Inhomogenous Media (Van Nostrand Reinhold, New York, 1990).

Phys. Rev. B (1)

Q. Cheng and T. J. Cui, "High power generation and transmission through a left-handed material," Phys. Rev. B, 72, 113112, 2005.
[CrossRef]

Phys. Rev. Lett. (2)

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

A. Grbic and G. V. Eleftheriades, "Overcoming the diffraction limit. with a planar left-handed transmission-line lens," Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef] [PubMed]

Science (1)

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

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)

W. C. Chew, Waves and Fields in Inhomogenous Media (Van Nostrand Reinhold, New York, 1990).

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Figures (5)

Fig. 1.
Fig. 1.

A three-dimensional linear electric dipole located in a planar waveguide filled with two-layered media.

Fig. 2.
Fig. 2.

The time-averaged power density in the waveguide along the region 3000 mm ≤ y ≤ 3600 mm. (a) Conventional air-filled waveguide. (b) Air-LHM-filled waveguide with δ = 10-4 and γε = γμ = 0.

Fig. 3.
Fig. 3.

The time averaged power density in the lossy air-LHM-filled waveguide along the region 3000 mm ≤ y ≤ 3600 mm. (a) δ = -10-4 and γε = γμ = 10-6. (b) δ = -10-2, γε = γμ = 10-4.

Fig. 4.
Fig. 4.

The time averaged power density in the air-filled and lossless air-LHM-filled waveguides along the region 3000 mm ≤ y ≤ 4000 mm when two guided modes exist. (a) Conventional air-filled waveguide. (b) lossless air-LHM-filled waveguide with δ = 10-4 and γε = γμ = 0.

Fig. 5.
Fig. 5.

The time averaged power density in the lossy air-LHM-filled waveguide along the region 3000 mm ≤ y ≤ 4000 mm when two guided modes exist. (a) δ = -10-4 and γε = γμ = 10-6. (b) δ = -10-2 and γε = γμ = 10-4.

Equations (24)

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ε r 1 = 1 / ( 1 + δ ) + i γ ε , μ r 1 = ( 1 + δ ) + i γ μ
E iz = Il 8 πω ε 0 k ρ 3 k 0 z E ˜ iz H 0 ( 1 ) ( k ρ ρ ) d k ρ ,
E = iIl 8 πω ε 0 k ρ 2 E ˜ H 1 ( 1 ) ( k ρ ρ ) d k ρ ,
H = iIl 8 π k ρ 2 k 0 z E ˜ iz H 1 ( 1 ) ( k ρ ρ ) d k ρ ,
E ˜ 0 z = e i k 0 z z + R + e i k 0 z z + R e i k 0 z z ,
E ˜ 1 z = C e i k 1 z z + C + e i k 1 z z ,
E ˜ 0 ρ = z e i k 0 z z z + R + e i k 0 z z R e i k 0 z z ,
E ˜ 1 ρ = C e i k 1 z z + C + e i k 1 z z .
R + = ( a c p + a + c + ) D ,
R = 1 + R + e i 2 k 0 z d 0 ,
C = ( a b a + b + ) ε r 0 ( ε r 1 D ) ,
C + = C e i 2 k 1 z d 2 ,
D = ( p b + c + b c + ) k 0 z ,
a ± = e i k 0 z d 1 ± e i k 0 z d 1 ,
b ± = e i k 0 z d 1 ± e i k 0 z ( d 1 2 d 0 ) ,
c ± = e i k 1 z d 1 ± e i k 1 z ( d 1 2 d 2 ) ,
p = ( ε r 0 k 1 z ) ( ε r 1 k 0 z ) .
D = ( 2 2 e i 2 k 0 z ( d 0 d 2 ) ) k 0 z .
k 0 z = ( d 2 d 0 ) , ( n = 1,2… )
E z = A e i k 0 z z H 0 ( 1 ) ( k ρ ρ ) ,
E 0 z = A H 0 ( 1 ) ( k ρ ρ ) .
ε r 1 = 1 ( 1 + δ ) , μ r 1 = ( 1 + δ ) ,
D = δ k 0 z ( e i 2 k 0 z d 2 e i 2 k 0 z d 0 ) ( 1 + δ ) .
E 1 z = ( A cos k 1 z z + B sin k 1 z z ) H 0 ( 1 ) ( k ρ ρ ) ,

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