Abstract

A Green’s function analysis for cylindrically anisotropic media is presented that can be used in the design of various metamaterial devices. The resonance cones, which describe the direction of power flow, result from the Green’s function singularity when the permittivity tensor elements have opposite signs. Shadow and accessible regions for the source are also identified.

© 2011 Optical Society of America

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  1. A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103(2006).
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    [CrossRef] [PubMed]
  4. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
    [CrossRef] [PubMed]
  5. J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, Nat. Mater. 8, 931 (2009).
    [CrossRef] [PubMed]
  6. J. K. H. Wong, K. G. Balmain, and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 54, 2742 (2006).
    [CrossRef]
  7. B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115116 (2006).
    [CrossRef]
  8. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE, 1994).
    [CrossRef]
  9. L. B. Felsen, IEEE Trans. Antennas Propag. 11, 469 (1963).
    [CrossRef]
  10. D. G. Dudley, Mathematical Foundations for Electromagnetic Theory (IEEE, 1994).
    [CrossRef]
  11. The COMSOL Group, http://www.comsol.com/products/.
  12. Z. Jacob, L. V. Alekseyev, and E. Narimanov, J. Opt. Soc. Am. A 24, A52 (2007).
    [CrossRef]
  13. H. Liu and K. J. Webb, Opt. Lett. 35, 1869 (2010).
    [CrossRef] [PubMed]
  14. H. Liu, Shivanand, and K. J. Webb, Opt. Lett. 34, 2243(2009).
    [PubMed]

2010 (1)

2009 (2)

H. Liu, Shivanand, and K. J. Webb, Opt. Lett. 34, 2243(2009).
[PubMed]

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, Nat. Mater. 8, 931 (2009).
[CrossRef] [PubMed]

2007 (3)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, J. Opt. Soc. Am. A 24, A52 (2007).
[CrossRef]

2006 (4)

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103(2006).
[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, Opt. Express 14, 8247 (2006).
[CrossRef] [PubMed]

J. K. H. Wong, K. G. Balmain, and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 54, 2742 (2006).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115116 (2006).
[CrossRef]

1963 (1)

L. B. Felsen, IEEE Trans. Antennas Propag. 11, 469 (1963).
[CrossRef]

Alekseyev, L. V.

Balmain, K. G.

J. K. H. Wong, K. G. Balmain, and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 54, 2742 (2006).
[CrossRef]

Bartal, G.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, Nat. Mater. 8, 931 (2009).
[CrossRef] [PubMed]

Davis, C. C.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

Dudley, D. G.

D. G. Dudley, Mathematical Foundations for Electromagnetic Theory (IEEE, 1994).
[CrossRef]

Eleftheriades, G. V.

J. K. H. Wong, K. G. Balmain, and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 54, 2742 (2006).
[CrossRef]

Engheta, N.

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103(2006).
[CrossRef]

Felsen, L. B.

L. B. Felsen, IEEE Trans. Antennas Propag. 11, 469 (1963).
[CrossRef]

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE, 1994).
[CrossRef]

Fok, L.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, Nat. Mater. 8, 931 (2009).
[CrossRef] [PubMed]

Hung, Y.-J.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

Jacob, Z.

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Li, J.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, Nat. Mater. 8, 931 (2009).
[CrossRef] [PubMed]

Liu, H.

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Marcuvitz, N.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE, 1994).
[CrossRef]

Narimanov, E.

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Salandrino, A.

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103(2006).
[CrossRef]

Shivanand,

Smolyaninov, I. I.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Webb, K. J.

Wong, J. K. H.

J. K. H. Wong, K. G. Balmain, and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 54, 2742 (2006).
[CrossRef]

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

Yin, X.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, Nat. Mater. 8, 931 (2009).
[CrossRef] [PubMed]

Zhang, X.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, Nat. Mater. 8, 931 (2009).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag. (2)

J. K. H. Wong, K. G. Balmain, and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 54, 2742 (2006).
[CrossRef]

L. B. Felsen, IEEE Trans. Antennas Propag. 11, 469 (1963).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nat. Mater. (1)

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, Nat. Mater. 8, 931 (2009).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (2)

A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103(2006).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Science (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
[CrossRef] [PubMed]

Other (3)

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE, 1994).
[CrossRef]

D. G. Dudley, Mathematical Foundations for Electromagnetic Theory (IEEE, 1994).
[CrossRef]

The COMSOL Group, http://www.comsol.com/products/.

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Figures (3)

Fig. 1
Fig. 1

Line source in a cylindrically anisotropic half-space bounded by a perfect planar absorber.

Fig. 2
Fig. 2

Full-wave-simulated (finite element method) real part of the H z distribution for cylindrically anisotropic metamaterials with (a)  ϵ ρ = 3 , ϵ ϕ = 10 ; (b)  ϵ ρ = 3 , ϵ ϕ = 10 ; and (c)  ϵ ρ = 3 , ϵ ϕ = 5 . The power distribution is shown for (d)  ϵ ρ = 3 , ϵ ϕ = 10 ; (e)  ϵ ρ = 3 , ϵ ϕ = 10 ; and (f)  ϵ ρ = 3 + i 0.5 , ϵ ϕ = 5 + i 0.5 . The current source is located at ( x = 0 , y = 2 μm ) . The red dashed lines denote the resonance cone surfaces calculated through Eq. (6). The operating wavelength is λ = 0.5 μm .

Fig. 3
Fig. 3

Full-wave-simulated real part of H z and the power distribution for cylindrically anisotropic metamaterials with (a), (c)  ϵ ρ / ϵ ϕ 0 and (b), (d)  ϵ ρ / ϵ ϕ . The current source is located at ( x = 0 , y = 2 μm ) . The operating wavelength is λ = 0.5 μm .

Equations (12)

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1 ϵ ϕ 1 ρ ρ ( ρ H z ρ ) + 1 ϵ ρ 1 ρ 2 2 H z ϕ 2 + k 0 2 H z = i ω ϵ 0 I 0 δ ( ρ ρ ) δ ( ϕ ϕ ) ρ ,
1 ϵ ϕ 1 ρ ρ ( ρ g ρ ) + 1 ϵ ρ 1 ρ 2 2 g ϕ 2 + k 0 2 g = δ ( ρ ρ ) δ ( ϕ ϕ ) ρ .
g = i ϵ ϕ ϵ ρ 4 H 0 ( 1 ) ( ϵ ϕ k 0 2 ρ 2 + ϵ ϕ k 0 2 ρ 2 2 ϵ ϕ k 0 2 ρ ρ cos [ ϵ ρ ϵ ϕ ( ϕ ϕ ) ] ) ,
g = i ϵ ϕ ϵ ρ 4 H 0 ( 1 ) ( ϵ ϕ k 0 2 ρ 2 + ϵ ϕ k 0 2 ρ 2 2 ϵ ϕ k 0 2 ρ ρ cosh [ ϵ ρ ϵ ϕ ( ϕ ϕ ) ] ) .
ρ 2 + ρ 2 = 2 ρ ρ cosh [ ϵ ρ ϵ ϕ ( ϕ ϕ ) ] ,
ρ = ρ exp [ ± ϵ ρ ϵ ϕ ( ϕ ϕ ) ] .
ϵ ϕ [ ρ 2 + ρ 2 2 ρ ρ cosh ( ϵ ρ ϵ ϕ ( ϕ ϕ ) ) ] > 0 .
ln ρ ρ > ϵ ρ ϵ ϕ | ϕ ϕ | , ln ρ ρ < ϵ ρ ϵ ϕ | ϕ ϕ | ,
ϵ ρ ϵ ϕ | ϕ ϕ | > ln ρ ρ > ϵ ρ ϵ ϕ | ϕ ϕ | ,
g = i ϵ ϕ ϵ ρ 4 H 0 ( 1 ) ( ϵ ϕ k 0 | ρ ρ | ) ,
1 ρ ρ ( ρ g ρ ) + ϵ ϕ k 0 2 g = ϵ ϕ δ ( ρ ρ ) δ ( ϕ ϕ ) ρ ,
g = i π ϵ ϕ 2 δ ( ϕ ϕ ) { H 0 ( 1 ) ( ϵ ϕ k 0 ρ ) J 0 ( ϵ ϕ k 0 ρ ) , ρ < ρ H 0 ( 1 ) ( ϵ ϕ k 0 ρ ) J 0 ( ϵ ϕ k 0 ρ ) , ρ > ρ .

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