Abstract

Resonance cones, the regions where major power and high-intensity fields are concentrated, form with cylindrically anisotropic media when the permittivity tensor elements have opposite signs. The resonance cones inside a circular layer of cylindrically anisotropic material is shown to experience multiple internal reflections from the layer boundaries. We introduce a spectrometer class by exploiting the dispersive properties of a metal-insulator stack metamaterial. The cones can exhibit negative refraction at the interface of two such circular layers, leading to a far-field bilayer subwavelength imaging system with more flexibility in the material parameter and operating wavelength spaces.

© 2011 Optical Society of America

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  1. K. G. Balmain, A. A. E. Lüttgen, and P. C. Kremer, IEEE Antennas Wirel. Propag. Lett. 1, 146 (2002).
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    [PubMed]
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    [PubMed]
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    [PubMed]
  13. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, Science 315, 1699 (2007).
    [PubMed]
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    [PubMed]
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  16. A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103(2006).
  17. E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1998).
  18. H. Yoshikawa and S. Adachi, Jpn. J. Appl. Phys. Part 1 36, 6237 (1997).

2010 (1)

2009 (2)

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

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

2008 (1)

2007 (2)

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

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

2006 (3)

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115(2006).

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

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

2003 (2)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405(2003).
[PubMed]

2002 (1)

K. G. Balmain, A. A. E. Lüttgen, and P. C. Kremer, IEEE Antennas Wirel. Propag. Lett. 1, 146 (2002).

1997 (1)

H. Yoshikawa and S. Adachi, Jpn. J. Appl. Phys. Part 1 36, 6237 (1997).

1963 (1)

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

Adachi, S.

H. Yoshikawa and S. Adachi, Jpn. J. Appl. Phys. Part 1 36, 6237 (1997).

Balmain, K. G.

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

K. G. Balmain, A. A. E. Lüttgen, and P. C. Kremer, IEEE Antennas Wirel. Propag. Lett. 1, 146 (2002).

Bartal, G.

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

Davis, C. C.

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

Eleftheriades, G. V.

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

Engheta, N.

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

Felsen, L. B.

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

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

Fok, L.

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

Hung, Y. -J.

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

Kremer, P. C.

K. G. Balmain, A. A. E. Lüttgen, and P. C. Kremer, IEEE Antennas Wirel. Propag. Lett. 1, 146 (2002).

Lee, H.

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

Li, J.

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

Liu, H.

Liu, Z.

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

Lüttgen, A. A. E.

K. G. Balmain, A. A. E. Lüttgen, and P. C. Kremer, IEEE Antennas Wirel. Propag. Lett. 1, 146 (2002).

Marcuvitz, N.

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

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115(2006).

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).

Ramakrishna, S. A.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).

Salandrino, A.

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

Schurig, D.

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405(2003).
[PubMed]

Shivanand,

Smith, D. R.

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405(2003).
[PubMed]

Smolyaninov, I. I.

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

Stewart, W. J.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).

Sun, C.

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

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115(2006).

Webb, K. J.

Wiltshire, M. C. K.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).

Wong, J. K. H.

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

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115(2006).

Xiong, Y.

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

Yin, X.

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

Yoshikawa, H.

H. Yoshikawa and S. Adachi, Jpn. J. Appl. Phys. Part 1 36, 6237 (1997).

Zhang, X.

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

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

IEEE Antennas Wirel. Propag. Lett. (1)

K. G. Balmain, A. A. E. Lüttgen, and P. C. Kremer, IEEE Antennas Wirel. Propag. Lett. 1, 146 (2002).

IEEE Trans. Antennas Propag. (2)

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

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

J. Mod. Opt. (1)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).

Jpn. J. Appl. Phys. Part 1 (1)

H. Yoshikawa and S. Adachi, Jpn. J. Appl. Phys. Part 1 36, 6237 (1997).

Nat. Mater. (1)

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

Opt. Lett. (3)

Phys. Rev. B (2)

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

B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115(2006).

Phys. Rev. Lett. (1)

D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405(2003).
[PubMed]

Science (2)

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

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

Other (4)

E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1998).

http://www.comsol.com/products/.

H. Liu and K. J. Webb, in Frontiers in Optics (Optical Society of America, 2010), p. FWO7.

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

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Figures (5)

Fig. 1
Fig. 1

A cylindrically anisotropic slab with a perfect planar absorber boundary excited by a line source.

Fig. 2
Fig. 2

Full-wave (finite element method) simulation results for cylindrically anisotropic metamaterials with ϵ ρ = 5 , ϵ ϕ = 1 . A current source is located at ( x = 0 , y = 1 μm ), and the operating wavelength is λ = 0.5 μm . (a) Real part of H z . (b) Normalized field magnitude plot | E ( ρ , ϕ ) | . The dashed curves denote the resonance cone surfaces calculated through Eq. (3).

Fig. 3
Fig. 3

Reflections of resonance cones from boundaries of a cylindrically anisotropic slab. The radii of the inner and outer boundaries are ρ 0 = 1 μm , ρ 1 = 2 μm , respectively, the permittivity tensor elements are ϵ ρ = 5.0 , ϵ ϕ = 1.0 , the operating wavelength is λ = 0.5 μm , and the polarization is TM. The line source is located at ρ = ρ 0 , ϕ = π / 2 . (a) Normalized | E ( ρ , ϕ ) | from full-wave simulations, compared with a schematic of resonance cones (dashed curves) calculated through Eq. (3). (b) The normalized field magnitude at the plane ρ = ρ 1 as a function of the azimuthal angle.

Fig. 4
Fig. 4

(a) A two-dimensional bulk cylindrical anisotropic slab from a metal-insulator stack. (b) Numerical results for | E ( ρ = ρ 1 = 2 μm ) | with ρ = ρ 0 = 1 μm , ϕ = π / 2 , for a homogenized Ag/ZnO multilayer stack, using published material data [17, 18], with D = 0.5 .

Fig. 5
Fig. 5

Full-wave (finite element method) simulations of a cylindrically anisotropic bilayer with ρ 0 = 1 μm , ρ 1 = 2 μm , ρ 2 = 4 μm , ϵ 1 ρ = 5.0 , ϵ 1 ϕ = 1.0 , ϵ 2 ρ = 5.0 , ϵ 2 ϕ = 1.0 , operating at λ = 0.5 μm with TM polarization. The two line sources located at the ρ = ρ 0 plane are separated by 5 ° in azimuth. (a) Normalized | E ( ρ , ϕ ) | . (b) The normalized field profile at both the source surface ρ = ρ 0 and the image surface ρ = ρ 2 as a function of the azimuthal angle.

Equations (6)

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ϵ = ϕ ^ ϕ ^ ϵ ϕ + ( ρ ^ ρ ^ + z ^ z ^ ) ϵ ρ , with ϵ ϕ ϵ ρ < 0 ,
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 = ρ exp [ ± ϵ ρ ϵ ϕ ( ϕ ϕ ) ] .
ϕ = ϕ ± ( 2 p + 1 ) ϵ ϕ ϵ ρ ln ( ρ 1 ρ 0 ) , p = 0 , 1 , 2 ,
ϕ 1 = ϕ 0 ± ϵ 1 ϕ ϵ 1 ρ ln ( ρ 1 ρ 0 ) , ϕ 2 = ϕ 1 ϵ 2 ϕ ϵ 2 ρ ln ( ρ 2 ρ 1 ) , ϕ 2 = ϕ 0 ,
ln ρ 1 ln ρ 0 ln ρ 2 ln ρ 1 = ϵ 1 ρ / ϵ 1 ϕ ϵ 2 ρ / ϵ 2 ϕ , ϵ 1 ρ ϵ 2 ρ < 0 ,

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