Abstract

The imaging properties of a uniaxial anisotropic slab lens, where the dielectric tensor components are of the opposite sign, are studied as a function of the structure parameters. While hypothetical parameters yield various levels of performance, a design principle to achieve good subwavelength resolution is suggested. The anisotropy can be implemented with a metal-insulator stack.

© 2008 Optical Society of America

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  1. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  2. D. R. Smith, D. Schurig, M. Rosenbluth, and S. Schultz, Appl. Phys. Lett. 82, 1506 (2003).
    [CrossRef]
  3. C. M. Soukoulis, M. Kafesaki, and E. N. Economou, Adv. Mater. 18, 1941 (2006).
    [CrossRef]
  4. V. M. Shalaev, Nat. Photonics 1, 41 (2007).
    [CrossRef]
  5. P. A. Belov, Microwave Opt. Technol. Lett. 37, 259 (2003).
    [CrossRef]
  6. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).
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    [CrossRef]
  8. P. A. Belov and C. R. Simovski, Phys. Rev. B 71, 193105 (2005).
    [CrossRef]
  9. B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115116 (2006).
    [CrossRef]
  10. P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
    [CrossRef]
  11. P. A. Belov and M. G. Silveirinha, Phys. Rev. E 73,056607 (2006).
    [CrossRef]
  12. L. V. Alekseyev and E. Narimanov, Opt. Express 14, 11184 (2006).
    [CrossRef] [PubMed]
  13. K. J. Webb and M. Yang, Opt. Lett. 31, 2130 (2006).
    [CrossRef] [PubMed]
  14. H. Liu, Shivanand, and K. J. Webb, in CLEO/QELS and PhAST 2008 Technical Digest (Optical Society of America, 2008), paper JThA133.
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    [CrossRef]
  16. R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, J. Opt. Soc. Am. B 23, 498 (2006).
    [CrossRef]
  17. A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
    [CrossRef] [PubMed]
  18. C. Wang, Y. Zhao, D. Gan, C. Du, and X. Luo, Opt. Express 16, 4217 (2008).
    [CrossRef] [PubMed]
  19. http://www.comsol.com/products/.
  20. S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101 (2003).
    [CrossRef]
  21. J. K. H. Wong, K. G. Balmain, and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 54, 2742 (2006).
    [CrossRef]

2008 (2)

H. Liu, Shivanand, and K. J. Webb, in CLEO/QELS and PhAST 2008 Technical Digest (Optical Society of America, 2008), paper JThA133.

C. Wang, Y. Zhao, D. Gan, C. Du, and X. Luo, Opt. Express 16, 4217 (2008).
[CrossRef] [PubMed]

2007 (2)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

2006 (8)

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

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
[CrossRef]

P. A. Belov and M. G. Silveirinha, Phys. Rev. E 73,056607 (2006).
[CrossRef]

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

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, J. Opt. Soc. Am. B 23, 498 (2006).
[CrossRef]

K. J. Webb and M. Yang, Opt. Lett. 31, 2130 (2006).
[CrossRef] [PubMed]

L. V. Alekseyev and E. Narimanov, Opt. Express 14, 11184 (2006).
[CrossRef] [PubMed]

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, Adv. Mater. 18, 1941 (2006).
[CrossRef]

2005 (2)

V. A. Podolskiy, L. V. Alekseyev, and E. E. Narimanov, J. Mod. Opt. 52, 2343 (2005).
[CrossRef]

P. A. Belov and C. R. Simovski, Phys. Rev. B 71, 193105 (2005).
[CrossRef]

2003 (4)

P. A. Belov, Microwave Opt. Technol. Lett. 37, 259 (2003).
[CrossRef]

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

D. R. Smith, D. Schurig, M. Rosenbluth, and S. Schultz, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101 (2003).
[CrossRef]

2001 (1)

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

Alekseyev, L. V.

L. V. Alekseyev and E. Narimanov, Opt. Express 14, 11184 (2006).
[CrossRef] [PubMed]

V. A. Podolskiy, L. V. Alekseyev, and E. E. Narimanov, J. Mod. Opt. 52, 2343 (2005).
[CrossRef]

Balmain, K. G.

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

Belov, P. A.

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
[CrossRef]

P. A. Belov and M. G. Silveirinha, Phys. Rev. E 73,056607 (2006).
[CrossRef]

P. A. Belov and C. R. Simovski, Phys. Rev. B 71, 193105 (2005).
[CrossRef]

P. A. Belov, Microwave Opt. Technol. Lett. 37, 259 (2003).
[CrossRef]

Du, C.

Economou, E. N.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, Adv. Mater. 18, 1941 (2006).
[CrossRef]

Eleftheriades, G. V.

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

Elser, J.

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

Gan, D.

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

Hao, Y.

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

Kafesaki, M.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, Adv. Mater. 18, 1941 (2006).
[CrossRef]

Kalinin, V.

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

Liu, H.

H. Liu, Shivanand, and K. J. Webb, in CLEO/QELS and PhAST 2008 Technical Digest (Optical Society of America, 2008), paper JThA133.

Luo, X.

Narimanov, E.

Narimanov, E. E.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, J. Opt. Soc. Am. B 23, 498 (2006).
[CrossRef]

V. A. Podolskiy, L. V. Alekseyev, and E. E. Narimanov, J. Mod. Opt. 52, 2343 (2005).
[CrossRef]

Pendry, J. B.

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

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

S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101 (2003).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Podolskiy, V. A.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, J. Opt. Soc. Am. B 23, 498 (2006).
[CrossRef]

V. A. Podolskiy, L. V. Alekseyev, and E. E. Narimanov, J. Mod. Opt. 52, 2343 (2005).
[CrossRef]

Ramakrishna, S. A.

S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101 (2003).
[CrossRef]

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

Ringhofer, K.

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, and S. Schultz, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, and S. Schultz, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Schurig, D.

D. R. Smith, D. Schurig, M. Rosenbluth, and S. Schultz, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

Shamonina, E.

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

Shivanand,

H. Liu, Shivanand, and K. J. Webb, in CLEO/QELS and PhAST 2008 Technical Digest (Optical Society of America, 2008), paper JThA133.

Silveirinha, M. G.

P. A. Belov and M. G. Silveirinha, Phys. Rev. E 73,056607 (2006).
[CrossRef]

Simovski, C. R.

P. A. Belov and C. R. Simovski, Phys. Rev. B 71, 193105 (2005).
[CrossRef]

Sivco, D. L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

Smith, D. R.

D. R. Smith, D. Schurig, M. Rosenbluth, and S. Schultz, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Solymar, L.

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, Adv. Mater. 18, 1941 (2006).
[CrossRef]

Stewart, W. J.

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

Tsai, D. P.

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

Wang, C.

Wangberg, R.

Wasserman, D.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

Webb, K. J.

H. Liu, Shivanand, and K. J. Webb, in CLEO/QELS and PhAST 2008 Technical Digest (Optical Society of America, 2008), paper JThA133.

K. J. Webb and M. Yang, Opt. Lett. 31, 2130 (2006).
[CrossRef] [PubMed]

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).
[CrossRef]

Wood, B.

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

Yang, M.

Zhao, Y.

Adv. Mater. (1)

C. M. Soukoulis, M. Kafesaki, and E. N. Economou, Adv. Mater. 18, 1941 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

D. R. Smith, D. Schurig, M. Rosenbluth, and S. Schultz, Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Electron. Lett. (1)

E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, Electron. Lett. 37, 1243 (2001).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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

J. Mod. Opt. (2)

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

V. A. Podolskiy, L. V. Alekseyev, and E. E. Narimanov, J. Mod. Opt. 52, 2343 (2005).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

P. A. Belov, Microwave Opt. Technol. Lett. 37, 259 (2003).
[CrossRef]

Nat. Mater. (1)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, Nat. Mater. 6, 946 (2007).
[CrossRef] [PubMed]

Nat. Photonics (1)

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (4)

S. A. Ramakrishna and J. B. Pendry, Phys. Rev. B 67, 201101 (2003).
[CrossRef]

P. A. Belov and C. R. Simovski, Phys. Rev. B 71, 193105 (2005).
[CrossRef]

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

P. A. Belov and Y. Hao, Phys. Rev. B 73, 113110 (2006).
[CrossRef]

Phys. Rev. E (1)

P. A. Belov and M. G. Silveirinha, Phys. Rev. E 73,056607 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Other (2)

H. Liu, Shivanand, and K. J. Webb, in CLEO/QELS and PhAST 2008 Technical Digest (Optical Society of America, 2008), paper JThA133.

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

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Figures (4)

Fig. 1
Fig. 1

Anisotropic slab structure.

Fig. 2
Fig. 2

Finite element simulation of a λ = 700 nm TM wave (with H y , E x , E z ) incident from the left onto a metallic mask ( ϵ = 1 j 4.0 × 10 4 ) of thickness 80 nm with a double slit having 3 nm slits and 23 nm center-to-center distance. E ( x , z ) is shown for an anisotropic slab having d = 400 nm , ϵ x = 0.01 j 0.01 , and ϵ z = 100 . Throughout, we assume a source plane located at z = 1.0 μ m , and the image plane is at the right interface of the anisotropic slab.

Fig. 3
Fig. 3

Transmission spectrum for (a) lossy or optically amplifying media and (b) the ϵ z lens. The parameters are λ = 700 nm and d = 400 nm .

Fig. 4
Fig. 4

Double slit resolution of an anisotropic slab lens, based on finite element simulations, with the mask of Fig. 2 and various material parameters. (a) ϵ x ϵ z is constant; (b) ϵ x ϵ z is constant; (c) ϵ x 0 , ϵ z and the perfect lens condition; (d) ϵ x 0 , ϵ z and a deviation from the perfect lens condition. The parameters are λ = 700 nm and d = 400 nm .

Equations (8)

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T ( k x ) = 1 cos ( k z d ) + j 2 ( Z s Z 0 + Z 0 Z s ) sin ( k z d ) ,
tan ( k z d 2 ) = j Z 0 Z s , tan ( k z d 2 ) = j Z s Z 0 .
T ( k x ) = [ cos ( ϵ x ϵ z k x d ) + 1 2 ( ϵ x ϵ z 1 ϵ x ϵ z ) sin ( ϵ x ϵ z k x d ) ] 1 .
α = α + j α ϵ x ϵ z k x d , β = β + j β ϵ x ϵ z .
T ( k x ) = { cos α cosh α + 1 2 ( β β β 2 ) sin α cosh α 1 2 ( β + β β 2 ) cos α sinh α + j [ sin α sinh α + 1 2 ( β β β 2 ) cos α sinh α + 1 2 ( β + β β 2 ) sin α cosh α ] } 1 .
T ( k x ) = [ cos ( ϵ x k 0 d ) + j 2 ( ϵ x ( k 0 2 k x 2 ) k 0 2 + k 0 2 ϵ x ( k 0 2 k x 2 ) ) sin ( ϵ x k 0 d ) ] 1 .
k x k 0 = 1 + ( k 0 d 2 ) 2 ,
T ( k x ) = ( 1 + j 2 k x ϵ x d ) 1 ,

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