Abstract

A nonmagnetic compensating bilayer imaging system having two uniaxially anisotropic layers is described. Evanescent fields in vacuum are converted to propagating waves in the bilayer, and one layer compensates the phase progression of the other. In this way, subwavelength imaging performance is possible with substantial flexibility in operating wavelength. Conditions for enhanced resolution and sensitivity to the material parameters are examined with a view to fabrication.

© 2009 Optical Society of America

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  1. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, J. Mod. Opt. 50, 1419 (2003).
  2. P. A. Belov and C. R. Simovski, Phys. Rev. B 71, 193105 (2005).
    [CrossRef]
  3. K. J. Webb and M. Yang, Opt. Lett. 31, 2130 (2006).
    [CrossRef] [PubMed]
  4. H. Liu, Shivanand, and K. J. Webb, Opt. Lett. 33, 2562 (2008).
    [PubMed]
  5. V. A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71, 201101 (2005).
    [CrossRef]
  6. 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]
  7. B. Wood, J. B. Pendry, and D. P. Tsai, Phys. Rev. B 74, 115116 (2006).
    [CrossRef]
  8. J. K. H. Wong, K. G. Balmain, and G. V. Eleftheriades, IEEE Trans. Antennas Propag. 54, 2742 (2006).
    [CrossRef]
  9. K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602 (2004).
    [CrossRef]
  10. D. R. Smith and D. Schurig, Phys. Rev. Lett. 90, 077405 (2003).
    [CrossRef] [PubMed]
  11. G. X. Li, H. L. Tam, F. Y. Wang, and K. W. Cheah, J. Appl. Phys. 102, 116101 (2007).
    [CrossRef]
  12. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  13. http://www.comsol.com/products/.
  14. Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1998).

2008

2007

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]

G. X. Li, H. L. Tam, F. Y. Wang, and K. W. Cheah, J. Appl. Phys. 102, 116101 (2007).
[CrossRef]

2006

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

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

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

2005

V. A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71, 201101 (2005).
[CrossRef]

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

2004

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602 (2004).
[CrossRef]

2003

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

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

2000

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]

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

Cheah, K. W.

G. X. Li, H. L. Tam, F. Y. Wang, and K. W. Cheah, J. Appl. Phys. 102, 116101 (2007).
[CrossRef]

Eleftheriades, G. V.

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

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]

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]

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]

Li, G. X.

G. X. Li, H. L. Tam, F. Y. Wang, and K. W. Cheah, J. Appl. Phys. 102, 116101 (2007).
[CrossRef]

Liu, H.

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]

V. A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71, 201101 (2005).
[CrossRef]

Nelson, K. A.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602 (2004).
[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).

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]

V. A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71, 201101 (2005).
[CrossRef]

Ramakrishna, S. A.

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

Schurig, D.

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

Shivanand,

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

Stewart, W. J.

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

Tam, H. L.

G. X. Li, H. L. Tam, F. Y. Wang, and K. W. Cheah, J. Appl. Phys. 102, 116101 (2007).
[CrossRef]

Tsai, D. P.

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

Wang, F. Y.

G. X. Li, H. L. Tam, F. Y. Wang, and K. W. Cheah, J. Appl. Phys. 102, 116101 (2007).
[CrossRef]

Ward, D. W.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602 (2004).
[CrossRef]

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.

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.

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

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602 (2004).
[CrossRef]

IEEE Trans. Antennas Propag.

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

J. Appl. Phys.

G. X. Li, H. L. Tam, F. Y. Wang, and K. W. Cheah, J. Appl. Phys. 102, 116101 (2007).
[CrossRef]

J. Mod. Opt.

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

Nat. Mater.

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]

Opt. Lett.

Phys. Rev. B

V. A. Podolskiy and E. E. Narimanov, Phys. Rev. B 71, 201101 (2005).
[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]

Phys. Rev. E

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, Phys. Rev. E 70, 035602 (2004).
[CrossRef]

Phys. Rev. Lett.

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

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

Other

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

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

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Figures (4)

Fig. 1
Fig. 1

A nonmagnetic anisotropic bilayer implemented using metal–insulator stacks or metallic nanowires embedded in a dielectric host.

Fig. 2
Fig. 2

(a) Magnitude of the transmission coefficient for a bilayer lens with ϵ 1 x = 1.0 , ϵ 1 z = 2.0 , ϵ 2 x = 1.0 , ϵ 2 z = 2.0 , d 1 = d 2 = 200   nm , and free-space wavelength λ = 700   nm . The transmission coefficients of the two individual layers are also shown for comparison. (b) Field intensity plot | E | of the bilayer, from a finite element simulation for a λ = 700   nm TM wave incident from the left onto a metallic mask ( ϵ = 1 + i 1.0 × 10 4 ) of thickness 50 nm with a double slit having 5 nm slits and 75 nm center-to-center distance. Perturbational material losses ( Im ( ϵ ) = 0.01 ) are added.

Fig. 3
Fig. 3

Magnitude of the transmission coefficient for unmatched bilayer lenses. λ = 700   nm , d 1 = 200   nm , ϵ 1 x = 1.0 , ϵ 1 z = 2.0 . (a) ϵ 2 x = 1.0 , ϵ 2 z = 2.0 , d 2 = 0.8 d 1 . (b) ϵ 2 x = 2.0 , ϵ 2 z = 4.0 , d 2 = d 1 . (c) ϵ 2 x = 0.05 , ϵ 2 z = 0.1 , d 2 = d 1 .

Fig. 4
Fig. 4

Numerical simulations of a Ag/MgO bulk anisotropic bilayer having d 1 = 50   nm and d 2 = 370   nm , operating at λ = 1550   nm with TM wave illumination. The volume fraction for Ag is 0.5, and with ϵ Ag = 86.64 + i 8.74 and ϵ MgO = 2.94 [14], ϵ 1 x = ϵ 2 z = ϵ = 41.85 + i 4.37 and ϵ 1 z = ϵ 2 x = ϵ = 6.08 + i 2.13 × 10 2 . (a) Magnitude of the bilayer transmission coefficient. (b) Phase of the bilayer transmission coefficient. (c) Field intensity plot | E ( x , z ) | for the simulation setup as specified in Fig. 2b, with 10 nm slits and 50 nm center-to-center distance. (d) The field profile at the image plane (the right interface of the second slab).

Equations (6)

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T = 2 Z 0 Z 1 Z 2 { Z 0 [ 2 Z 1 Z 2   cos ( ϕ 1 ) cos ( ϕ 2 ) ( Z 1 2 + Z 2 2 ) sin ( ϕ 1 ) sin ( ϕ 2 ) ] i [ Z 1 ( Z 0 2 + Z 2 2 ) cos ( ϕ 1 ) sin ( ϕ 2 ) + Z 2 ( Z 0 2 + Z 1 2 ) sin ( ϕ 1 ) cos ( ϕ 2 ) ] } 1 ,
ϕ 1 ϵ 1 x / ϵ 1 z k x d 1 ,     ϕ 2 ϵ 2 x / ϵ 2 z k x d 2 ,
Z 1 k x ω ϵ 0 ϵ 1 x ϵ 1 z ,     Z 2 k x ω ϵ 0 ϵ 2 x ϵ 2 z .
ϵ 1 x / ϵ 1 z d 1 = ϵ 2 x / ϵ 2 z d 2 ,     ϵ 1 x ϵ 1 z = ϵ 2 x ϵ 2 z ,
ϵ 1 x ϵ 2 x < 0 ,
| Z 0 | ( Z 1 2 + Z 2 2 ) tan 2 ( ϕ ) + ( | Z 0 | 2 + Z 1 Z 2 ) ( Z 2 Z 1 ) tan ( ϕ ) + 2 | Z 0 | Z 1 Z 2 = 0.

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