Abstract

We present a technique capable of producing subwavelength focal spots in planar nonresonant structures not limited to the near-field of the source. The approach combines the diffraction gratings that generate the high-wave-vector-number modes and planar slabs of homogeneous anisotropic metamaterials that propagate these waves and combine them at the subwavelength focal spots. In a sense, the technique combines the benefits of Fresnel lens, near-field zone plates, hyperlens, and superlens and at the same time resolves their fundamental limitations. Several realizations of the proposed technique for visible, near-IR, and mid-IR frequencies are proposed, and their performance is analyzed theoretically and numerically. Generalizations of the developed approach for subdiffractional imaging and on-chip photonics are suggested.

© 2009 Optical Society of America

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  1. J. Pendry, D. Schurig, and D. Smith, Science 312, 1780 (2006).
    [CrossRef] [PubMed]
  2. A. Kildishev and V. Shalaev, Opt. Lett. 33, 43 (2008).
    [CrossRef]
  3. Z. Jacob, L. Alekseyev, and E. Narimanov, Opt. Express 14, 8247 (2006).
    [CrossRef] [PubMed]
  4. A. Salandrino and N. Engheta, Phys. Rev. B 74, 075103 (2006).
    [CrossRef]
  5. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
    [CrossRef] [PubMed]
  6. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  7. R. Merlin, Science 317, 927 (2007).
    [CrossRef] [PubMed]
  8. L. Makley, X. Wong, Y. Wang, and G. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
    [CrossRef]
  9. Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 93, 111116 (2008).
    [CrossRef]
  10. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  11. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  12. D. Schurig and D. R. Smith, New J. Phys. 7, 162 (2005).
    [CrossRef]
  13. V. Podolskiy and E. Narimanov, Opt. Lett. 30, 75 (2005).
    [CrossRef] [PubMed]
  14. R. Wangberg, J. Elser, E. E. Narimanov, and V. A. Podolskiy, J. Opt. Soc. Am. B 23, 498 (2006).
    [CrossRef]
  15. 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, Nature Mater. 6, 946 (2007).
    [CrossRef]
  16. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
    [CrossRef] [PubMed]
  17. C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
    [CrossRef]
  18. E.Palik, ed., The Handbook of Optical Constants of Solids (Academic, 1997).
  19. F. V. Bunkin, Sov. Phys. JETP 5, 277 (1957).
  20. K. G. Balmain, A. Luttgen, and P. Kremer, IEEE Antennas Wireless Propag. Lett. 1, 146 (2002).
    [CrossRef]
  21. P. Belov, C. Simovski, and P. Ikonen, Phys. Rev. B 71, 193105 (2005).
    [CrossRef]

2008 (4)

A. Kildishev and V. Shalaev, Opt. Lett. 33, 43 (2008).
[CrossRef]

L. Makley, X. Wong, Y. Wang, and G. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef]

Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 93, 111116 (2008).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

2007 (3)

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, Nature Mater. 6, 946 (2007).
[CrossRef]

R. Merlin, Science 317, 927 (2007).
[CrossRef] [PubMed]

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

2006 (5)

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

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

J. Pendry, D. Schurig, and D. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

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

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
[CrossRef]

2005 (3)

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

D. Schurig and D. R. Smith, New J. Phys. 7, 162 (2005).
[CrossRef]

V. Podolskiy and E. Narimanov, Opt. Lett. 30, 75 (2005).
[CrossRef] [PubMed]

2002 (1)

K. G. Balmain, A. Luttgen, and P. Kremer, IEEE Antennas Wireless Propag. Lett. 1, 146 (2002).
[CrossRef]

2000 (1)

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

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

1957 (1)

F. V. Bunkin, Sov. Phys. JETP 5, 277 (1957).

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, Nature Mater. 6, 946 (2007).
[CrossRef]

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

Balmain, K. G.

K. G. Balmain, A. Luttgen, and P. Kremer, IEEE Antennas Wireless Propag. Lett. 1, 146 (2002).
[CrossRef]

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Belov, P.

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

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Bunkin, F. V.

F. V. Bunkin, Sov. Phys. JETP 5, 277 (1957).

Chichkovet, B.

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
[CrossRef]

Dickson, W.

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
[CrossRef]

Eleftheriades, G.

L. Makley, X. Wong, Y. Wang, and G. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef]

Elser, J.

Engheta, N.

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

Evans, P.

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (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, Nature Mater. 6, 946 (2007).
[CrossRef]

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, Nature Mater. 6, 946 (2007).
[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, Nature Mater. 6, 946 (2007).
[CrossRef]

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, Nature Mater. 6, 946 (2007).
[CrossRef]

Ikonen, P.

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

Jacob, Z.

Kildishev, A.

Kremer, P.

K. G. Balmain, A. Luttgen, and P. Kremer, IEEE Antennas Wireless Propag. Lett. 1, 146 (2002).
[CrossRef]

Lee, H.

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

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Liu, Z.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 93, 111116 (2008).
[CrossRef]

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

Luttgen, A.

K. G. Balmain, A. Luttgen, and P. Kremer, IEEE Antennas Wireless Propag. Lett. 1, 146 (2002).
[CrossRef]

Makley, L.

L. Makley, X. Wong, Y. Wang, and G. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef]

Merlin, R.

R. Merlin, Science 317, 927 (2007).
[CrossRef] [PubMed]

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, Nature Mater. 6, 946 (2007).
[CrossRef]

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

Passinger, S.

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
[CrossRef]

Pendry, J.

J. Pendry, D. Schurig, and D. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Pendry, J. B.

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

Podolskiy, V.

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, Nature Mater. 6, 946 (2007).
[CrossRef]

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

Pollard, R.

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
[CrossRef]

Reinhardt, C.

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
[CrossRef]

Salandrino, A.

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

Schurig, D.

J. Pendry, D. Schurig, and D. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig and D. R. Smith, New J. Phys. 7, 162 (2005).
[CrossRef]

Shalaev, V.

Simovski, C.

P. Belov, C. Simovski, and P. Ikonen, 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, Nature Mater. 6, 946 (2007).
[CrossRef]

Smith, D.

J. Pendry, D. Schurig, and D. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Smith, D. R.

D. Schurig and D. R. Smith, New J. Phys. 7, 162 (2005).
[CrossRef]

Stacy, A.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

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

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Wang, Y.

L. Makley, X. Wong, Y. Wang, and G. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

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, Nature Mater. 6, 946 (2007).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Wong, X.

L. Makley, X. Wong, Y. Wang, and G. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef]

Wurtz, G.

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
[CrossRef]

Xiong, Y.

Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 93, 111116 (2008).
[CrossRef]

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

Yao, J.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Zayats, A.

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
[CrossRef]

Zhang, X.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 93, 111116 (2008).
[CrossRef]

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

Appl. Phys. Lett. (2)

Y. Xiong, Z. Liu, and X. Zhang, Appl. Phys. Lett. 93, 111116 (2008).
[CrossRef]

C. Reinhardt, S. Passinger, B. Chichkovet, W. Dickson, G. Wurtz, P. Evans, R. Pollard, and A. Zayats, Appl. Phys. Lett. 89, 231117 (2006).
[CrossRef]

IEEE Antennas Wireless Propag. Lett. (1)

K. G. Balmain, A. Luttgen, and P. Kremer, IEEE Antennas Wireless Propag. Lett. 1, 146 (2002).
[CrossRef]

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

Nature 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, Nature Mater. 6, 946 (2007).
[CrossRef]

New J. Phys. (1)

D. Schurig and D. R. Smith, New J. Phys. 7, 162 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (2)

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

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

Phys. Rev. Lett. (2)

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

L. Makley, X. Wong, Y. Wang, and G. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
[CrossRef]

Science (4)

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. Stacy, and X. Zhang, Science 321, 930 (2008).
[CrossRef] [PubMed]

R. Merlin, Science 317, 927 (2007).
[CrossRef] [PubMed]

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

J. Pendry, D. Schurig, and D. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

F. V. Bunkin, Sov. Phys. JETP 5, 277 (1957).

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (2)

E.Palik, ed., The Handbook of Optical Constants of Solids (Academic, 1997).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of hypergrating, 1D grating is shown. (b) Diffraction-limited propagation in Si, λ 0 = 15 μ m , d 1 = 200 nm , x 1 = 0 , ϵ z = ϵ x y = 16 . (c), (d) subdiffraction propagation in (c) nanowire and (d) nanolayer anisotropic metamaterials, (c) d 1 = 100 nm and (d) d 1 = 200 nm . Dashed lines show the direction of k x c ω 1 modes [Eq. (4)]. Panels (e)–(g) show spectra of the systems in (b)–(d), respectively.

Fig. 2
Fig. 2

Subdiffractional photonics in the bulk of (a) nanowire- and (b) nanolayer-metamaterials. Normalized field profile at several foci from (a) and (b) is shown in (c) and (d), respectively. Dashed and solid lines in (a),(b) correspond to the positions of profiles shown in (c),(d). Geometry parameters: (a),(c), slit thickness d 1 = d 2 = d 3 = d 4 = 100 nm , slit positions x 1 = 500 nm , x 2 = 300 nm , x 3 = 300 nm , x 4 = 500 nm . (b),(d), d 1 = d 2 = d 3 = d 4 = 200 nm , x 1 = 7 μ m , x 2 = 4 μ m , x 3 = 4 μ m , x 4 = 7 μ m .

Fig. 3
Fig. 3

Effect of losses on the resolution of hypergratings. Sizes and positions of the slits are given by Eq. (5). Panels (a), (b) correspond to low-loss (a) nanowire and (c) nanolayer structures ( ϵ is reduced 10 times with respect to values shown in this Letter). Panels (c), (d) show field profiles in focal planes of (solid curves) low-loss systems and (dashed curves) full-loss structures.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

H y ( x , z ) = S ( k x ) T ( k x , z ) e i k x x d k x ,
S ( k x ; x 1 , d 1 ) = 2 sin ( d 1 k x 2 ) k x e i k x x 1 ,
T ( k x , z ) = exp [ ± i ϵ x y ( ω 2 c 2 k x 2 ϵ z ) z ] .
tan θ = ϵ x y k x ϵ z ϵ x y ( ω 2 c 2 k x 2 ϵ z ) ϵ x y ϵ z ,
ϵ x y f 2 + ϵ z x m 2 ϵ x y f 2 + ϵ z x 0 2 = ± m π c ω ,
Δ z ϵ x y ϵ z ( ϵ x y ϵ x y + ϵ z ϵ z ) .

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