Abstract

The conventional approach for radiationless interference exploits the interference of evanescent components for the purpose of deep-subwavelength focusing and image formation. As a result, deep subwavelength feature size is achieved at the price of severe exponential decay of the field strength. We propose to overcome the limitation of the conventional approach by combining radiationless interference with evanescent field amplification as provided by the surface polaritons at the interface between positive- and negative-dielectric materials. Our approach removes the exponential decay and, moreover, allows a much wider range of wave vectors, including both propagating and evanescent field components, to participate in the image-formation process.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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  7. L. E. Helseth, Phys. Rev. A 78, 013819 (2008).
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  8. A. Grbic and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
    [CrossRef]
  9. A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
    [CrossRef] [PubMed]
  10. L. Markley, A. Wong, Y. Wang, and G. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
    [CrossRef] [PubMed]
  11. G. V. Eleftheriades and A. M. H. Wong, IEEE Microw. Wirel. Compon. Lett. 18, 236 (2008).
    [CrossRef]
  12. A. B. Evlyukhin and S. I. Bozhevolnyi, Opt. Express 16, 17429 (2008).
    [CrossRef] [PubMed]
  13. R. Gordon, Phys. Rev. Lett. 102, 207402 (2009).
    [CrossRef] [PubMed]
  14. M. F. Imani and A. Grbic, IEEE Antennas Wireless Propag. Lett. 8, 421 (2009).
    [CrossRef]
  15. V. Intaraprasonk and S. Fan, Opt. Lett. 34, 2967 (2009).
    [CrossRef] [PubMed]
  16. E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).
  17. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
    [CrossRef] [PubMed]
  18. J. T. Shen, P. B. Catrysse, and S. Fan, Phys. Rev. Lett. 94, 197401 (2005).
    [CrossRef] [PubMed]

2009 (3)

R. Gordon, Phys. Rev. Lett. 102, 207402 (2009).
[CrossRef] [PubMed]

M. F. Imani and A. Grbic, IEEE Antennas Wireless Propag. Lett. 8, 421 (2009).
[CrossRef]

V. Intaraprasonk and S. Fan, Opt. Lett. 34, 2967 (2009).
[CrossRef] [PubMed]

2008 (8)

M. G. Silveirinha, C. A. Fernandes, and J. R. Costa, Phys. Rev. B 78, 195121 (2008).
[CrossRef]

L. E. Helseth, Opt. Commun. 281, 1981 (2008).
[CrossRef]

L. E. Helseth, Phys. Rev. A 78, 013819 (2008).
[CrossRef]

A. Grbic and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
[CrossRef]

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

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

G. V. Eleftheriades and A. M. H. Wong, IEEE Microw. Wirel. Compon. Lett. 18, 236 (2008).
[CrossRef]

A. B. Evlyukhin and S. I. Bozhevolnyi, Opt. Express 16, 17429 (2008).
[CrossRef] [PubMed]

2007 (1)

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

2005 (2)

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

J. T. Shen, P. B. Catrysse, and S. Fan, Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

2004 (2)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef] [PubMed]

D. Melville, R. Blaikie, and C. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

2000 (1)

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

Blaikie, R.

D. Melville, R. Blaikie, and C. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

Bozhevolnyi, S. I.

Catrysse, P. B.

J. T. Shen, P. B. Catrysse, and S. Fan, Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

Costa, J. R.

M. G. Silveirinha, C. A. Fernandes, and J. R. Costa, Phys. Rev. B 78, 195121 (2008).
[CrossRef]

Eleftheriades, G.

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

Eleftheriades, G. V.

G. V. Eleftheriades and A. M. H. Wong, IEEE Microw. Wirel. Compon. Lett. 18, 236 (2008).
[CrossRef]

Evlyukhin, A. B.

Fan, S.

V. Intaraprasonk and S. Fan, Opt. Lett. 34, 2967 (2009).
[CrossRef] [PubMed]

J. T. Shen, P. B. Catrysse, and S. Fan, Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

Fernandes, C. A.

M. G. Silveirinha, C. A. Fernandes, and J. R. Costa, Phys. Rev. B 78, 195121 (2008).
[CrossRef]

Garcia-Vidal, F. J.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef] [PubMed]

Gordon, R.

R. Gordon, Phys. Rev. Lett. 102, 207402 (2009).
[CrossRef] [PubMed]

Grbic, A.

M. F. Imani and A. Grbic, IEEE Antennas Wireless Propag. Lett. 8, 421 (2009).
[CrossRef]

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

A. Grbic and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
[CrossRef]

Helseth, L. E.

L. E. Helseth, Opt. Commun. 281, 1981 (2008).
[CrossRef]

L. E. Helseth, Phys. Rev. A 78, 013819 (2008).
[CrossRef]

Imani, M. F.

M. F. Imani and A. Grbic, IEEE Antennas Wireless Propag. Lett. 8, 421 (2009).
[CrossRef]

Intaraprasonk, V.

Jiang, L.

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

Markley, L.

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

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef] [PubMed]

Melville, D.

D. Melville, R. Blaikie, and C. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

Merlin, R.

A. Grbic and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
[CrossRef]

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

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

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef] [PubMed]

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

Shen, J. T.

J. T. Shen, P. B. Catrysse, and S. Fan, Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

Silveirinha, M. G.

M. G. Silveirinha, C. A. Fernandes, and J. R. Costa, Phys. Rev. B 78, 195121 (2008).
[CrossRef]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

Wang, Y.

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

Wolf, C.

D. Melville, R. Blaikie, and C. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

Wong, A.

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

Wong, A. M. H.

G. V. Eleftheriades and A. M. H. Wong, IEEE Microw. Wirel. Compon. Lett. 18, 236 (2008).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

D. Melville, R. Blaikie, and C. Wolf, Appl. Phys. Lett. 84, 4403 (2004).
[CrossRef]

IEEE Antennas Wireless Propag. Lett. (1)

M. F. Imani and A. Grbic, IEEE Antennas Wireless Propag. Lett. 8, 421 (2009).
[CrossRef]

IEEE Microw. Wirel. Compon. Lett. (1)

G. V. Eleftheriades and A. M. H. Wong, IEEE Microw. Wirel. Compon. Lett. 18, 236 (2008).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

A. Grbic and R. Merlin, IEEE Trans. Antennas Propag. 56, 3159 (2008).
[CrossRef]

Opt. Commun. (1)

L. E. Helseth, Opt. Commun. 281, 1981 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

L. E. Helseth, Phys. Rev. A 78, 013819 (2008).
[CrossRef]

Phys. Rev. B (1)

M. G. Silveirinha, C. A. Fernandes, and J. R. Costa, Phys. Rev. B 78, 195121 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

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

R. Gordon, Phys. Rev. Lett. 102, 207402 (2009).
[CrossRef] [PubMed]

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

J. T. Shen, P. B. Catrysse, and S. Fan, Phys. Rev. Lett. 94, 197401 (2005).
[CrossRef] [PubMed]

Science (4)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

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

A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
[CrossRef] [PubMed]

Other (1)

E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

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Figures (3)

Fig. 1
Fig. 1

(a) Subwavelength focusing using initial field distribution following [5], d = λ 15 , FWHM = λ 18 . Following [5] the plot is generated such that each z plane has maximum amplitude of 1. (b) Same as (a) but in linear scale. The peak amplitude actually decays significantly (to 7.8% at focal point). (c) Schematic for the focusing with evanescent amplification. (d) Result of (c) in linear scale. The negative-permittivity material is SiC at λ = 10.56 μ m with ϵ m = 1.035 + 0.13 i . We achieve the same values of d and FWHM as (a) and (b) but get an amplitude gain of 3.

Fig. 2
Fig. 2

(a) Dispersion curve of k SP at the interface between SiC and air. The black (blue)/gray (red) curves are calculated with or without the material loss, respectively. The dashed–dotted line shows the surface polariton frequency ω SP , where real part of ϵ m = 1 . The solid straight line shows the operating frequency used throughout the paper: ω = 1.785 × 10 14 rad s , λ = 10.56 μ m , ϵ m = 1.035 + 0.13 i . (b) Absolute value of the amplitude transfer function with (solid curve) or without (dashed curve) the SiC. The SiC is assumed lossless with ϵ m = 1.035 , d = λ 15 . (c) Same as (b) but with material loss, ϵ m = 1.035 + 0.13 i .

Fig. 3
Fig. 3

The green (dashed–dotted), blue (dashed), and red (solid) curves are the amplitude transfer function, the incident field amplitude spectrum, and the field amplitude spectrum at the focal point, respectively. (a) With evanescent amplification. (b) Without evanescent amplification.

Equations (9)

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( 2 y 2 + 2 z 2 + k d 2 ) F = 0 ,
F ( k y , z ) = F ( k y , z = 0 ) T f ( k y , z ) ,
T f ( k y , z ) = exp ( i k z , d ( k y ) z ) .
T f ( k y , z ) exp ( k y z ) .
F t ( k y , d ) = F i ( k y , 0 ) T ( k y ) ,
T ( k y ) = ( 1 + r ( k y ) ) exp ( i k z , d d ) .
r ( k y ) = ( k z , d ϵ d k z , m ϵ m ) ( k z , d ϵ d + k z , m ϵ m )
k y = k SP ( ω c ) ϵ m ϵ d ϵ m + ϵ d ,
F i ( k y , 0 ) = { 1 T ( k y ) , q m < k y < q m 0 , otherwise } ,

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