Abstract

Perfect lensing using negative refractive index materials and radiationless electromagnetic interference both provides extreme subwavelength focusing by “amplifying” evanescent wave components that are usually lost. This Letter provides a relation between the achievable focus spot size, the amplification available, and the focal length. This may be considered as a revised version of Abbe’s diffraction limit for focusing systems that have evanescent wave amplification. It is useful in comparing the amplification achieved in various subwavelength focusing implementations as well as determining when it is better to use existing near-field techniques, such as simple diffraction from an aperture or slit, than to attempt complicated superfocusing.

© 2012 Optical Society of America

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References

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  1. E. Abbe, Archiv Mikr. Anat. 9, 413 (1873).
    [CrossRef]
  2. E. Abbe, in Vol. 1 of Proceedings of the Bristol Naturalists’ Society (Williams and Norgate, 1874), pp. 200, translated by H. E. Fripp.
  3. H. Helmholtz, Mon. Microscop. J. 16, 15 (1876).
  4. L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006), Chap. 4.2.
  5. A. Lipson, S. G. Lipson, and H. Lipson, Optical Physics, 4th ed. (Cambridge University, 2011), Chap. 12.6.
  6. M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
    [CrossRef]
  7. W. Denk, J. Strickler, and W. Webb, Science 248, 73(1990).
    [CrossRef]
  8. S. W. Hell and J. Wichmann, Opt. Lett. 19, 780 (1994).
    [CrossRef]
  9. A. Lewis, M. Isaacson, A. Harootunian, and A. Murray, Ultramicroscopy 13, 227 (1984).
    [CrossRef]
  10. D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
    [CrossRef]
  11. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef]
  12. R. Merlin, Science 317, 927 (2007).
    [CrossRef]
  13. C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. (Wiley, 2004).
  14. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  15. A. Grbic, L. Jiang, and R. Merlin, Science 320, 511 (2008).
    [CrossRef]
  16. L. Markley, A. M. H. Wong, Y. Wang, and G. V. Eleftheriades, Phys. Rev. Lett. 101, 113901 (2008).
    [CrossRef]

2008

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

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

2007

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

2006

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

2000

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

1994

1990

W. Denk, J. Strickler, and W. Webb, Science 248, 73(1990).
[CrossRef]

1984

A. Lewis, M. Isaacson, A. Harootunian, and A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1876

H. Helmholtz, Mon. Microscop. J. 16, 15 (1876).

1873

E. Abbe, Archiv Mikr. Anat. 9, 413 (1873).
[CrossRef]

Abbe, E.

E. Abbe, Archiv Mikr. Anat. 9, 413 (1873).
[CrossRef]

E. Abbe, in Vol. 1 of Proceedings of the Bristol Naturalists’ Society (Williams and Norgate, 1874), pp. 200, translated by H. E. Fripp.

Balanis, C. A.

C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. (Wiley, 2004).

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Denk, W.

W. Denk, J. Strickler, and W. Webb, Science 248, 73(1990).
[CrossRef]

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

Eleftheriades, G. V.

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

Grbic, A.

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

Harootunian, A.

A. Lewis, M. Isaacson, A. Harootunian, and A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006), Chap. 4.2.

Hell, S. W.

Helmholtz, H.

H. Helmholtz, Mon. Microscop. J. 16, 15 (1876).

Isaacson, M.

A. Lewis, M. Isaacson, A. Harootunian, and A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

Jiang, L.

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

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Lanz, M.

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

Lewis, A.

A. Lewis, M. Isaacson, A. Harootunian, and A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

Lipson, A.

A. Lipson, S. G. Lipson, and H. Lipson, Optical Physics, 4th ed. (Cambridge University, 2011), Chap. 12.6.

Lipson, H.

A. Lipson, S. G. Lipson, and H. Lipson, Optical Physics, 4th ed. (Cambridge University, 2011), Chap. 12.6.

Lipson, S. G.

A. Lipson, S. G. Lipson, and H. Lipson, Optical Physics, 4th ed. (Cambridge University, 2011), Chap. 12.6.

Markley, L.

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

Merlin, R.

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

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

Murray, A.

A. Lewis, M. Isaacson, A. Harootunian, and A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006), Chap. 4.2.

Pendry, J. B.

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

Pohl, D. W.

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

Strickler, J.

W. Denk, J. Strickler, and W. Webb, Science 248, 73(1990).
[CrossRef]

Wang, Y.

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

Webb, W.

W. Denk, J. Strickler, and W. Webb, Science 248, 73(1990).
[CrossRef]

Wichmann, J.

Wong, A. M. H.

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

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

Appl. Phys. Lett.

D. W. Pohl, W. Denk, and M. Lanz, Appl. Phys. Lett. 44, 651 (1984).
[CrossRef]

Archiv Mikr. Anat.

E. Abbe, Archiv Mikr. Anat. 9, 413 (1873).
[CrossRef]

Mon. Microscop. J.

H. Helmholtz, Mon. Microscop. J. 16, 15 (1876).

Nat. Methods

M. J. Rust, M. Bates, and X. Zhuang, Nat. Methods 3, 793 (2006).
[CrossRef]

Opt. Lett.

Phys. Rev. B

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Phys. Rev. Lett.

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

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

Science

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

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

W. Denk, J. Strickler, and W. Webb, Science 248, 73(1990).
[CrossRef]

Ultramicroscopy

A. Lewis, M. Isaacson, A. Harootunian, and A. Murray, Ultramicroscopy 13, 227 (1984).
[CrossRef]

Other

C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. (Wiley, 2004).

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2006), Chap. 4.2.

A. Lipson, S. G. Lipson, and H. Lipson, Optical Physics, 4th ed. (Cambridge University, 2011), Chap. 12.6.

E. Abbe, in Vol. 1 of Proceedings of the Bristol Naturalists’ Society (Williams and Norgate, 1874), pp. 200, translated by H. E. Fripp.

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Figures (1)

Fig. 1.
Fig. 1.

Comparison of a subwavelength focus achieved using a 40 nm metal slab of varying permittivity (particularly ϵ), excited with a magnetic line source 20 nm away and imaging at the focal plane 20 nm away from the other side of the slab. For comparison, the free-space (ϵ=1) diffraction of the line source at a distance of 20 nm and 80 nm are shown.

Equations (15)

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

d=λ2NA,
G(kx)=exp(ikz(kx)z),
kx=(lnG(kx)z)2+k02.
kxd=π,
d=π(lnG(kx)z)2+k02.
dλ/2,
g=lnG(kx)πz/d.
G(kx)=exp(ikz(kx)zkx22σk2),
gmax=lnGmax=z2σk22k022σk2.
σkσx=1,
gmax=z22d2k02d22,
g=π/2
G(kx)exp(ikzz)=4ϵ(ϵ+1)2exp(2ikzz)(ϵ1)2.
G(kx)exp(ikz(kx)z)1(ϵ/2)2exp(2kxz)+1.
g=ln(2/ϵ).

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