Abstract

We propose a multilayered superlens comprising alternately layered metal and dielectric films with layers of nonequal thickness to realize subwavelength imaging, even when permittivities of the metal and dielectric are mismatched. Based on ideal imaging conditions, the exact constraint relations about the thickness of each dielectric layer and the permittivity of the surrounding medium of the multilayered superlens are first acquired when the superlens is modeled by the effective medium theory. Theoretical analysis and numerical simulations indicate that a multilayered superlens with constraint relations can realize subwavelength imaging at wavelengths of 335 to 385nm.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  2. K. Lee, Y. Jung, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
    [CrossRef]
  3. S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
    [CrossRef]
  4. J. B. Pendry and S. A. Ramakrishna, “Refining the perfect lens,” Phys. B 338, 329–332 (2003).
    [CrossRef]
  5. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430(2003).
  6. P. F. Cao, X. P. Zhang, L. Cheng, and Q. Q. Meng, “Far field imaging research based on multilayer positive- and negative-refractive-index media under off-axis illumination,” PIER 98, 283–298 (2009).
    [CrossRef]
  7. C. P. Moore, M. D. Arnold, P. J. Bones, and R. J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlenses,” J. Opt. Soc. Am. A 25, 911–918 (2008).
    [CrossRef]
  8. C. P. Moore, R. J. Blaikie, and M. D. Arnold, “Improved analytical models for single- and multi-layer silver superlenses,” Proc. MRS 1182, 1182-EE11-02 (2009).
    [CrossRef]
  9. C. T. Wang, Y. H. Zhao, D. C. Gan, C. L. Du, and X. G. Luo, “Subwavelength imaging with anistropic structure comprising alternately layered metal and dielectric films,” Opt. Express 16, 4217–4227 (2008).
    [CrossRef] [PubMed]
  10. D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
    [CrossRef]
  11. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal–dielectric system,” Phys. Rev. B 74, 115116 (2006).
    [CrossRef]
  12. K. Lee, Y. Jung, and K. Kim, “Near-field phase correction for superresolution enhancement,” Phys. Rev. B 80, 033109(2009).
    [CrossRef]
  13. D. O. S. Melville, “Planar lensing lithography: enhancing the optical near field,” Ph.D. thesis (University of Canterbury, 2006).
  14. M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.
  15. H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Design, fabrication and characterization of a far-field superlens,” Solid State Commun. 146, 202–207 (2008).
    [CrossRef]
  16. Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67, 193106 (2003).
    [CrossRef]

2009

K. Lee, Y. Jung, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

P. F. Cao, X. P. Zhang, L. Cheng, and Q. Q. Meng, “Far field imaging research based on multilayer positive- and negative-refractive-index media under off-axis illumination,” PIER 98, 283–298 (2009).
[CrossRef]

K. Lee, Y. Jung, and K. Kim, “Near-field phase correction for superresolution enhancement,” Phys. Rev. B 80, 033109(2009).
[CrossRef]

C. P. Moore, R. J. Blaikie, and M. D. Arnold, “Improved analytical models for single- and multi-layer silver superlenses,” Proc. MRS 1182, 1182-EE11-02 (2009).
[CrossRef]

2008

2006

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal–dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

2003

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

J. B. Pendry and S. A. Ramakrishna, “Refining the perfect lens,” Phys. B 338, 329–332 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430(2003).

Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67, 193106 (2003).
[CrossRef]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

1982

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Arnold, M. D.

C. P. Moore, R. J. Blaikie, and M. D. Arnold, “Improved analytical models for single- and multi-layer silver superlenses,” Proc. MRS 1182, 1182-EE11-02 (2009).
[CrossRef]

C. P. Moore, M. D. Arnold, P. J. Bones, and R. J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlenses,” J. Opt. Soc. Am. A 25, 911–918 (2008).
[CrossRef]

Aspnes, D. E.

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Blaikie, R. J.

C. P. Moore, R. J. Blaikie, and M. D. Arnold, “Improved analytical models for single- and multi-layer silver superlenses,” Proc. MRS 1182, 1182-EE11-02 (2009).
[CrossRef]

C. P. Moore, M. D. Arnold, P. J. Bones, and R. J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlenses,” J. Opt. Soc. Am. A 25, 911–918 (2008).
[CrossRef]

Bones, P. J.

Cao, P. F.

P. F. Cao, X. P. Zhang, L. Cheng, and Q. Q. Meng, “Far field imaging research based on multilayer positive- and negative-refractive-index media under off-axis illumination,” PIER 98, 283–298 (2009).
[CrossRef]

Cheng, L.

P. F. Cao, X. P. Zhang, L. Cheng, and Q. Q. Meng, “Far field imaging research based on multilayer positive- and negative-refractive-index media under off-axis illumination,” PIER 98, 283–298 (2009).
[CrossRef]

Chettiar, U. K.

M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.

Drachev, V. P.

M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.

Du, C. L.

Gan, D. C.

Jung, Y.

K. Lee, Y. Jung, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

K. Lee, Y. Jung, and K. Kim, “Near-field phase correction for superresolution enhancement,” Phys. Rev. B 80, 033109(2009).
[CrossRef]

Kildishev, A. V.

M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.

Kim, K.

K. Lee, Y. Jung, and K. Kim, “Near-field phase correction for superresolution enhancement,” Phys. Rev. B 80, 033109(2009).
[CrossRef]

K. Lee, Y. Jung, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

Lee, H.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Design, fabrication and characterization of a far-field superlens,” Solid State Commun. 146, 202–207 (2008).
[CrossRef]

Lee, K.

K. Lee, Y. Jung, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

K. Lee, Y. Jung, and K. Kim, “Near-field phase correction for superresolution enhancement,” Phys. Rev. B 80, 033109(2009).
[CrossRef]

Liu, Z.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Design, fabrication and characterization of a far-field superlens,” Solid State Commun. 146, 202–207 (2008).
[CrossRef]

Liu, Z. T.

M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.

Luo, X. G.

Melville, D. O. S.

D. O. S. Melville, “Planar lensing lithography: enhancing the optical near field,” Ph.D. thesis (University of Canterbury, 2006).

Meng, Q. Q.

P. F. Cao, X. P. Zhang, L. Cheng, and Q. Q. Meng, “Far field imaging research based on multilayer positive- and negative-refractive-index media under off-axis illumination,” PIER 98, 283–298 (2009).
[CrossRef]

Moore, C. P.

C. P. Moore, R. J. Blaikie, and M. D. Arnold, “Improved analytical models for single- and multi-layer silver superlenses,” Proc. MRS 1182, 1182-EE11-02 (2009).
[CrossRef]

C. P. Moore, M. D. Arnold, P. J. Bones, and R. J. Blaikie, “Image fidelity for single-layer and multi-layer silver superlenses,” J. Opt. Soc. Am. A 25, 911–918 (2008).
[CrossRef]

Nyga, P.

M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.

Pack, M. V.

M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.

Park, H.

K. Lee, Y. Jung, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

Pendry, J. B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal–dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

J. B. Pendry and S. A. Ramakrishna, “Refining the perfect lens,” Phys. B 338, 329–332 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430(2003).

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Ramakrishna, S. A.

J. B. Pendry and S. A. Ramakrishna, “Refining the perfect lens,” Phys. B 338, 329–332 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430(2003).

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

Shalaev, V. M.

M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.

Stewart, W. J.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430(2003).

Sun, C.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Design, fabrication and characterization of a far-field superlens,” Solid State Commun. 146, 202–207 (2008).
[CrossRef]

Thoreson, M. D.

M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal–dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Wang, C. T.

Wiltshire, M. C. K.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430(2003).

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal–dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

Xiong, Y.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Design, fabrication and characterization of a far-field superlens,” Solid State Commun. 146, 202–207 (2008).
[CrossRef]

Ye, Z.

Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67, 193106 (2003).
[CrossRef]

Zhang, X.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Design, fabrication and characterization of a far-field superlens,” Solid State Commun. 146, 202–207 (2008).
[CrossRef]

Zhang, X. P.

P. F. Cao, X. P. Zhang, L. Cheng, and Q. Q. Meng, “Far field imaging research based on multilayer positive- and negative-refractive-index media under off-axis illumination,” PIER 98, 283–298 (2009).
[CrossRef]

Zhao, Y. H.

Am. J. Phys.

D. E. Aspnes, “Local-field effects and effective-medium theory: a microscopic perspective,” Am. J. Phys. 50, 704–709 (1982).
[CrossRef]

Appl. Phys. Lett.

K. Lee, Y. Jung, H. Park, and K. Kim, “Active phase control of a Ag near-field superlens via the index mismatch approach,” Appl. Phys. Lett. 94, 101113 (2009).
[CrossRef]

J. Mod. Opt.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419–1430(2003).

J. Opt. Soc. Am. A

Opt. Express

Phys. B

J. B. Pendry and S. A. Ramakrishna, “Refining the perfect lens,” Phys. B 338, 329–332 (2003).
[CrossRef]

Phys. Rev. B

S. A. Ramakrishna and J. B. Pendry, “Removal of absorption and increase in resolution in a near-field lens via optical gain,” Phys. Rev. B 67, 201101 (2003).
[CrossRef]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal–dielectric system,” Phys. Rev. B 74, 115116 (2006).
[CrossRef]

K. Lee, Y. Jung, and K. Kim, “Near-field phase correction for superresolution enhancement,” Phys. Rev. B 80, 033109(2009).
[CrossRef]

Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67, 193106 (2003).
[CrossRef]

Phys. Rev. Lett.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

PIER

P. F. Cao, X. P. Zhang, L. Cheng, and Q. Q. Meng, “Far field imaging research based on multilayer positive- and negative-refractive-index media under off-axis illumination,” PIER 98, 283–298 (2009).
[CrossRef]

Proc. MRS

C. P. Moore, R. J. Blaikie, and M. D. Arnold, “Improved analytical models for single- and multi-layer silver superlenses,” Proc. MRS 1182, 1182-EE11-02 (2009).
[CrossRef]

Solid State Commun.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Design, fabrication and characterization of a far-field superlens,” Solid State Commun. 146, 202–207 (2008).
[CrossRef]

Other

D. O. S. Melville, “Planar lensing lithography: enhancing the optical near field,” Ph.D. thesis (University of Canterbury, 2006).

M. D. Thoreson, Z. T. Liu, U. K. Chettiar, P. Nyga, A. V. Kildishev, V. P. Drachev, M. V. Pack, and V. M. Shalaev, “Studies on metal-dielectric plasmonic structures,” Sandia report, SAND2009-7034, Sandia National Laboratories, Albuquerque, N. Mex., 2009.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Multilayered superlens imaging system.

Fig. 2
Fig. 2

MTF and PTF curves for various ε and η corresponding to wavelengths of (a), (b) 335, (c), (d) 360, and (e), (f)  385 nm . The dashed–dotted curves denote the MTF and PTF when the superlens has the same thickness of individual layers with 5 nm and the surrounding is air, the dashed curves denote the MTF and PTF when the thickness of each dielectric layer is calculated by Eq. (11) while the surrounding is air, and the solid curves denote the MTF and PTF when the thickness of each dielectric layer is calculated by Eq. (11) in the surrounding calculated by Eq. (12), respectively.

Fig. 3
Fig. 3

Lateral intensity distributions for various ε and η corresponding to wavelengths of (a) 335, (b) 360, and (c)  385 nm when d obj = 20 nm and d p - p = 80 nm .

Fig. 4
Fig. 4

Lateral intensity distributions obtained by EMT and TMM before and after applying the constraint relation expressed by Eq. (11) in the air surrounding with ε = 1 . The wavelengths correspond to (a) 335, (b) 360, and (c)  385 nm . d obj = 20 nm and d p - p = 80 nm . The curves with EMT are intensity distributions obtained by EMT, while those with TMM are intensity distributions obtained by TMM.

Fig. 5
Fig. 5

Lateral intensity distributions obtained by EMT and TMM before and after applying the constraint relation expressed by Eq. (11) in the surrounding with ε 2 = ε 1 2 + ε 1 2 . The wavelengths correspond to (a) 335, (b) 360, and (c)  385 nm . d obj = 20 nm and d p - p = 80 nm . The curves with EMT are the intensity distributions obtained by EMT, while those with TMM are intensity distributions obtained by TMM.

Equations (16)

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

ε x = ε 1 + η ε 2 1 + η ,
ε z 1 = ε 1 1 + η ε 2 1 1 + η ,
η = d 2 / d 1 .
OTF ( k x ) = 2 2 cos ( k z D ) i ( k z ε k z ε x + k z ε x k z ε ) sin ( k z D ) ,
k x 2 ε z + k z 2 ε x = k 0 2 = ( ω c ) 2 .
OTF ( k x ) = MTF ( k x ) exp [ i PTF ( k x ) ] .
MTF ( k x ) = 1 , PTF ( k x ) = 0.
OTF ( k x ) 2 2 ε k 0 2 k x D + P k x ,
| P | 2 = ( ε 1 ε 2 + ε ε 2 1 ) 2 d 2 2 + ε 1 2 ( ε 1 + ε ε 1 2 + ε 1 2 ) 2 d 1 2 + 2 ε 1 ( ε 1 + ε ε 1 2 + ε 1 2 ) ( ε 1 ε 2 + ε ε 2 1 ) d 1 d 2 + ε 1 2 ( ε 1 ε ε 1 2 + ε 1 2 ) 2 d 1 2 .
( ε 1 ε 2 + ε ε 2 1 ) d 2 + ε 1 ( ε 1 + ε ε 1 2 + ε 1 2 ) d 1 = 0.
η = d 2 d 1 = ε 1 ( ε 1 + ε ε 1 2 + ε 1 2 ) ( ε 1 ε 2 + ε ε 2 1 ) .
ε 2 = ε 1 2 + ε 1 2 .
MTF ( k x ) 2 2 ε k 0 2 k x D + P k x = 2 2 ε k 0 2 k x D ,
PTF ( k x ) arctan ε 1 ( 1 ε ε ε 1 2 + ε 1 2 ) d 1 2 ε k 0 2 k x D + ( ε 2 ε + ε ε 2 ) d 2 + ε 1 ( 1 ε + ε ε 1 2 + ε 1 2 ) d 1 = 0.
H obj ( k x ) = 2 d obj Sa ( k x d obj 2 ) cos ( k x d p - p 2 ) ,
H img ( x ) = 1 2 π + H obj ( k x ) OTF ( k x ) exp ( i k x x ) d k x .

Metrics