Abstract

We discuss the properties of the transmission function in the k-space for a generic multi-layered structure. In particular we analytically demonstrate that a transmission greater than one in the evanescent spectrum (amplification of the evanescent modes) can be directly linked to the guided modes supported by the structure. Moreover we show that the slope of the phase of the transmission function in the propagating spectrum is inversely proportional to the ability of the structure to compensate the diffraction of the propagating modes. We apply these findings to discuss several examples where super-resolution is achieved thanks to the simultaneous availability of the amplification of the evanescent modes and the diffraction compensation of the propagating modes.

© 2009 OSA

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References

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  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  2. R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84(8), 1290 (2004).
    [CrossRef]
  3. 3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
    [CrossRef] [PubMed]
  4. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, “Imaging the near field,” J. Mod. Opt. 50, 1419 (2003).
  5. M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high trasparency in the visible range,” Appl. Phys. Lett. 90(17), 174113 (2007).
    [CrossRef]
  6. M. Bloemer, G. D’Aguanno, M. Scalora, N. Mattiucci, and D. de Ceglia, “Energy considertions for a superlens based on metal/dielectric multilayers,” Opt. Express 16, 19342–19353 (2008).
    [CrossRef]
  7. G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Influence of losses on the super-resolution performances of an impedance matched negative index material,” J. Opt. Soc. Am. B 25(2), 236 (2008).
    [CrossRef]
  8. L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).
  9. J. Lekner, Theory of reflection, Martin Nijhoff Publishers Dordrecht (1987).
  10. S. A. Shakir and A. F. Turner, “Method of Poles for Multilayer Thin-Film Waveguides,” Appl. Phys., A Mater. Sci. Process. 29(3), 151–155 (1982).
    [CrossRef]
  11. E. S. C. Ching, P. T. Leung, A Maassen van den Brink, W. M Suen, S. S Tong, and K Young, “Quasi-normal modes expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545 (1998).
    [CrossRef]
  12. M. Tsang and D. Psaltis, “Reflectionless evanescent-wave amplification by two dielectric planar waveguides,” Opt. Lett. 31(18), 2741–2743 (2006).
    [CrossRef] [PubMed]
  13. D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
    [CrossRef]
  14. P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105–1-4 (2005).
    [CrossRef]
  15. G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77(4), 043825 (2008).
    [CrossRef]
  16. E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press Inc., New York, 1991).
  17. Y. S. Kivshar, and G. P. Agrawal, Optical Solitons, (Academic Press, San Diego 2003).
  18. P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73(11), 113110 (2006).
    [CrossRef]
  19. P. Yeh, Optical Waves in Layered Media, (Wiley, New York, 1988).

2008 (4)

M. Bloemer, G. D’Aguanno, M. Scalora, N. Mattiucci, and D. de Ceglia, “Energy considertions for a superlens based on metal/dielectric multilayers,” Opt. Express 16, 19342–19353 (2008).
[CrossRef]

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Influence of losses on the super-resolution performances of an impedance matched negative index material,” J. Opt. Soc. Am. B 25(2), 236 (2008).
[CrossRef]

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77(4), 043825 (2008).
[CrossRef]

2007 (1)

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high trasparency in the visible range,” Appl. Phys. Lett. 90(17), 174113 (2007).
[CrossRef]

2006 (2)

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73(11), 113110 (2006).
[CrossRef]

M. Tsang and D. Psaltis, “Reflectionless evanescent-wave amplification by two dielectric planar waveguides,” Opt. Lett. 31(18), 2741–2743 (2006).
[CrossRef] [PubMed]

2005 (2)

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105–1-4 (2005).
[CrossRef]

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

2004 (1)

R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84(8), 1290 (2004).
[CrossRef]

2003 (1)

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

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1998 (1)

E. S. C. Ching, P. T. Leung, A Maassen van den Brink, W. M Suen, S. S Tong, and K Young, “Quasi-normal modes expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545 (1998).
[CrossRef]

1982 (1)

S. A. Shakir and A. F. Turner, “Method of Poles for Multilayer Thin-Film Waveguides,” Appl. Phys., A Mater. Sci. Process. 29(3), 151–155 (1982).
[CrossRef]

Akozbek, N.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high trasparency in the visible range,” Appl. Phys. Lett. 90(17), 174113 (2007).
[CrossRef]

Belov, P. A.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73(11), 113110 (2006).
[CrossRef]

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105–1-4 (2005).
[CrossRef]

Blaikie, R. J.

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

Bloemer, M.

G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77(4), 043825 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, M. Scalora, N. Mattiucci, and D. de Ceglia, “Energy considertions for a superlens based on metal/dielectric multilayers,” Opt. Express 16, 19342–19353 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high trasparency in the visible range,” Appl. Phys. Lett. 90(17), 174113 (2007).
[CrossRef]

Bloemer, M. J.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Influence of losses on the super-resolution performances of an impedance matched negative index material,” J. Opt. Soc. Am. B 25(2), 236 (2008).
[CrossRef]

Cappeddu, M. G.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Centini, M.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Ching, E. S. C.

E. S. C. Ching, P. T. Leung, A Maassen van den Brink, W. M Suen, S. S Tong, and K Young, “Quasi-normal modes expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545 (1998).
[CrossRef]

D’Aguanno, G.

M. Bloemer, G. D’Aguanno, M. Scalora, N. Mattiucci, and D. de Ceglia, “Energy considertions for a superlens based on metal/dielectric multilayers,” Opt. Express 16, 19342–19353 (2008).
[CrossRef]

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Influence of losses on the super-resolution performances of an impedance matched negative index material,” J. Opt. Soc. Am. B 25(2), 236 (2008).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77(4), 043825 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high trasparency in the visible range,” Appl. Phys. Lett. 90(17), 174113 (2007).
[CrossRef]

de Ceglia, D.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, M. Scalora, N. Mattiucci, and D. de Ceglia, “Energy considertions for a superlens based on metal/dielectric multilayers,” Opt. Express 16, 19342–19353 (2008).
[CrossRef]

Desyatnikov, A.

G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77(4), 043825 (2008).
[CrossRef]

D'Orazio, A.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Fang, N.

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

Hao, Y.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73(11), 113110 (2006).
[CrossRef]

Haus, J. W.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

Ikonen, P.

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105–1-4 (2005).
[CrossRef]

Lee, H.

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

Leung, P. T.

E. S. C. Ching, P. T. Leung, A Maassen van den Brink, W. M Suen, S. S Tong, and K Young, “Quasi-normal modes expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545 (1998).
[CrossRef]

Maassen van den Brink, A

E. S. C. Ching, P. T. Leung, A Maassen van den Brink, W. M Suen, S. S Tong, and K Young, “Quasi-normal modes expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545 (1998).
[CrossRef]

Mattiucci, N.

G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Influence of losses on the super-resolution performances of an impedance matched negative index material,” J. Opt. Soc. Am. B 25(2), 236 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, M. Scalora, N. Mattiucci, and D. de Ceglia, “Energy considertions for a superlens based on metal/dielectric multilayers,” Opt. Express 16, 19342–19353 (2008).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77(4), 043825 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high trasparency in the visible range,” Appl. Phys. Lett. 90(17), 174113 (2007).
[CrossRef]

Melville, D. O. S.

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

Merlin, R.

R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84(8), 1290 (2004).
[CrossRef]

Pendry, J. B.

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

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Psaltis, D.

Ramakrishna, S. A.

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

Scalora, M.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, M. Scalora, N. Mattiucci, and D. de Ceglia, “Energy considertions for a superlens based on metal/dielectric multilayers,” Opt. Express 16, 19342–19353 (2008).
[CrossRef]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high trasparency in the visible range,” Appl. Phys. Lett. 90(17), 174113 (2007).
[CrossRef]

Shakir, S. A.

S. A. Shakir and A. F. Turner, “Method of Poles for Multilayer Thin-Film Waveguides,” Appl. Phys., A Mater. Sci. Process. 29(3), 151–155 (1982).
[CrossRef]

Simovski, C. R.

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105–1-4 (2005).
[CrossRef]

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 (2003).

Suen, W. M

E. S. C. Ching, P. T. Leung, A Maassen van den Brink, W. M Suen, S. S Tong, and K Young, “Quasi-normal modes expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545 (1998).
[CrossRef]

Sun, C.

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

Tong, S. S

E. S. C. Ching, P. T. Leung, A Maassen van den Brink, W. M Suen, S. S Tong, and K Young, “Quasi-normal modes expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545 (1998).
[CrossRef]

Tsang, M.

Turner, A. F.

S. A. Shakir and A. F. Turner, “Method of Poles for Multilayer Thin-Film Waveguides,” Appl. Phys., A Mater. Sci. Process. 29(3), 151–155 (1982).
[CrossRef]

Vincenti, M. A.

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

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 (2003).

Wolf, C. R.

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

Young, K

E. S. C. Ching, P. T. Leung, A Maassen van den Brink, W. M Suen, S. S Tong, and K Young, “Quasi-normal modes expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545 (1998).
[CrossRef]

Zhang, X.

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

R. Merlin, “Analytical solution of the almost-perfect-lens problem,” Appl. Phys. Lett. 84(8), 1290 (2004).
[CrossRef]

M. Bloemer, G. D’Aguanno, N. Mattiucci, M. Scalora, and N. Akozbek, “Broadband super-resolving lens with high trasparency in the visible range,” Appl. Phys. Lett. 90(17), 174113 (2007).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (1)

S. A. Shakir and A. F. Turner, “Method of Poles for Multilayer Thin-Film Waveguides,” Appl. Phys., A Mater. Sci. Process. 29(3), 151–155 (1982).
[CrossRef]

J. Mod. Opt. (1)

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

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (2)

D. de Ceglia, M. A. Vincenti, M. G. Cappeddu, M. Centini, N. Akozbek, A. D'Orazio, J. W. Haus, M. J. Bloemer, and M. Scalora, “Tailoring metallodielectric structures for superresolution and superguiding applications in the visible and near-ir ranges,” Phys. Rev. A 77(3), 033848 (2008).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Bloemer, and A. Desyatnikov, “Optical vortices during a superresolution process in a metamaterial,” Phys. Rev. A 77(4), 043825 (2008).
[CrossRef]

Phys. Rev. B (2)

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73(11), 113110 (2006).
[CrossRef]

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71(19), 193105–1-4 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

E. S. C. Ching, P. T. Leung, A Maassen van den Brink, W. M Suen, S. S Tong, and K Young, “Quasi-normal modes expansion for waves in open systems,” Rev. Mod. Phys. 70, 1545 (1998).
[CrossRef]

Science (1)

3N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, “Super-resolution imaging through a planar silver layer,” Opt. Express 13(6), 2127–2134 (2005).
[CrossRef] [PubMed]

Other (5)

L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University Press, 1995).

J. Lekner, Theory of reflection, Martin Nijhoff Publishers Dordrecht (1987).

P. Yeh, Optical Waves in Layered Media, (Wiley, New York, 1988).

E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press Inc., New York, 1991).

Y. S. Kivshar, and G. P. Agrawal, Optical Solitons, (Academic Press, San Diego 2003).

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Figures (12)

Fig. 1
Fig. 1

(a) TM dispersion curves for the guided modes of a 4 period structure (d1d2)4 with d1 = d2 = 40nm. (b) log10(T + 1) of the evanescent components vs. λ and kx/k0 with no absorption. (c) Same as (b) but with small absorption. (d) Same as (b) but with consistent absorption.

Fig. 2
Fig. 2

Transmittance spectrum for propagating modes (kx/k0<1) and evanescent modes(kx/k0>1) at different wavelengths and different values of the absorption.

Fig. 3
Fig. 3

(a) Dispersion curves for the guided modes as in Fig. 1(a) but for TE polarization. (b) log10(T + 1) for the evanescent modes vs. λ and kx/k0 in the case of no absorption.

Fig. 4
Fig. 4

Free space diffraction of the z-component of the Poynting vector in arbitrary units from 4 slits located at z = 0. The 4 slits are symmetrically located with respect to the axis x = 0. The two inner slits are 50nm wide and have a distance center to center of 150nm. The two outer slits are 250nm wide and have a distance center to center of 600nm.

Fig. 5
Fig. 5

Schematic representation of the lens and the slits geometry. The operative wavelength is λ = 532nm. The lens is placed in vacuo.

Fig. 6
Fig. 6

log10(T + 1) vs. λ and kx/k0 for the Ag/GaP lens described in Fig. 5. (a) TM polarization. (b) TE polarization.

Fig. 7
Fig. 7

(a) Free space diffraction of Sz from the 4 slits. (b) Diffraction with the lens in front of the scattering object for TE polarization. (c) Diffraction for TM polarization. (d) Section of Sz at z = 391nm (i.e. 50nm beyond the end of the lens). Superimposed (black line) the position of the 4 slits.

Fig. 8
Fig. 8

(a). Diffraction for TM polarization but with the evanescent modes removed from the spectrum of the scattering object. (b) Same but for TE polarization. (c) Section of Sz at z = 500nm.

Fig. 9
Fig. 9

(a) Transmittance of the lens at λ = 532nm vs. kx/k0 for propagation modes (kx/k0<1) and evanescent modes(kx/k0>1). (b) Phase of the transmission for the propagation modes.

Fig. 10
Fig. 10

Isofrequency curves at λ = 532nm. (a) Real part of the Bloch vector. (b) Imaginary part of the Bloch vector.

Fig. 11
Fig. 11

Diffraction with a metallo-dielectric lens whose number of periods is triple with respect to the lens described in Fig. 5. (a) TM polarization. (b) TE polarization. (c) Section of Sz at z = 500nm, i.e. in the middle of the lens. (d) Section of Sz at z = 1200nm, i.e. ~180nm beyond the output surface of the lens.

Fig. 12
Fig. 12

Diffraction with a metallo-dielectric lens whose number of periods is eight times greater than the lens described in Fig. 5. (a) TM polarization. (b) TE polarization. (c) Section of Sz at z = 2.73μm, i.e. few nanometers beyond the end of the lens. Superimposed the position of the slits.

Equations (7)

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(HL(1εdHdz)L)=(m11m12m21m22)(H0(1εdHdz)0),
(m11m12m21m22)=i=1N(cos((niωc)2kx2di)εi(niωc)2kx2sin((niωc)2kx2di)(niωc)2kx2εisin((niωc)2kx2di)cos((niωc)2kx2di)).
i((n0ωc)2kx2ε0m22+(nN+1ωc)2kx2εN+1m11)+((n0ωc)2kx2ε0(nN+1ωc)2kx2εN+1m12m21)=0,
t=2i(n0ωc)2kx2ε0i((n0ωc)2kx2ε0m22+(nN+1ωc)2kx2εN+1m11)+((n0ωc)2kx2ε0(nN+1ωc)2kx2εN+1m12m21).
ϕ(kx)=ϕ0+12ϕ''(kx=0)kx2+...       .
ϕF.S.(kx)=k02kx2L=k0LL2k0kx2+...     ,
LDLDF.S.=L|ϕ''(kx=0)|k0   ,

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