Abstract

We describe the change of the spatial distribution of the state of polarization occurring during two-dimensional (2D) imaging through a multilayer and in particular through a layered metallic flat lens. Linear or circular polarization of incident light is not preserved due to the difference in the amplitude transfer functions for the TM and TE polarizations. In effect, the transfer function and the point spread function (PSF) that characterize 2D imaging through a multilayer both have a matrix form, and cross-polarization coupling is observed for spatially modulated beams with a linear or circular incident polarization. The PSF in a matrix form is used to characterize the resolution of the superlens for different polarization states. We demonstrate how the 2D PSF may be used to design a simple diffractive nanoelement consisting of two radial slits. The structure assures the separation of nondiffracting radial beams originating from two slits in the mask and exhibits an interesting property of a backward power flow in between the two rings.

© 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. S. A. Ramakrishna, J. B. Pendry, D. Schurig, and D. R. Smith, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
    [CrossRef]
  3. D. O. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13, 2127–2134(2005).
    [CrossRef] [PubMed]
  4. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537(2005).
    [CrossRef] [PubMed]
  5. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705(2000).
    [CrossRef]
  6. H. Zhang, L. Shen, L. Ran, Y. Yuan, and J. Kong, “Layered superlensing in two-dimensional photonic crystals,” Opt. Express 14, 11178–11183 (2006).
    [CrossRef] [PubMed]
  7. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
    [CrossRef]
  8. A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004).
    [CrossRef] [PubMed]
  9. H. Zhang, H. Zhu, L. Qian, and D. Fan, “Collimations and negative refractions by slabs of 2D photonic crystals with periodically-aligned tube-type air holes,” Opt. Express 15, 3519–3530 (2007).
    [CrossRef] [PubMed]
  10. K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, “Metrics for negative-refractive-index materials,” Phys. Rev. E 70, 035602(2004).
    [CrossRef]
  11. D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
    [CrossRef]
  12. 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]
  13. 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]
  14. E. V. Ponizovskaya and A. M. Bratkovsky, “Metallic negative index nanostructures at optical frequencies: losses and effect of gain medium,” Appl. Phys. A 87, 161–165 (2007).
    [CrossRef]
  15. T. A. Fadeyeva, V. G. Shvedov, Y. V. Izdebskaya, A. V. Volyar, E. Brasselet, D. N. Neshev, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Spatially engineered polarization states and optical vortices in uniaxial crystals,” Opt. Express 18, 10848–10863 (2010).
    [CrossRef] [PubMed]
  16. X. L. Wang, Y. Li, J. Chen, C. S. Guo, J. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010).
    [CrossRef] [PubMed]
  17. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57(2009).
    [CrossRef]
  18. S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
    [CrossRef]
  19. B. Saleh and M. Teich, Fundamentals of Photonics, 2nd ed.(Wiley, 2007).
  20. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).
  21. 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]
  22. N. Mattiucci, D. Aguanno, M. Scalora, M. J. Bloemer, and C. Sibilia, “Transmission function properties for multi-layered structures: application to super-resolution,” Opt. Express 17, 17517–17529 (2009).
    [CrossRef] [PubMed]
  23. R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal–dielectric multilayers,” Opt. Lett. 35, 1133–1135 (2010).
    [CrossRef] [PubMed]
  24. R. Kotynski and T. Stefaniuk, “Comparison of imaging with sub-wavelength resolution in the canalization and resonant tunnelling regimes,” J. Opt. A Pure Appl. Opt. 11, 015001(2009).
    [CrossRef]
  25. R. Kotynski, “Fourier optics approach to imaging with sub-wavelength resolution through metal–dielectric multilayers,” Opto-Electron. Rev. 18, 366–375 (2010).
    [CrossRef]
  26. B. Lee, Ph. Lalanne, and Y. Fainman, eds., “Feature Issue on Plasmonic Diffractive Optics and Imaging,” Appl. Opt. 49(7), PD01, A01–A41 (2010).
    [CrossRef]
  27. A. W. Norfolk and E. J. Grace, “Reconstruction of optical fields with the quasi-discrete Hankel transform,” Opt. Express 18, 10551–10556 (2010).
    [CrossRef] [PubMed]
  28. E.Palik, ed., Handbook of Optical Constants of Solids(Academic, 1998).
  29. P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]

2010 (6)

2009 (3)

2008 (1)

2007 (2)

E. V. Ponizovskaya and A. M. Bratkovsky, “Metallic negative index nanostructures at optical frequencies: losses and effect of gain medium,” Appl. Phys. A 87, 161–165 (2007).
[CrossRef]

H. Zhang, H. Zhu, L. Qian, and D. Fan, “Collimations and negative refractions by slabs of 2D photonic crystals with periodically-aligned tube-type air holes,” Opt. Express 15, 3519–3530 (2007).
[CrossRef] [PubMed]

2006 (2)

H. Zhang, L. Shen, L. Ran, Y. Yuan, and J. Kong, “Layered superlensing in two-dimensional photonic crystals,” Opt. Express 14, 11178–11183 (2006).
[CrossRef] [PubMed]

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]

2005 (2)

D. O. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Express 13, 2127–2134(2005).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537(2005).
[CrossRef] [PubMed]

2004 (2)

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, “Metrics for negative-refractive-index materials,” Phys. Rev. E 70, 035602(2004).
[CrossRef]

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef] [PubMed]

2003 (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]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

2002 (2)

S. A. Ramakrishna, J. B. Pendry, D. Schurig, and D. R. Smith, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

2000 (2)

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

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705(2000).
[CrossRef]

1972 (1)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Aguanno, D.

Arnold, M. D.

Blaikie, R. J.

Bloemer, M. J.

Bones, P. J.

Brasselet, E.

Bratkovsky, A. M.

E. V. Ponizovskaya and A. M. Bratkovsky, “Metallic negative index nanostructures at optical frequencies: losses and effect of gain medium,” Appl. Phys. A 87, 161–165 (2007).
[CrossRef]

Chen, J.

Christy, R.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Desyatnikov, A. S.

Ding, J.

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef] [PubMed]

Fadeyeva, T. A.

Fainman, Y.

B. Lee, Ph. Lalanne, and Y. Fainman, eds., “Feature Issue on Plasmonic Diffractive Optics and Imaging,” Appl. Opt. 49(7), PD01, A01–A41 (2010).
[CrossRef]

Fan, D.

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537(2005).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

Grace, E. J.

Grbic, A.

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef] [PubMed]

Guo, C. S.

Izdebskaya, Y. V.

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Johnson, P.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Kivshar, Y. S.

Kong, J.

Kotynski, R.

R. Kotynski, “Fourier optics approach to imaging with sub-wavelength resolution through metal–dielectric multilayers,” Opto-Electron. Rev. 18, 366–375 (2010).
[CrossRef]

R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal–dielectric multilayers,” Opt. Lett. 35, 1133–1135 (2010).
[CrossRef] [PubMed]

R. Kotynski and T. Stefaniuk, “Comparison of imaging with sub-wavelength resolution in the canalization and resonant tunnelling regimes,” J. Opt. A Pure Appl. Opt. 11, 015001(2009).
[CrossRef]

Krolikowski, W.

Lalanne, Ph.

B. Lee, Ph. Lalanne, and Y. Fainman, eds., “Feature Issue on Plasmonic Diffractive Optics and Imaging,” Appl. Opt. 49(7), PD01, A01–A41 (2010).
[CrossRef]

Lee, B.

B. Lee, Ph. Lalanne, and Y. Fainman, eds., “Feature Issue on Plasmonic Diffractive Optics and Imaging,” Appl. Opt. 49(7), PD01, A01–A41 (2010).
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537(2005).
[CrossRef] [PubMed]

Li, Y.

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Mattiucci, N.

Melville, D. O.

Moore, C. P.

Nelson, K. A.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, “Metrics for negative-refractive-index materials,” Phys. Rev. E 70, 035602(2004).
[CrossRef]

Neshev, D. N.

Norfolk, A. W.

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705(2000).
[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]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[CrossRef]

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]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, and D. R. Smith, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

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

Ponizovskaya, E. V.

E. V. Ponizovskaya and A. M. Bratkovsky, “Metallic negative index nanostructures at optical frequencies: losses and effect of gain medium,” Appl. Phys. A 87, 161–165 (2007).
[CrossRef]

Qian, L.

Ramakrishna, S. A.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[CrossRef]

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]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, and D. R. Smith, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

Ran, L.

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[CrossRef]

Saleh, B.

B. Saleh and M. Teich, Fundamentals of Photonics, 2nd ed.(Wiley, 2007).

Scalora, M.

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

Schurig, D.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, and D. R. Smith, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

Shen, L.

Shvedov, V. G.

Sibilia, C.

Smith, D. R.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, and D. R. Smith, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

Stefaniuk, T.

R. Kotynski and T. Stefaniuk, “Multiscale analysis of subwavelength imaging with metal–dielectric multilayers,” Opt. Lett. 35, 1133–1135 (2010).
[CrossRef] [PubMed]

R. Kotynski and T. Stefaniuk, “Comparison of imaging with sub-wavelength resolution in the canalization and resonant tunnelling regimes,” J. Opt. A Pure Appl. Opt. 11, 015001(2009).
[CrossRef]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537(2005).
[CrossRef] [PubMed]

Teich, M.

B. Saleh and M. Teich, Fundamentals of Photonics, 2nd ed.(Wiley, 2007).

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]

Volyar, A. V.

Wang, H. T.

Wang, X. L.

Ward, D. W.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, “Metrics for negative-refractive-index materials,” Phys. Rev. E 70, 035602(2004).
[CrossRef]

Webb, K. J.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, “Metrics for negative-refractive-index materials,” Phys. Rev. E 70, 035602(2004).
[CrossRef]

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]

Yang, M.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, “Metrics for negative-refractive-index materials,” Phys. Rev. E 70, 035602(2004).
[CrossRef]

Yuan, Y.

Zhan, Q.

Zhang, H.

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537(2005).
[CrossRef] [PubMed]

Zhu, H.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

B. Lee, Ph. Lalanne, and Y. Fainman, eds., “Feature Issue on Plasmonic Diffractive Optics and Imaging,” Appl. Opt. 49(7), PD01, A01–A41 (2010).
[CrossRef]

Appl. Phys. A (1)

E. V. Ponizovskaya and A. M. Bratkovsky, “Metallic negative index nanostructures at optical frequencies: losses and effect of gain medium,” Appl. Phys. A 87, 161–165 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82, 1506–1508 (2003).
[CrossRef]

J. Mod. Opt. (2)

S. A. Ramakrishna, J. B. Pendry, D. Schurig, D. R. Smith, and S. Schultz, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, D. Schurig, and D. R. Smith, “The asymmetric lossy near-perfect lens,” J. Mod. Opt. 49, 1747–1762 (2002).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

R. Kotynski and T. Stefaniuk, “Comparison of imaging with sub-wavelength resolution in the canalization and resonant tunnelling regimes,” J. Opt. A Pure Appl. Opt. 11, 015001(2009).
[CrossRef]

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

Opt. Express (7)

Opt. Lett. (1)

Opto-Electron. Rev. (1)

R. Kotynski, “Fourier optics approach to imaging with sub-wavelength resolution through metal–dielectric multilayers,” Opto-Electron. Rev. 18, 366–375 (2010).
[CrossRef]

Phys. Rev. B (5)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[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]

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]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705(2000).
[CrossRef]

Phys. Rev. E (1)

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, “Metrics for negative-refractive-index materials,” Phys. Rev. E 70, 035602(2004).
[CrossRef]

Phys. Rev. Lett. (2)

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef] [PubMed]

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

Science (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537(2005).
[CrossRef] [PubMed]

Other (3)

B. Saleh and M. Teich, Fundamentals of Photonics, 2nd ed.(Wiley, 2007).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

E.Palik, ed., Handbook of Optical Constants of Solids(Academic, 1998).

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 (7)

Fig. 1
Fig. 1

Schematic of a layered metal–dielectric periodic lens with N = 4 periods. It is further assumed that λ = 430 nm , Λ = 57.5 nm , N = 10 , d Ag = 0.37 Λ , d SrTiO 3 = 0.63 Λ , n Ag = 0.04 + 2.46 i , n SrTiO 3 = 2.674 + 0.027 i .

Fig. 2
Fig. 2

(a) One-dimensional TF and PSF of the multilayer for in-plane propagation: H ^ TM , H ^ TE , TF for the TM and TE polarizations; (b) radial cross-section of 2D TF and PSFs of the multilayer for 3D propagation H ^ m = ( H ^ TM + H ^ TE ) / 2 , H ^ δ = ( H ^ TM H ^ TE ) / 2 . One-dimensional and 2D PSFs and TF corresponding to propagation in air for the same distance are also shown for comparison. Solid curves and dashed curves represent the amplitudes and phases of the complex functions, respectively.

Fig. 3
Fig. 3

Two-dimensional TF matrix of the multilayer. (a) Matrix elements H ^ x x ( k x , k y ) and H ^ x y ( k x , k y ) for linearly polarized light; (b) matrix elements H ^ σ + σ + ( k x , k y ) and H ^ σ + σ ( k x , k y ) for circularly polarized light. Phase isolines are drawn at the distances of π / 2 and are changed between solid and dashed lines every π.

Fig. 4
Fig. 4

Two-dimensional PSF matrix of the multilayer. (a) Matrix elements H x x ( x , y ) and H x y ( x , y ) for linearly polarized light; (b) matrix elements H σ + σ + ( x , y ) and H ^ σ + σ ( x , y ) for circularly polarized light; phase isolines are drawn at the distances of π / 2 and are changed between solid and dashed lines every π.

Fig. 5
Fig. 5

(a) Contributions to the axial Poynting vector P z from both polarizations at the output plane, resulting from a linearly x polarized incident point source; (b) axial component of the Poynting vector P z in the x z and y z cross-sections inside the structure normalized with respect to P z ( x = 0 , y = 0 , z = L ) . The simulations were performed using FDTD. The red lines separate areas with positive and negative direction of the power flow.

Fig. 6
Fig. 6

Intensity of the electric field and the state of polarization (a) inside the mask and (b) at the output plane of the multilayer. The mask consists of a PEC with two circular slits and is illuminated with a linearly x polarized Gaussian beam. FDTD simulation, linear intensity mapping.

Fig. 7
Fig. 7

Time-averaged Poynting vector component P z in the x z cross-section of the structure (where y = 0 ). The red lines separate areas with the positive and negative values of P z and the white arrows show the orientation of the energy flow in the vertical direction.

Equations (17)

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

Ψ ( x , y ) z = z out = ( 2 π ) 1 H ( x , y ) * Ψ ( x , y ) z = z inc .
Ψ ^ ( k x , k y ) z = z out = H ^ ( k x , k y ) · Ψ ^ ( k x , k y ) z = z inc ,
Ψ ( x , y ) z = ( 2 π ) 1 Ψ ^ ( k x , k y ) z e i ( k x x + k y y ) d k x d k y .
[ E ^ x ( k r , k φ ) E ^ y ( k r , k φ ) ] z = z out = H ^ lin ( k r , k φ ) · [ E ^ x ( k r , k φ ) E ^ y ( k r , k φ ) ] z = z in ,
[ E ^ σ + ( k r , k φ ) E ^ σ ( k r , k φ ) ] z = z out = H ^ circ ( k r , k φ ) · [ E ^ σ + ( k r , k φ ) E ^ σ ( k r , k φ ) ] z = z in ,
H ^ lin ( k r , k φ ) = [ H ^ x x ( k r , k φ ) H ^ y x ( k r , k φ ) H ^ x y ( k r , k φ ) H ^ y y ( k r , k φ ) ]
= R ( k φ ) · [ H ^ TM ( k r ) 0 0 H ^ TE ( k r ) ] · R ( k φ )
= H ^ m ( k r ) · [ 1 0 0 1 ] + H ^ δ ( k r ) · [ cos ( 2 k φ ) sin ( 2 k φ ) sin ( 2 k φ ) cos ( 2 k φ ) ] ,
H ^ circ ( k r , k φ ) = [ H ^ σ + σ + ( k r , k φ ) H ^ σ σ + ( k r , k φ ) H ^ σ + σ ( k r , k φ ) H ^ σ σ ( k r , k φ ) ]
= H ^ m ( k r ) · [ 1 0 0 1 ] + H ^ δ ( k r ) · [ 0 exp ( 2 i k φ ) exp ( 2 i k φ ) 0 ] .
g ^ ( k r , k φ ) = n = + ( i ) n c n · exp ( i n k φ ) · H n { g r ( r ) } ,
c n = 0 2 π g φ ( φ ) · exp ( i n φ ) d φ ,
H n { g r ( r ) } = 0 g r ( r ) · J n ( k r r ) · r · d r .
H lin ( r , φ ) = [ H x x ( r , φ ) H y x ( r , φ ) H x y ( r , φ ) H y y ( r , φ ) ]
= H m ( r ) · [ 1 0 0 1 ] H δ ( r ) · [ cos ( 2 φ ) sin ( 2 φ ) sin ( 2 φ ) cos ( 2 φ ) ] ,
H circ ( r , φ ) = [ H σ + σ + ( r , φ ) H σ σ + ( r , φ ) H σ + σ ( r , φ ) H σ σ ( r , φ ) ]
= H m ( r ) · [ 1 0 0 1 ] H δ ( r ) · [ 0 exp ( 2 i φ ) exp ( 2 i φ ) 0 ] ,

Metrics