Abstract

Based on coordinate transformation incorporated with conformal mapping approach, a sub-wavelength imaging device with magnification, called “planar hyperlens” is designed, capable of realizing far-field plane-to-plane imaging beyond the diffraction limit. The possible implementation method is proposed by using effective anisotropic metamaterial formed by alternating metallic and dielectric thin layers. The magnification performance of the designed multi-layer lensing structure is numerically simulated to confirm our theoretical analysis.

© 2008 Optical Society of America

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References

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  1. J. B. Pendry, "Negative refraction makes a perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  2. J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
    [CrossRef]
  3. F. D. M. Haldane, "Electromagnetic surface modes at interfaces with negative refractive index make a "not-quite-perfect" lens," cond-mat/0206420 (2002).
  4. R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  5. D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishnan, and J. B. Pendry, Appl. Phys. Lett. 82, 1506-1508 (2003).
    [CrossRef]
  6. M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
    [CrossRef] [PubMed]
  7. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  8. A. K. Iyer, P. C. Kremer, and G. V. Eleftheriades, "Experimental and theoretical verification of focusing in a large, periodically loaded transmission line negative refractive index metamaterial," Opt. Express 11, 696-708 (2003).
    [CrossRef] [PubMed]
  9. 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]
  10. 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]
  11. D. O. S. Melville and R. J. Blaikie, "Super-resolution imaging through a planar silver layer," Opt. Express 13, 2127-2134 (2005).
    [CrossRef] [PubMed]
  12. I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range," Science 315, 1699-1701 (2007).
    [CrossRef] [PubMed]
  13. V. Podolskiy and E. E. Narimanov, "Near-sighted superlens," Opt. Lett. 30, 75-77 (2005).
    [CrossRef] [PubMed]
  14. A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations," Phys. Rev. B 74, 075103 (2006).
    [CrossRef]
  15. Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Optical hyperlens: far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (2006).
    [CrossRef] [PubMed]
  16. L. V. Alekseyev and E. Narimanov, "Impedance-matched hyperlens," Opt. Lett. 32, 3432-3434 (2007)
    [CrossRef]
  17. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686-1687 (2007).
    [CrossRef] [PubMed]
  18. H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, "Development of optical hyperlens for imaging below the diffraction limit," Opt. Express 15, 15886-15891 (2007).
    [CrossRef] [PubMed]
  19. Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Semiclassical theory of the hyperlens," J. Opt. Soc. Am. A 24, 52-59 (2007).
    [CrossRef]
  20. W. Wang, L. Lin, X. F. Yang, J. H. Cui, C. L. Du, and X. G. Luo, "Design of oblate cylindrical perfect lens using coordinate transformation," Opt. Express 16, 8094-8105 (2008).
    [CrossRef] [PubMed]
  21. P. Moon and D. E. Spencer, Field Theory Handbook, (Springer-Verlag, New York, (1971).
    [CrossRef]
  22. P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  23. S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near filed," J. Mod. Opt. 50, 1419-1430 (2003).
  24. C. Wang, Y. Zhao, D. Gan, C. Du, and X. Luo, "Subwavelength imaging with anisotropic structure comprising alternately layered metal and dielectric films," Opt. Express 16, 4217-4227 (2008).
    [CrossRef] [PubMed]
  25. S. A. Ramakrishna and J.B. Pendry, "Optical gain removes absorption and increases resolution in a near-field lens", arXiv:cond-mat/0206566 v1 28 Jun (2002).

2008 (2)

2007 (5)

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, "Development of optical hyperlens for imaging below the diffraction limit," Opt. Express 15, 15886-15891 (2007).
[CrossRef] [PubMed]

L. V. Alekseyev and E. Narimanov, "Impedance-matched hyperlens," Opt. Lett. 32, 3432-3434 (2007)
[CrossRef]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range," Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686-1687 (2007).
[CrossRef] [PubMed]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Semiclassical theory of the hyperlens," J. Opt. Soc. Am. A 24, 52-59 (2007).
[CrossRef]

2006 (2)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Optical hyperlens: far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (2006).
[CrossRef] [PubMed]

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

2005 (3)

2004 (1)

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)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishnan, and J. B. Pendry, Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near filed," J. Mod. Opt. 50, 1419-1430 (2003).

A. K. Iyer, P. C. Kremer, and G. V. Eleftheriades, "Experimental and theoretical verification of focusing in a large, periodically loaded transmission line negative refractive index metamaterial," Opt. Express 11, 696-708 (2003).
[CrossRef] [PubMed]

2002 (1)

J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
[CrossRef]

2001 (3)

R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, "Negative refraction makes a perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Alekseyev, L. V.

Blaikie, R. J.

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Cui, J. H.

Davis, C. C.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range," Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Du, C.

Du, C. L.

Eleftheriades, G. V.

Engheta, N.

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

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]

Gan, D.

Gilderdale, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

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]

Hajnal, J. V.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

Heyman, E.

R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Hung, Y. J.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range," Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Iyer, A. K.

Jacob, Z.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Semiclassical theory of the hyperlens," J. Opt. Soc. Am. A 24, 52-59 (2007).
[CrossRef]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Optical hyperlens: far-field imaging beyond the diffraction limit," Opt. Express 14, 8247-8256 (2006).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kremer, P. C.

Larkman, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686-1687 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, "Development of optical hyperlens for imaging below the diffraction limit," Opt. Express 15, 15886-15891 (2007).
[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]

Lin, L.

Liu, Z.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, "Development of optical hyperlens for imaging below the diffraction limit," Opt. Express 15, 15886-15891 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686-1687 (2007).
[CrossRef] [PubMed]

Luo, X.

Luo, X. G.

Melville, D. O. S.

Narimanov, E.

Narimanov, E. E.

Pendry, J. B.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near filed," J. Mod. Opt. 50, 1419-1430 (2003).

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishnan, and J. B. Pendry, Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Platzman, P. M.

J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
[CrossRef]

Podolskiy, V.

Ramakrishna, S. A.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near filed," J. Mod. Opt. 50, 1419-1430 (2003).

Ramakrishnan, S. A.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishnan, and J. B. Pendry, Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishnan, and J. B. Pendry, Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Salandrino, A.

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishnan, and J. B. Pendry, Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Schurig, D.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishnan, and J. B. Pendry, Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shen, J. T.

J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
[CrossRef]

Smith, D. R.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishnan, and J. B. Pendry, Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range," Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Stewart, W. J.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near filed," J. Mod. Opt. 50, 1419-1430 (2003).

Sun, C.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, "Development of optical hyperlens for imaging below the diffraction limit," Opt. Express 15, 15886-15891 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686-1687 (2007).
[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]

Wang, C.

Wang, W.

Wiltshire, M. C. K.

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near filed," J. Mod. Opt. 50, 1419-1430 (2003).

Wiltshire, M. C. K.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686-1687 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, "Development of optical hyperlens for imaging below the diffraction limit," Opt. Express 15, 15886-15891 (2007).
[CrossRef] [PubMed]

Yang, X. F.

Young, I. R.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686-1687 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, "Development of optical hyperlens for imaging below the diffraction limit," Opt. Express 15, 15886-15891 (2007).
[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]

Zhao, Y.

Ziolkowski, R. W.

R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

J. T. Shen and P. M. Platzman, "Near field imaging with negative dielectric constant lenses," Appl. Phys. Lett. 80, 3286-3288 (2002).
[CrossRef]

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishnan, and J. B. Pendry, Appl. Phys. Lett. 82, 1506-1508 (2003).
[CrossRef]

J. Mod. Opt. (1)

S. A. Ramakrishna, J. B. Pendry, M. C. K. Wiltshire, and W. J. Stewart, "Imaging the near filed," J. Mod. Opt. 50, 1419-1430 (2003).

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

Z. Jacob, L. V. Alekseyev, and E. Narimanov, "Semiclassical theory of the hyperlens," J. Opt. Soc. Am. A 24, 52-59 (2007).
[CrossRef]

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. B (2)

A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations," Phys. Rev. B 74, 075103 (2006).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical Constants of the Noble Metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Phys. Rev. E (1)

R. W. Ziolkowski, and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

J. B. Pendry, "Negative refraction makes a perfect Lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

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]

Science (5)

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]

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured Magnetic Materials for RF Flux Guides in Magnetic Resonance Imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, "Magnifying superlens in the visible frequency range," Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science 315, 1686-1687 (2007).
[CrossRef] [PubMed]

Other (3)

P. Moon and D. E. Spencer, Field Theory Handbook, (Springer-Verlag, New York, (1971).
[CrossRef]

F. D. M. Haldane, "Electromagnetic surface modes at interfaces with negative refractive index make a "not-quite-perfect" lens," cond-mat/0206420 (2002).

S. A. Ramakrishna and J.B. Pendry, "Optical gain removes absorption and increases resolution in a near-field lens", arXiv:cond-mat/0206566 v1 28 Jun (2002).

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Figures (5)

Fig. 1.
Fig. 1.

2D diagrams of curvilinear orthogonal coordinate systems. (a). The oblate cylindrical system represented by (u 1,v 1,w 1). (b). The ln tan curves represented by (u 2,v 2,w 2) in Cartesian space. The conformal transformation between the complex space and Cartesian space applied here conforms to the following equation z=(2π/a) ln tan(w)-ia, where w=u 2(x,y)+iv 2(x,y) and z=x+iy [21].

Fig. 2.
Fig. 2.

2D sketches of the designed planar hyperlens. (a) The combination of the two curvilinear orthogonal coordinate systems. (b) The multi-layered structure with alternating metal (black) and dielectric (gray) curved thin films. The yellow curves represent the coordinate curves normal to the film interfaces in (a) and the trajectories that the light follows in (b).

Fig. 3.
Fig. 3.

Normalized magnetic field distribution in the planar hyperlens. The two pairs of testing TM wave sources are symmetrically located at the object plane, each has 30nm in width. The original magnetic intensities of these sources are normalized to be unit.

Fig. 4.
Fig. 4.

(a). Unified magnetic field along the lines of y=0 (the object plane) in xy-plane. (b) Magnetic field distribution y=1.25µm (the imaging plane) in xy-plane.

Fig. 5.
Fig. 5.

Magnification of the planar hyperlens for the different locations at the object plane along the x axis. The five colored curves correspond to the magnification features for the cases with different structural parameter of v 1.

Equations (7)

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

k r 2 ε θ k θ 2 ε r = ( ω c ) 2 ,
k v 2 ε u k u 2 ε v = ( ω c ) 2 ,
ε u ( ε m d 1 + ε d d 2 ) ( d 1 + d 2 ) ,
ε v ( d 1 + d 2 ) ( d 1 ε m + d 2 ε d ) , ( u = u 1 , u 2 v = v 1 , v 2 ) .
M 1 = [ 1 + ( cosh 2 v 1 1 ) ( 1 cos 2 u 1 ) ] 1 2 .
M 2 = l 2 l 1 = ( sin 2 2 u 2 + sinh 2 2 v 2 in ) sin 2 2 u 2 = 1 + ( sinh 2 2 v 2 in sin 2 2 u 2 ) .
M = M 1 M 2 = [ 1 + ( cosh 2 v 1 1 ) ( 1 cos 2 u 1 ) ] 1 2 [ 1 + ( sinh 2 2 v 1 sin 2 2 u 2 ) ] .

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