Abstract

Optical lenses are pervasive in various areas of sciences and technologies. It is well known that conventional lenses have symmetrical imaging properties along forward and backward directions. In this letter, we show that hyperbolic plasmonic metamaterial based negative refraction lenses perform as either converging lenses or diverging lenses depending on the illumination directions. New imaging equations and properties that are different from those of all the existing optical lenses are also presented. These new imaging properties, including symmetry breaking as well as the super resolving power, significantly expand the horizon of imaging optics and optical system design.

©2012 Optical Society of America

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  4. Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75(26), 4064–4066 (1999).
    [Crossref]
  5. S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78(26), 4071–4073 (2001).
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  6. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
    [Crossref] [PubMed]
  7. J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
    [Crossref] [PubMed]
  8. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
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  9. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
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  10. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
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  11. Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
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  12. E. E. Narimanov, “Far-field superlens: optical nanoscope,” Nat. Photonics 1(5), 260–261 (2007).
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  13. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
    [Crossref] [PubMed]
  14. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
    [Crossref] [PubMed]
  15. Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett. 94(20), 203108 (2009).
    [Crossref]
  16. I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
    [Crossref] [PubMed]
  17. S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9(10), 3447–3452 (2009).
    [Crossref] [PubMed]
  18. F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
    [Crossref] [PubMed]
  19. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902–033904 (2009).
    [Crossref] [PubMed]
  20. X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008).
    [Crossref] [PubMed]
  21. C. Ma, R. Aguinaldo, and Z. Liu, “Advances in the hyperlens,” Chin. Sci. Bull. 55(24), 2618–2624 (2010).
    [Crossref]
  22. C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express 18(5), 4838–4844 (2010).
    [Crossref] [PubMed]
  23. C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010).
    [Crossref]
  24. C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscale plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011).
    [Crossref]
  25. S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009).
    [Crossref] [PubMed]
  26. T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical “Janus” device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.) 22(23), 2561–2564 (2010).
    [Crossref] [PubMed]
  27. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  28. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [Crossref] [PubMed]
  29. C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform propertties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
    [Crossref]

2011 (2)

C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscale plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011).
[Crossref]

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform propertties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[Crossref]

2010 (4)

T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical “Janus” device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.) 22(23), 2561–2564 (2010).
[Crossref] [PubMed]

C. Ma, R. Aguinaldo, and Z. Liu, “Advances in the hyperlens,” Chin. Sci. Bull. 55(24), 2618–2624 (2010).
[Crossref]

C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express 18(5), 4838–4844 (2010).
[Crossref] [PubMed]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010).
[Crossref]

2009 (5)

S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009).
[Crossref] [PubMed]

Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett. 94(20), 203108 (2009).
[Crossref]

S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9(10), 3447–3452 (2009).
[Crossref] [PubMed]

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[Crossref] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902–033904 (2009).
[Crossref] [PubMed]

2008 (2)

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008).
[Crossref] [PubMed]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

2007 (5)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[Crossref] [PubMed]

E. E. Narimanov, “Far-field superlens: optical nanoscope,” Nat. Photonics 1(5), 260–261 (2007).
[Crossref]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 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(5819), 1686 (2007).
[Crossref] [PubMed]

2006 (3)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical Hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

2005 (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

2001 (1)

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78(26), 4071–4073 (2001).
[Crossref]

2000 (1)

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

1999 (1)

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75(26), 4064–4066 (1999).
[Crossref]

1873 (1)

E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech. 9(1), 413–418 (1873).
[Crossref]

Abbe, E.

E. Abbe, “Beitrage zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech. 9(1), 413–418 (1873).
[Crossref]

Aguinaldo, R.

C. Ma, R. Aguinaldo, and Z. Liu, “Advances in the hyperlens,” Chin. Sci. Bull. 55(24), 2618–2624 (2010).
[Crossref]

Alekseyev, L. V.

Bartal, G.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902–033904 (2009).
[Crossref] [PubMed]

Conway, J.

S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9(10), 3447–3452 (2009).
[Crossref] [PubMed]

Davis, C. C.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

Durant, S.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[Crossref] [PubMed]

Escobar, M. A.

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform propertties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[Crossref]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902–033904 (2009).
[Crossref] [PubMed]

Fang, N.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Feke, G. D.

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75(26), 4064–4066 (1999).
[Crossref]

Ghislain, L. P.

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75(26), 4064–4066 (1999).
[Crossref]

Goldberg, B. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78(26), 4071–4073 (2001).
[Crossref]

Grober, R. D.

Q. Wu, G. D. Feke, R. D. Grober, and L. P. Ghislain, “Realization of numerical aperture 2.0 using a gallium phosphide solid immersion lens,” Appl. Phys. Lett. 75(26), 4064–4066 (1999).
[Crossref]

Huang, F. M.

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[Crossref] [PubMed]

Hung, Y. J.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

Ippolito, S. B.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78(26), 4071–4073 (2001).
[Crossref]

Jacob, Z.

Lee, H.

S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9(10), 3447–3452 (2009).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Li, J.

T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical “Janus” device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.) 22(23), 2561–2564 (2010).
[Crossref] [PubMed]

Liu, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Liu, Z.

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform propertties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[Crossref]

C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscale plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011).
[Crossref]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010).
[Crossref]

C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express 18(5), 4838–4844 (2010).
[Crossref] [PubMed]

C. Ma, R. Aguinaldo, and Z. Liu, “Advances in the hyperlens,” Chin. Sci. Bull. 55(24), 2618–2624 (2010).
[Crossref]

Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithography and imaging with half-pitch resolution down to 20 nm,” Appl. Phys. Lett. 94(20), 203108 (2009).
[Crossref]

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater. 7(6), 435–441 (2008).
[Crossref] [PubMed]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (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(5819), 1686 (2007).
[Crossref] [PubMed]

Ma, C.

C. Ma and Z. Liu, “Designing super-resolution metalenses by the combination of metamaterials and nanoscale plasmonic waveguide couplers,” J. Nanophotonics 5(1), 051604 (2011).
[Crossref]

C. Ma, M. A. Escobar, and Z. Liu, “Extraordinary light focusing and Fourier transform propertties of gradient-index metalenses,” Phys. Rev. B 84(19), 195142 (2011).
[Crossref]

C. Ma and Z. Liu, “A super resolution metalens with phase compensation mechanism,” Appl. Phys. Lett. 96(18), 183103 (2010).
[Crossref]

C. Ma and Z. Liu, “Focusing light into deep subwavelength using metamaterial immersion lenses,” Opt. Express 18(5), 4838–4844 (2010).
[Crossref] [PubMed]

C. Ma, R. Aguinaldo, and Z. Liu, “Advances in the hyperlens,” Chin. Sci. Bull. 55(24), 2618–2624 (2010).
[Crossref]

Narimanov, E.

Narimanov, E. E.

E. E. Narimanov, “Far-field superlens: optical nanoscope,” Nat. Photonics 1(5), 260–261 (2007).
[Crossref]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

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

Pikus, Y.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (2007).
[Crossref] [PubMed]

Podolskiy, V. A.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1(1), 41–48 (2007).
[Crossref]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

Stacy, A. M.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Staffaroni, M.

S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9(10), 3447–3452 (2009).
[Crossref] [PubMed]

Sun, C.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7(2), 403–408 (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(5819), 1686 (2007).
[Crossref] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Tang, J.

S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9(10), 3447–3452 (2009).
[Crossref] [PubMed]

Tapia, N.

T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical “Janus” device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.) 22(23), 2561–2564 (2010).
[Crossref] [PubMed]

Thongrattanasiri, S.

Unlu, M. S.

S. B. Ippolito, B. B. Goldberg, and M. S. Unlu, “High spatial resolution subsurface microscopy,” Appl. Phys. Lett. 78(26), 4071–4073 (2001).
[Crossref]

Valentine, J.

T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical “Janus” device for integrated photonics,” Adv. Mater. (Deerfield Beach Fla.) 22(23), 2561–2564 (2010).
[Crossref] [PubMed]

Vedantam, S.

S. Vedantam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9(10), 3447–3452 (2009).
[Crossref] [PubMed]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902–033904 (2009).
[Crossref] [PubMed]

Wang, Y.

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004).
[Crossref] [PubMed]

Wu, Q.

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Figures (4)

Fig. 1
Fig. 1

Imaging behaviors of a conventional converging lens. An object is placed beyond 2f in (a), at 2f in (b), between f and 2f in (c), and within f in (d). f is the focal length of the lens.

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Fig. 2
Fig. 2

Focusing behaviors of a hyperbolic metalens. (a) Plane wave from air converges to a focus (Fm) in metamaterial. (c) Plane wave from metamaterial diverges in air, resulting in a virtual focus (Fd) also in metamaterial. The arrows in (a) and (c) are eye-guiding rays. (b) and (d) Symbolized representation of (a) and (c). The dashed vertical lines represent phase compensating elements at the interfaces, i.e. the PWC.

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Fig. 3
Fig. 3

(a) Schematic representation of forming an image by a hyperbolic metalens. Imaging behavior of a hyperbolic metalens for an object in air: (b) Ray diagram, (b) Numerical result.

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Fig. 4
Fig. 4

Imaging behavior of a hyperbolic metalens for an object in metamaterial. (a) Object is inside point Fm. (c) Object is between points Fm and 2Fm. (e) Object is at point 2Fm. (g) Object is outside point 2Fm. (b), (d), (f), (h), Numerical verifications of (a), (c), (e), (g), respectively.

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Tables (2)

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Table 1 Imaging Properties of a Conventional Converging Lens.

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Table 2 Imaging Properties of a Hyperbolic Metalens. fm>0 and fd < 0.

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Equations (4)

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

1 v d 2 + x 2 + ε z ' ε x ' v m 2 + ε z ' x 2 = ε z ' ε x ' f m 2 + ε z ' x 2
1 v d + ε z ' / ε x ' v m = ε z ' / ε x ' f m
1 v d + ε z ' / ε x ' v m = 1 f d
M T = u m u d =− g m f m =− f d g d

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