Abstract

We propose an approach for far-field optical subwavelength imaging by using a dielectric metamaterial magnifier with gradient refractive index. Different from previous superlens and hyperlens that form a real image with subwavelength features within narrowband, this magnifier creates a virtual color image with sub-100 nm resolution over broadband that can be captured directly by a conventional microscope in the far field. Because the magnifier is made of isotropic dielectric materials, the fabrication will be greatly simplified with existing metamaterial technologies.

© 2010 Optical Society of America

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References

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  1. M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).
  2. S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316, 1153–1158 (2008).
    [CrossRef]
  3. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [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. T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313, 1597 (2006).
    [CrossRef]
  6. 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]
  7. A. Salandrino, and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 075103 (2006).
  8. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315, 1686 (2007).
    [CrossRef] [PubMed]
  9. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying Superlens in the Visible Frequency Range,” Science 315, 1699–1701 (2007).
    [CrossRef] [PubMed]
  10. A. V. Kildishev, and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. Lett. 33, 43–45 (2008).
    [CrossRef]
  11. D. P. Gaillot, C. Croenne, F. Zhang, and D. Lippens, “Transformation optics for the full dielectric electromagnetic cloak and metal-dielectric planar hyperlens,” N. J. Phys. 10, 115039 (2008).
    [CrossRef]
  12. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
    [CrossRef] [PubMed]
  13. U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (2006).
    [CrossRef] [PubMed]
  14. U. Leonhardt, and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 69 (2009).
    [CrossRef]
  15. J. R. Wait, Electromagnetic Waves in Stratified Media, (IEEE Press, New York, 1996).
  16. J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
    [CrossRef]
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, 1997).

2009 (2)

U. Leonhardt, and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 69 (2009).
[CrossRef]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

2008 (3)

A. V. Kildishev, and V. M. Shalaev, “Engineering space for light via transformation optics,” Opt. Lett. 33, 43–45 (2008).
[CrossRef]

S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316, 1153–1158 (2008).
[CrossRef]

D. P. Gaillot, C. Croenne, F. Zhang, and D. Lippens, “Transformation optics for the full dielectric electromagnetic cloak and metal-dielectric planar hyperlens,” N. J. Phys. 10, 115039 (2008).
[CrossRef]

2007 (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315, 1686 (2007).
[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]

2006 (5)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313, 1597 (2006).
[CrossRef]

A. Salandrino, and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 075103 (2006).

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]

2005 (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]

2000 (1)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Alekseyev, L. V.

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

Croenne, C.

D. P. Gaillot, C. Croenne, F. Zhang, and D. Lippens, “Transformation optics for the full dielectric electromagnetic cloak and metal-dielectric planar hyperlens,” N. J. Phys. 10, 115039 (2008).
[CrossRef]

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]

Engheta, N.

A. Salandrino, and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 075103 (2006).

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]

Gaillot, D. P.

D. P. Gaillot, C. Croenne, F. Zhang, and D. Lippens, “Transformation optics for the full dielectric electromagnetic cloak and metal-dielectric planar hyperlens,” N. J. Phys. 10, 115039 (2008).
[CrossRef]

Hell, S. W.

S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316, 1153–1158 (2008).
[CrossRef]

Hillenbrand, R.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313, 1597 (2006).
[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]

Jacob, Z.

Kildishev, A. V.

Korobkin, D.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313, 1597 (2006).
[CrossRef]

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 (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]

Leonhardt, U.

U. Leonhardt, and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 69 (2009).
[CrossRef]

U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

Li, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

Lippens, D.

D. P. Gaillot, C. Croenne, F. Zhang, and D. Lippens, “Transformation optics for the full dielectric electromagnetic cloak and metal-dielectric planar hyperlens,” N. J. Phys. 10, 115039 (2008).
[CrossRef]

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315, 1686 (2007).
[CrossRef] [PubMed]

Narimanov, E.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Philbin, T. G.

U. Leonhardt, and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 69 (2009).
[CrossRef]

Salandrino, A.

A. Salandrino, and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 075103 (2006).

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

Shvets, G.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313, 1597 (2006).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[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]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315, 1686 (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]

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313, 1597 (2006).
[CrossRef]

Urzhumov, Y.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313, 1597 (2006).
[CrossRef]

Valentine, J.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

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 (2007).
[CrossRef] [PubMed]

Zentgraf, T.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

Zhang, F.

D. P. Gaillot, C. Croenne, F. Zhang, and D. Lippens, “Transformation optics for the full dielectric electromagnetic cloak and metal-dielectric planar hyperlens,” N. J. Phys. 10, 115039 (2008).
[CrossRef]

Zhang, X.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315, 1686 (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]

N. J. Phys. (1)

D. P. Gaillot, C. Croenne, F. Zhang, and D. Lippens, “Transformation optics for the full dielectric electromagnetic cloak and metal-dielectric planar hyperlens,” N. J. Phys. 10, 115039 (2008).
[CrossRef]

Nat. Mater. (1)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Salandrino, and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 075103 (2006).

Phys. Rev. Lett. (1)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Prog. Opt. (1)

U. Leonhardt, and T. G. Philbin, “Transformation Optics and the Geometry of Light,” Prog. Opt. 53, 69 (2009).
[CrossRef]

Science (7)

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]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313, 1597 (2006).
[CrossRef]

S. W. Hell, “Far-Field Optical Nanoscopy,” Science 316, 1153–1158 (2008).
[CrossRef]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science 315, 1686 (2007).
[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]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[CrossRef] [PubMed]

U. Leonhardt, “Optical Conformal Mapping,” Science 312, 1777–1780 (2006).
[CrossRef] [PubMed]

Other (3)

M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).

J. R. Wait, Electromagnetic Waves in Stratified Media, (IEEE Press, New York, 1996).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, 1997).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Geometry of the 2D GRIN magnifier. (b) A stratified medium created from transformation. (c) The layer with extended thickness pushes the left half part of the stratified medium to the left. (d) Profiles of refractive index in terms of e . The blue solid line represents the case in (b). The red dotted line corresponds to the case in (c).

Fig. 2.
Fig. 2.

Radiation from two coherent and in-phase point sources (a) in free space with separation λ 0/4 along x-axis, (b) in the complete magnifier with separation λ 0/4 along x-axis, (c) in free space with separation 2λ 0 along x-axis, and (d) attached to the bottom interface of a semi-cylinder magnifier with separation λ 0/4 along x-axis. (a-c) are calculated analytically. (d) is obtained from FEA simulation.

Fig. 3.
Fig. 3.

Image intensity of two equally bright incoherent point sources with different separations at free-space wavelengths of (a) 506 nm, (b) 605 nm and (c) 709 nm, respectively.

Fig. 4.
Fig. 4.

Color image intensity of a 6-line object. (a) The original object that will radiate at wavelengths of 506 nm (green), 605 nm (orange) and 709 nm (red) with equal brightness. (b-d) The image intensity at wavelengths of 506 nm, 605 nm and 709 nm, respectively. (e) Combined image by superposing all three color components. (f) Combined image whose color is determined by the maximum intensity of three color components at each point. (g) The same as (f) while all normalized intensity below 0.97 is not shown. In all figures, the maximum intensity is normalized to 1.

Equations (2)

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n ( r ) = { b / a r < a b / r a < r < b 1 r > b
E z = m = J m ( k r < ) H m ( 1 ) ( k r > ) e i m ( ϕ ϕ ) ,

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