Abstract

Despite strong experimental and theoretical evidence supporting superresolution imaging based on microlenses, the imaging mechanisms involved are not well understood. Based on the transformation optics approach, we demonstrate that a microlens may act as a two-dimensional fish-eye or an inverted Eaton lens. An asymmetric inverted Eaton lens may exhibit considerable image magnification, which has been confirmed experimentally.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  8. J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  16. S. Guenneau, A. Diatta, and R. C. McPhedran, J. Mod. Opt. 57, 511 (2010).
    [CrossRef]

2010 (4)

D. R. Mason, M. V. Jouravlev, and K. S. Kim, Opt. Lett. 35, 2007 (2010).
[CrossRef] [PubMed]

R. J. Blaikie, New J. Phys. 12, 058001 (2010).
[CrossRef]

U. Leonhardt, New J. Phys. 12, 058002 (2010).
[CrossRef]

S. Guenneau, A. Diatta, and R. C. McPhedran, J. Mod. Opt. 57, 511 (2010).
[CrossRef]

2009 (3)

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef] [PubMed]

U. Leonhardt, New J. Phys. 11, 093040 (2009).
[CrossRef]

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

2006 (3)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

J. C. Minano, Opt. Express 14, 9627 (2006).
[CrossRef] [PubMed]

2005 (2)

A. V. Zayats, I. I. Smolyaninov, and A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, Phys. Rev. Lett. 94, 057401 (2005).
[CrossRef] [PubMed]

2002 (1)

J. de Rosny and M. Fink, Phys. Rev. Lett. 89, 124301 (2002).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1988 (1)

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Reed, 1988).

Blaikie, R. J.

R. J. Blaikie, New J. Phys. 12, 058001 (2010).
[CrossRef]

Bose, R.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Davis, C. C.

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, Phys. Rev. Lett. 94, 057401 (2005).
[CrossRef] [PubMed]

de Rosny, J.

J. de Rosny and M. Fink, Phys. Rev. Lett. 89, 124301 (2002).
[CrossRef] [PubMed]

Diatta, A.

S. Guenneau, A. Diatta, and R. C. McPhedran, J. Mod. Opt. 57, 511 (2010).
[CrossRef]

Elliott, J.

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, Phys. Rev. Lett. 94, 057401 (2005).
[CrossRef] [PubMed]

Fink, M.

J. de Rosny and M. Fink, Phys. Rev. Lett. 89, 124301 (2002).
[CrossRef] [PubMed]

Guenneau, S.

S. Guenneau, A. Diatta, and R. C. McPhedran, J. Mod. Opt. 57, 511 (2010).
[CrossRef]

Hong, B. H.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Hwang, I.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Jouravlev, M. V.

D. R. Mason, M. V. Jouravlev, and K. S. Kim, Opt. Lett. 35, 2007 (2010).
[CrossRef] [PubMed]

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Kaufman, L. J.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Kildishev, A. V.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef] [PubMed]

Kim, K. S.

D. R. Mason, M. V. Jouravlev, and K. S. Kim, Opt. Lett. 35, 2007 (2010).
[CrossRef] [PubMed]

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Kim, P.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Kim, W. Y.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Kim, Y.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Reed, 1988).

Lee, J. Y.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Leonhardt, U.

U. Leonhardt, New J. Phys. 12, 058002 (2010).
[CrossRef]

U. Leonhardt, New J. Phys. 11, 093040 (2009).
[CrossRef]

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

Y. G. Ma, C. K. Ong, S. Sahebdivan, T. Tyc, and U. Leonhardt, “Perfect imaging without negative refraction for microwaves,” arXiv:1007.2530v1.

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Reed, 1988).

Ma, Y. G.

Y. G. Ma, C. K. Ong, S. Sahebdivan, T. Tyc, and U. Leonhardt, “Perfect imaging without negative refraction for microwaves,” arXiv:1007.2530v1.

Maradudin, A.

A. V. Zayats, I. I. Smolyaninov, and A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Mason, D. R.

McPhedran, R. C.

S. Guenneau, A. Diatta, and R. C. McPhedran, J. Mod. Opt. 57, 511 (2010).
[CrossRef]

Min, S. K.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Minano, J. C.

Ong, C. K.

Y. G. Ma, C. K. Ong, S. Sahebdivan, T. Tyc, and U. Leonhardt, “Perfect imaging without negative refraction for microwaves,” arXiv:1007.2530v1.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Sahebdivan, S.

Y. G. Ma, C. K. Ong, S. Sahebdivan, T. Tyc, and U. Leonhardt, “Perfect imaging without negative refraction for microwaves,” arXiv:1007.2530v1.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef] [PubMed]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef] [PubMed]

A. V. Zayats, I. I. Smolyaninov, and A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, Phys. Rev. Lett. 94, 057401 (2005).
[CrossRef] [PubMed]

Smolyaninova, V. N.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef] [PubMed]

Tyc, T.

Y. G. Ma, C. K. Ong, S. Sahebdivan, T. Tyc, and U. Leonhardt, “Perfect imaging without negative refraction for microwaves,” arXiv:1007.2530v1.

Wong, C. W.

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, Phys. Rev. Lett. 94, 057401 (2005).
[CrossRef] [PubMed]

J. Mod. Opt. (1)

S. Guenneau, A. Diatta, and R. C. McPhedran, J. Mod. Opt. 57, 511 (2010).
[CrossRef]

Nature (1)

J. Y. Lee, B. H. Hong, W. Y. Kim, S. K. Min, Y. Kim, M. V. Jouravlev, R. Bose, K. S. Kim, I. Hwang, L. J. Kaufman, C. W. Wong, P. Kim, and K. S. Kim, Nature 460, 498 (2009).
[CrossRef]

New J. Phys. (3)

U. Leonhardt, New J. Phys. 11, 093040 (2009).
[CrossRef]

R. J. Blaikie, New J. Phys. 12, 058001 (2010).
[CrossRef]

U. Leonhardt, New J. Phys. 12, 058002 (2010).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. Maradudin, Phys. Rep. 408, 131 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

I. I. Smolyaninov, J. Elliott, A. V. Zayats, and C. C. Davis, Phys. Rev. Lett. 94, 057401 (2005).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, Phys. Rev. Lett. 102, 213901 (2009).
[CrossRef] [PubMed]

J. de Rosny and M. Fink, Phys. Rev. Lett. 89, 124301 (2002).
[CrossRef] [PubMed]

Science (2)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[CrossRef] [PubMed]

U. Leonhardt, Science 312, 1777 (2006).
[CrossRef] [PubMed]

Other (2)

L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Reed, 1988).

Y. G. Ma, C. K. Ong, S. Sahebdivan, T. Tyc, and U. Leonhardt, “Perfect imaging without negative refraction for microwaves,” arXiv:1007.2530v1.

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Figures (7)

Fig. 1
Fig. 1

Typical profiles of a microdroplet that emulates either the fish-eye lens ( R = 7 μm ) or the inverted Eaton lens ( R = 5 μm ) for the following set of parameters: l = 1 , λ = 1.5 μm , n d = 1.5 , and n 1 = 0.65 .

Fig. 2
Fig. 2

Numerical simulations of imaging properties of the (a) fish-eye and (c) inverted Eaton lenses. Points near the edge of the fish-eye and Eaton lenses are imaged into opposite points. Refractive index distributions in these lenses are shown to their right in panels (b) and (d).

Fig. 3
Fig. 3

Experimental testing of the imaging mechanism of the glycerin microdroplets shown at different magnifications. The droplet is illuminated near the edge with the tapered fiber tip of an NSOM. The image of the NSOM tip is clearly seen at the opposite edge of the droplet.

Fig. 4
Fig. 4

Numerical simulations of image magnification ( M = 2 ) using the inverted Eaton lens. Since the sides of the lens play no role in imaging, the overall shape of the imaging device can be altered to achieve the shape of a “deformed droplet.”

Fig. 5
Fig. 5

Experimental testing of image magnification of the “deformed droplet.” The NSOM probe tip was moved along the droplet edge. The bottom row presents results of our numerical simulations in the cases of one and two point sources. The shape of the “deformed droplet” used in numerical simulations closely resembles the shape of the actual droplet.

Fig. 6
Fig. 6

“Deformed” glycerin droplets were formed in desired locations by (a) bringing a small probe wetted in glycerin into close proximity to a sample. The probe was prepared from a tapered optical fiber and has an epoxy microdroplet near its apex. Bringing the probe to a surface region covered with glycerin led to (b) a glycerin microdroplet formation under the probe.

Fig. 7
Fig. 7

Measurements of image magnification by the “deformed droplet”: position of the NSOM tip and its image in the second frame are shown by red dots (marked by arrows) in the first frame.

Equations (5)

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

ω 2 n d 2 c 2 = k x 2 + k y 2 + π 2 l 2 d ( r ) 2 ,
ω 2 n 2 ( r ) c 2 = k x 2 + k y 2 ,
d = l λ 2 n d 2 n 2 ( r ) .
n = 2 n 1 ( 1 + r 2 R 2 ) 1 ,
n = 1 for r < R , n = 2 R r 1 for r > R ,

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