Abstract

The energy streamline method based on the Poynting vector of the coupled forward and backward waves is used to study photon tunneling phenomenon associated with the lateral shift of energy path. Each point on the energy streamline indicates the direction of the net energy flow of a plane wave. In the tunneling configuration, the light energy of the propagating waves is squeezed to the inside of a cone, whereas the streamlines of the coupled evanescent waves go through the barrier inside or outside the cone. This observation provides insight of the photon tunneling phenomenon. A relationship between the energy refraction angle and the incidence angle exists in the proximity limit and can be used to evaluate the lateral shift of the energy path. Furthermore, the energy streamline method can help gain deeper understanding of nanoscale radiation where photon tunneling plays an important role in the heat transfer enhancement.

© 2006 Optical Society of America

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    [CrossRef]
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2006 (1)

C. J. Fu and Z. M. Zhang, "Nanoscale radiation heat transfer for silicon at different doping levels," Int. J. Heat Mass Transfer 49, 1703−1718 (2006).
[CrossRef]

2005 (6)

M.-C. Yang and K. J. Webb, "Poynting vector analysis of a superlens," Opt. Lett. 30, 2382−2384 (2005).
[CrossRef]

M. V. Bashevoy, V. A. Fedotov, and N. I. Zheludev, "Optical whirlpool on an absorbing metallic nanoparticle," Opt. Express 13, 8372−8379 (2005).
[CrossRef]

Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

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

Y.-Y. Chen, Z.-M. Huang, Q. Wang, C.-F. Li, and J.-L. Shi, "Photon tunnelling in one-dimensional metamaterial photonic crystals," J. Opt. A, Pure Appl. Opt. 7, 519−524 (2005).
[CrossRef]

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, and J. A. Kong, "Properties of left-handed metamaterials: Transmission, backward phase, negative refraction, and focusing," IEEE Trans. Microwave Theory Tech. 53, 2956−2967 (2005).

2004 (4)

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403−4405 (2004).
[CrossRef]

K.-Y. Kim, "Photon tunneling in composite layers of negative- and positive-index media," Phys. Rev. E 70, 047603 (2004).
[CrossRef]

J. B. Brock, A. A. Houck, and I. L. Chuang, "Focusing inside negative index materials," Appl. Phys. Lett. 85, 2472−2474 (2004).
[CrossRef]

T. J. Cui, Z.-C. Hao, X. X. Yin, W. Hong, and J. A. Kong, "Study of lossy effects on the propagation of propagating and evanescent waves in left-handed materials," Phys. Lett. A 323, 484−494 (2004).
[CrossRef]

2003 (5)

C.-F. Li, "Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects," Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef]

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling, and transparency," IEEE Trans. Antennas Propag. 51, 2558−2571 (2003).
[CrossRef]

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett 83, 2713−2715 (2003).
[CrossRef]

2002 (3)

Z. M. Zhang and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," Appl. Phys. Lett. 80, 1097−1099 (2002).
[CrossRef]

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, "Enhanced radiative heat transfer at nanometric distance," Microscale Thermophys. Eng. 6, 209−222 (2002).
[CrossRef]

J. Broe and O. Keller, "Quantum-well enhancement of the Goos-Hänchen shift for p-polarized beams in a two-prism configuration," J. Opt. Soc. Am. A 19, 1212−1222 (2002).

2001 (1)

A. I. Volokitin and B. N. J. Persson, "Radiative heat transfer between nanostructures," Phys. Rev. B 63, 205404 (2001)
[CrossRef]

2000 (2)

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, "Energy-flux pattern in the Goos-Hänchen effect," Phys. Rev. E 62, 7330-7339 (2000).
[CrossRef]

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

1994 (1)

A. M. Steinberg and R. Y. Chiao, "Tunneling delay times in one and two dimensions," Phys. Rev. A 49, 3283−3295 (1994).
[CrossRef]

1986 (1)

1902 (1)

E. E. Hall, "The penetration of totally reflected light into the rarer medium," Phys. Rev. Ser. I 15, 73−106 (1902).

Alù, A.

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling, and transparency," IEEE Trans. Antennas Propag. 51, 2558−2571 (2003).
[CrossRef]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Bashevoy, M. V.

Blaikie, R. J.

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403−4405 (2004).
[CrossRef]

Brock, J. B.

J. B. Brock, A. A. Houck, and I. L. Chuang, "Focusing inside negative index materials," Appl. Phys. Lett. 85, 2472−2474 (2004).
[CrossRef]

Broe, J.

Carminati, R.

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, "Enhanced radiative heat transfer at nanometric distance," Microscale Thermophys. Eng. 6, 209−222 (2002).
[CrossRef]

Chen, X.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, and J. A. Kong, "Properties of left-handed metamaterials: Transmission, backward phase, negative refraction, and focusing," IEEE Trans. Microwave Theory Tech. 53, 2956−2967 (2005).

Chen, Y.-Y.

Y.-Y. Chen, Z.-M. Huang, Q. Wang, C.-F. Li, and J.-L. Shi, "Photon tunnelling in one-dimensional metamaterial photonic crystals," J. Opt. A, Pure Appl. Opt. 7, 519−524 (2005).
[CrossRef]

Chiao, R. Y.

A. M. Steinberg and R. Y. Chiao, "Tunneling delay times in one and two dimensions," Phys. Rev. A 49, 3283−3295 (1994).
[CrossRef]

Chuang, I. L.

J. B. Brock, A. A. Houck, and I. L. Chuang, "Focusing inside negative index materials," Appl. Phys. Lett. 85, 2472−2474 (2004).
[CrossRef]

Chuang, S. L.

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Cui, T. J.

T. J. Cui, Z.-C. Hao, X. X. Yin, W. Hong, and J. A. Kong, "Study of lossy effects on the propagation of propagating and evanescent waves in left-handed materials," Phys. Lett. A 323, 484−494 (2004).
[CrossRef]

Engheta, N.

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling, and transparency," IEEE Trans. Antennas Propag. 51, 2558−2571 (2003).
[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]

Fedotov, V. A.

Foteinopolou, S.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Fu, C. J.

C. J. Fu and Z. M. Zhang, "Nanoscale radiation heat transfer for silicon at different doping levels," Int. J. Heat Mass Transfer 49, 1703−1718 (2006).
[CrossRef]

Z. M. Zhang and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," Appl. Phys. Lett. 80, 1097−1099 (2002).
[CrossRef]

Greffet, J.-J.

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, "Enhanced radiative heat transfer at nanometric distance," Microscale Thermophys. Eng. 6, 209−222 (2002).
[CrossRef]

Grzegorczyk, T. M.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, and J. A. Kong, "Properties of left-handed metamaterials: Transmission, backward phase, negative refraction, and focusing," IEEE Trans. Microwave Theory Tech. 53, 2956−2967 (2005).

Hall, E. E.

E. E. Hall, "The penetration of totally reflected light into the rarer medium," Phys. Rev. Ser. I 15, 73−106 (1902).

Hao, Z.-C.

T. J. Cui, Z.-C. Hao, X. X. Yin, W. Hong, and J. A. Kong, "Study of lossy effects on the propagation of propagating and evanescent waves in left-handed materials," Phys. Lett. A 323, 484−494 (2004).
[CrossRef]

Hong, W.

T. J. Cui, Z.-C. Hao, X. X. Yin, W. Hong, and J. A. Kong, "Study of lossy effects on the propagation of propagating and evanescent waves in left-handed materials," Phys. Lett. A 323, 484−494 (2004).
[CrossRef]

Houck, A. A.

J. B. Brock, A. A. Houck, and I. L. Chuang, "Focusing inside negative index materials," Appl. Phys. Lett. 85, 2472−2474 (2004).
[CrossRef]

Huang, Z.-M.

Y.-Y. Chen, Z.-M. Huang, Q. Wang, C.-F. Li, and J.-L. Shi, "Photon tunnelling in one-dimensional metamaterial photonic crystals," J. Opt. A, Pure Appl. Opt. 7, 519−524 (2005).
[CrossRef]

Joulain, K.

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, "Enhanced radiative heat transfer at nanometric distance," Microscale Thermophys. Eng. 6, 209−222 (2002).
[CrossRef]

Keller, O.

Kim, K.-Y.

K.-Y. Kim, "Photon tunneling in composite layers of negative- and positive-index media," Phys. Rev. E 70, 047603 (2004).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett 83, 2713−2715 (2003).
[CrossRef]

Kong, J. A.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, and J. A. Kong, "Properties of left-handed metamaterials: Transmission, backward phase, negative refraction, and focusing," IEEE Trans. Microwave Theory Tech. 53, 2956−2967 (2005).

T. J. Cui, Z.-C. Hao, X. X. Yin, W. Hong, and J. A. Kong, "Study of lossy effects on the propagation of propagating and evanescent waves in left-handed materials," Phys. Lett. A 323, 484−494 (2004).
[CrossRef]

Kwok, C. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, "Energy-flux pattern in the Goos-Hänchen effect," Phys. Rev. E 62, 7330-7339 (2000).
[CrossRef]

Lai, H. M.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, "Energy-flux pattern in the Goos-Hänchen effect," Phys. Rev. E 62, 7330-7339 (2000).
[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]

Li, C.-F.

Y.-Y. Chen, Z.-M. Huang, Q. Wang, C.-F. Li, and J.-L. Shi, "Photon tunnelling in one-dimensional metamaterial photonic crystals," J. Opt. A, Pure Appl. Opt. 7, 519−524 (2005).
[CrossRef]

C.-F. Li, "Negative lateral shift of a light beam transmitted through a dielectric slab and interaction of boundary effects," Phys. Rev. Lett. 91, 133903 (2003).
[CrossRef]

Loo, Y. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, "Energy-flux pattern in the Goos-Hänchen effect," Phys. Rev. E 62, 7330-7339 (2000).
[CrossRef]

Lu, J.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, and J. A. Kong, "Properties of left-handed metamaterials: Transmission, backward phase, negative refraction, and focusing," IEEE Trans. Microwave Theory Tech. 53, 2956−2967 (2005).

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

Lu, Z.

Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Melville, D. O. S.

D. O. S. Melville, R. J. Blaikie, and C. R. Wolf, "Submicron imaging with a planar silver lens," Appl. Phys. Lett. 84, 4403−4405 (2004).
[CrossRef]

Moss, C. D.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, and J. A. Kong, "Properties of left-handed metamaterials: Transmission, backward phase, negative refraction, and focusing," IEEE Trans. Microwave Theory Tech. 53, 2956−2967 (2005).

Mulet, J.-P.

J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, "Enhanced radiative heat transfer at nanometric distance," Microscale Thermophys. Eng. 6, 209−222 (2002).
[CrossRef]

Murakowski, J. A.

Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Pacheco, J.

T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, and J. A. Kong, "Properties of left-handed metamaterials: Transmission, backward phase, negative refraction, and focusing," IEEE Trans. Microwave Theory Tech. 53, 2956−2967 (2005).

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

Pendry, J. B.

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

Persson, B. N. J.

A. I. Volokitin and B. N. J. Persson, "Radiative heat transfer between nanostructures," Phys. Rev. B 63, 205404 (2001)
[CrossRef]

Prather, D. W.

Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Schneider, G. J.

Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Schuetz, C. A.

Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett 83, 2713−2715 (2003).
[CrossRef]

Shi, J.-L.

Y.-Y. Chen, Z.-M. Huang, Q. Wang, C.-F. Li, and J.-L. Shi, "Photon tunnelling in one-dimensional metamaterial photonic crystals," J. Opt. A, Pure Appl. Opt. 7, 519−524 (2005).
[CrossRef]

Shi, S.

Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, "Three-dimensional subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies," Phys. Rev. Lett. 95, 153901 (2005).
[CrossRef]

Soukoulis, C. M.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou, and C. M. Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

Steinberg, A. M.

A. M. Steinberg and R. Y. Chiao, "Tunneling delay times in one and two dimensions," Phys. Rev. A 49, 3283−3295 (1994).
[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]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: Imaging by flat lens using negative refraction," Nature 426, 404 (2003).
[CrossRef]

Volokitin, A. I.

A. I. Volokitin and B. N. J. Persson, "Radiative heat transfer between nanostructures," Phys. Rev. B 63, 205404 (2001)
[CrossRef]

Wang, Q.

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H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, "Energy-flux pattern in the Goos-Hänchen effect," Phys. Rev. E 62, 7330-7339 (2000).
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T. J. Cui, Z.-C. Hao, X. X. Yin, W. Hong, and J. A. Kong, "Study of lossy effects on the propagation of propagating and evanescent waves in left-handed materials," Phys. Lett. A 323, 484−494 (2004).
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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).
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C. J. Fu and Z. M. Zhang, "Nanoscale radiation heat transfer for silicon at different doping levels," Int. J. Heat Mass Transfer 49, 1703−1718 (2006).
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I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett 83, 2713−2715 (2003).
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Appl. Phys. Lett (1)

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett 83, 2713−2715 (2003).
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Z. M. Zhang and C. J. Fu, "Unusual photon tunneling in the presence of a layer with a negative refractive index," Appl. Phys. Lett. 80, 1097−1099 (2002).
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T. M. Grzegorczyk, C. D. Moss, J. Lu, X. Chen, J. Pacheco, and J. A. Kong, "Properties of left-handed metamaterials: Transmission, backward phase, negative refraction, and focusing," IEEE Trans. Microwave Theory Tech. 53, 2956−2967 (2005).

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C. J. Fu and Z. M. Zhang, "Nanoscale radiation heat transfer for silicon at different doping levels," Int. J. Heat Mass Transfer 49, 1703−1718 (2006).
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Y.-Y. Chen, Z.-M. Huang, Q. Wang, C.-F. Li, and J.-L. Shi, "Photon tunnelling in one-dimensional metamaterial photonic crystals," J. Opt. A, Pure Appl. Opt. 7, 519−524 (2005).
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J.-P. Mulet, K. Joulain, R. Carminati, and J.-J. Greffet, "Enhanced radiative heat transfer at nanometric distance," Microscale Thermophys. Eng. 6, 209−222 (2002).
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K.-Y. Kim, "Photon tunneling in composite layers of negative- and positive-index media," Phys. Rev. E 70, 047603 (2004).
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J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966−3969 (2000).
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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).
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