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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  1. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966−3969 (2000).
    [CrossRef] [PubMed]
  2. 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] [PubMed]
  3. J. B. Brock, A. A. Houck, and I. L. Chuang, "Focusing inside negative index materials," Appl. Phys. Lett. 85, 2472−2474 (2004).
    [CrossRef]
  4. 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] [PubMed]
  5. 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] [PubMed]
  6. 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]
  7. 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]
  8. 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]
  9. E. E. Hall, "The penetration of totally reflected light into the rarer medium," Phys. Rev. Ser. I 15, 73−106 (1902).
  10. 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]
  11. A. M. Steinberg and R. Y. Chiao, "Tunneling delay times in one and two dimensions," Phys. Rev. A 49, 3283−3295 (1994).
    [CrossRef] [PubMed]
  12. 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).
    [CrossRef]
  13. K.-Y. Kim, "Photon tunneling in composite layers of negative- and positive-index media," Phys. Rev. E 70, 047603 (2004).
    [CrossRef]
  14. 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]
  15. 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]
  16. 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]
  17. 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).
    [CrossRef]
  18. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  19. M. V. Bashevoy, V. A. Fedotov, and N. I. Zheludev, "Optical whirlpool on an absorbing metallic nanoparticle," Opt. Express 13, 8372−8379 (2005).
    [CrossRef] [PubMed]
  20. 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] [PubMed]
  21. M.-C. Yang and K. J. Webb, "Poynting vector analysis of a superlens," Opt. Lett. 30, 2382−2384 (2005).
    [CrossRef] [PubMed]
  22. S. L. Chuang, "Lateral shift of an optical beam due to leaky surface-plasomon excitations," J. Opt. Soc. Am. A 3, 593−599 (1986).
    [CrossRef]
  23. 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]
  24. A. I. Volokitin and B. N. J. Persson, "Radiative heat transfer between nanostructures," Phys. Rev. B 63, 205404 (2001)
    [CrossRef]
  25. 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]
  26. W. J. Choyke and E. D. Palik, "Silicon Carbide (SiC)," in Handbook of Optical Constants of Solids, (Academic Press, San Diego, CA, 1998).
  27. 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]

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)

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).
[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] [PubMed]

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

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] [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]

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]

2004 (4)

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

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]

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

2003 (5)

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] [PubMed]

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] [PubMed]

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]

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] [PubMed]

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)

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).
[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]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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).
[CrossRef]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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).
[CrossRef]

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).
[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]

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] [PubMed]

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] [PubMed]

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).
[CrossRef]

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] [PubMed]

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] [PubMed]

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).
[CrossRef]

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] [PubMed]

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] [PubMed]

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).
[CrossRef]

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] [PubMed]

Pendry, J. B.

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

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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] [PubMed]

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.

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]

Webb, K. J.

Wolf, C. R.

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]

Xu, B. Y.

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]

Yang, M.-C.

Yin, X. X.

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]

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).
[CrossRef] [PubMed]

Zhang, Z. M.

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]

Zharov, A. A.

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]

Zheludev, N. I.

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).
[CrossRef]

Appl. Phys. Lett. (3)

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

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]

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]

IEEE Trans. Antennas Propag. (1)

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]

IEEE Trans. Microwave Theory Tech. (1)

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).
[CrossRef]

Int. J. Heat Mass Transfer (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]

J. Opt. A, Pure Appl. Opt. (1)

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]

J. Opt. Soc. Am. A (2)

Microscale Thermophys. Eng. (1)

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]

Nature (1)

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] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (1)

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]

Phys. Rev. A (1)

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

Phys. Rev. B (1)

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

Phys. Rev. E (2)

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

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]

Phys. Rev. Lett. (4)

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

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] [PubMed]

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] [PubMed]

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] [PubMed]

Phys. Rev. Ser. I (1)

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

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).
[CrossRef] [PubMed]

Other (2)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

W. J. Choyke and E. D. Palik, "Silicon Carbide (SiC)," in Handbook of Optical Constants of Solids, (Academic Press, San Diego, CA, 1998).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic of the three layer structure in this study, where media 1 and 3 are semi-infinite, and medium 2 has a thickness of d. The incidence angle θ1 is determined by the wavevector. Each medium is linear, homogeneous, and isotropic. The complex permittivity and permeability, relative to vacuum, are given as ε’s and µ’s, whereas A’s and B’s are the coefficients of the forward and backward wave at the interface.

Fig. 2.
Fig. 2.

Energy streamlines for prism-DNG-prism and prism-SNG-prism configurations at various incidence angles: θ1=20° (solid), 30° (dotted), 41.81° (dash-dot), and 50° (dashed). The prism has ε=2.25 and µ=1, so θ1=41.81° corresponds to the critical angle for DNG in (a) and (b). Only evanescent waves exist in medium 2 for SNG in (c) and (d). The energy transmittance (T) from medium 1 to 3 is shown for each incidence angle. A different scale is used for the y axis in (d).

Fig. 3.
Fig. 3.

The energy streamline for vacuum-dielectric-vacuum configuration at θ1=30° when (a) d/λ=1 and (b) d/λ=0.01.

Fig. 4.
Fig. 4.

Photon tunneling in the vacuum gap sandwiched by semi-infinite SiC slabs when surface waves are excited at d=1 nm, 10 nm, or 100 nm: (a) exchange function due to evanescent waves and (b) normalized lateral shift. The shaded area in (a) and (b) corresponds to 31.4ω/c<ky <60.8ω/c.

Equations (9)

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H z ( x , y ) = [ A ( x ) e i k x x + B ( x ) e i k x x ] e i k y y
S x = 1 2 ω ε 0 Re ( k x ε ) [ A 2 e 2 β x B 2 e 2 β x ] 1 ω ε 0 Im ( k x ε ) Im ( A B * e 2 i η x )
S y = k y 2 ω ε 0 Re ( 1 ε ) [ A 2 e 2 β x + B 2 e 2 β x ] + k y ω ε 0 Re ( 1 ε ) Re ( A B * e 2 i η x )
B 1 = ξ 1 ξ 2 ( e i k 2 x d e i k 2 x d ) ζ
A 2 = 2 k 1 x ξ 1 e i k 2 x d ( ε 1 ζ )
B 2 = 2 k 1 x ξ 2 e i k 2 x d ( ε 1 ζ )
A 3 = 4 k 1 x k 2 x ( ε 1 ε 2 ζ )
ϕ 1 = θ 1 and tan ϕ 2 = ( ε 1 ε 2 ) tan ϕ 1
Z evan = Im ( r 21 p ) Im ( r 23 p ) e 2 Im ( k 2 x ) d 1 r 21 p r 23 p e 2 Im ( k 2 x ) d 2 , k y > ω c

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