Abstract

We analyze focusing of electromagnetic waves inside a photonic crystal slab by means of finite-difference time-domain simulations. At the frequency of the source, the photonic crystal behaves as an effective medium with an effective index of refraction of -1. Despite of the strong Bloch modulation of the field inside the slab, the presence of a well-definite internal focus is evident. The dimensions of the internal focus are similar to those of the external focus. The effect of the frequency of the wave on the focusing is also discussed.

© 2005 Optical Society of America

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [CrossRef]
  2. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Tech. 47, 2075–2084 (1999).
    [CrossRef]
  4. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
    [CrossRef] [PubMed]
  5. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef] [PubMed]
  6. A. Grbic and G. V. Eleftheriades, “Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens,” Phys. Rev. Lett. 92, 117403 (2004).
    [CrossRef] [PubMed]
  7. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
    [CrossRef]
  8. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
    [CrossRef]
  9. S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
    [CrossRef]
  10. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  11. A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical study of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
    [CrossRef]
  12. H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70, 113101 (2004).
    [CrossRef]
  13. C.-H. Kuo and Z. Ye, “Negative-refraction-like behavior revealed by arrays of dielectric cylinders,” Phys. Rev. E 70, 026608 (2004).
    [CrossRef]
  14. P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, “Imaging by flat lens using negative refraction,” Nature (London) 426, 404 (2003).
    [CrossRef]
  15. Z.-Y. Li and L.-L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
    [CrossRef]
  16. X. Wang, Z. F. Ren, and K. Kempa, “Unrestricted superlensing in a triangular two-dimensional photonic crystal,” Opt. Express 12, 2919–2924 (2004).
    [CrossRef] [PubMed]
  17. A. Martínez and J. Martí, submitted to Phys. Rev. B.
  18. A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
    [CrossRef] [PubMed]
  19. S. Xiao, M. Qiu, Z. Ruan, and S. He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269–4271 (2004).
    [CrossRef]
  20. K. Guven, K. Aydin, K. B. Alici, C. M. Soukoulis, and E. Ozbay, “Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens,” Phys Rev. B 70, 205125 (2004).
    [CrossRef]
  21. X. Zhang, “Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. B 70, 195110 (2004).
    [CrossRef]
  22. X. Wang and K. Kempa, “Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs,” Phys. Rev. B 71, 085101 (2005).
    [CrossRef]
  23. A. Taflove, Computational Electrodynamics—The Finite Difference Time-Domain Method (Artech House, Boston, 1995).
  24. J. P. Berenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,” J. Comput. Phys. 114, 185–200 (1994).
    [CrossRef]
  25. Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, “Coupling between plane waves and Bloch waves in photonic crystals with negative refraction,” Phys. Rev. B 71, 045111 (2005).
    [CrossRef]
  26. X. Ao and S. He, “Three-dimensional photonic crystal of negative refraction achieved by interference lithography,” Opt. Lett. 29, 2542–2544 (2004).
    [CrossRef] [PubMed]

2005 (2)

X. Wang and K. Kempa, “Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs,” Phys. Rev. B 71, 085101 (2005).
[CrossRef]

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, “Coupling between plane waves and Bloch waves in photonic crystals with negative refraction,” Phys. Rev. B 71, 045111 (2005).
[CrossRef]

2004 (10)

X. Ao and S. He, “Three-dimensional photonic crystal of negative refraction achieved by interference lithography,” Opt. Lett. 29, 2542–2544 (2004).
[CrossRef] [PubMed]

A. Grbic and G. V. Eleftheriades, “Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef] [PubMed]

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical study of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70, 113101 (2004).
[CrossRef]

C.-H. Kuo and Z. Ye, “Negative-refraction-like behavior revealed by arrays of dielectric cylinders,” Phys. Rev. E 70, 026608 (2004).
[CrossRef]

X. Wang, Z. F. Ren, and K. Kempa, “Unrestricted superlensing in a triangular two-dimensional photonic crystal,” Opt. Express 12, 2919–2924 (2004).
[CrossRef] [PubMed]

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

S. Xiao, M. Qiu, Z. Ruan, and S. He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269–4271 (2004).
[CrossRef]

K. Guven, K. Aydin, K. B. Alici, C. M. Soukoulis, and E. Ozbay, “Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens,” Phys Rev. B 70, 205125 (2004).
[CrossRef]

X. Zhang, “Image resolution depending on slab thickness and object distance in a two-dimensional photonic-crystal-based superlens,” Phys. Rev. B 70, 195110 (2004).
[CrossRef]

2003 (3)

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

Z.-Y. Li and L.-L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
[CrossRef]

2002 (1)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

2000 (2)

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

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Tech. 47, 2075–2084 (1999).
[CrossRef]

1998 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

1994 (1)

J. P. Berenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Alici, K. B.

K. Guven, K. Aydin, K. B. Alici, C. M. Soukoulis, and E. Ozbay, “Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens,” Phys Rev. B 70, 205125 (2004).
[CrossRef]

Anand, S.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Ao, X.

Aydin, K.

K. Guven, K. Aydin, K. B. Alici, C. M. Soukoulis, and E. Ozbay, “Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens,” Phys Rev. B 70, 205125 (2004).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,” J. Comput. Phys. 114, 185–200 (1994).
[CrossRef]

Berrier, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Chen, C.-C.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70, 113101 (2004).
[CrossRef]

Chien, H.-T.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70, 113101 (2004).
[CrossRef]

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, “Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef] [PubMed]

Foteinopoulou, S.

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Grbic, A.

A. Grbic and G. V. Eleftheriades, “Overcoming the Diffraction Limit with a Planar Left-Handed Transmission-Line Lens,” Phys. Rev. Lett. 92, 117403 (2004).
[CrossRef] [PubMed]

Griol, A.

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical study of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

Guven, K.

K. Guven, K. Aydin, K. B. Alici, C. M. Soukoulis, and E. Ozbay, “Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens,” Phys Rev. B 70, 205125 (2004).
[CrossRef]

He, S.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, “Coupling between plane waves and Bloch waves in photonic crystals with negative refraction,” Phys. Rev. B 71, 045111 (2005).
[CrossRef]

X. Ao and S. He, “Three-dimensional photonic crystal of negative refraction achieved by interference lithography,” Opt. Lett. 29, 2542–2544 (2004).
[CrossRef] [PubMed]

S. Xiao, M. Qiu, Z. Ruan, and S. He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269–4271 (2004).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Tech. 47, 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Kempa, K.

X. Wang and K. Kempa, “Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs,” Phys. Rev. B 71, 085101 (2005).
[CrossRef]

X. Wang, Z. F. Ren, and K. Kempa, “Unrestricted superlensing in a triangular two-dimensional photonic crystal,” Opt. Express 12, 2919–2924 (2004).
[CrossRef] [PubMed]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Kuo, C.-H.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70, 113101 (2004).
[CrossRef]

C.-H. Kuo and Z. Ye, “Negative-refraction-like behavior revealed by arrays of dielectric cylinders,” Phys. Rev. E 70, 026608 (2004).
[CrossRef]

Li, Z.-Y.

Z.-Y. Li and L.-L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[CrossRef]

Lin, L.-L.

Z.-Y. Li and L.-L. Lin, “Evaluation of lensing in photonic crystal slabs exhibiting negative refraction,” Phys. Rev. B 68, 245110 (2003).
[CrossRef]

Lu, W. T.

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

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Martí, J.

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical study of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

A. Martínez and J. Martí, submitted to Phys. Rev. B.

Martínez, A.

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical study of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

A. Martínez and J. Martí, submitted to Phys. Rev. B.

Míguez, H.

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical study of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

Mulot, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Ozbay, E.

K. Guven, K. Aydin, K. B. Alici, C. M. Soukoulis, and E. Ozbay, “Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens,” Phys Rev. B 70, 205125 (2004).
[CrossRef]

Parimi, P. V.

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

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

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

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Tech. 47, 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

Qiu, M.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, “Coupling between plane waves and Bloch waves in photonic crystals with negative refraction,” Phys. Rev. B 71, 045111 (2005).
[CrossRef]

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

S. Xiao, M. Qiu, Z. Ruan, and S. He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269–4271 (2004).
[CrossRef]

Ren, Z. F.

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Tech. 47, 2075–2084 (1999).
[CrossRef]

Ruan, Z.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, “Coupling between plane waves and Bloch waves in photonic crystals with negative refraction,” Phys. Rev. B 71, 045111 (2005).
[CrossRef]

S. Xiao, M. Qiu, Z. Ruan, and S. He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269–4271 (2004).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

K. Guven, K. Aydin, K. B. Alici, C. M. Soukoulis, and E. Ozbay, “Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens,” Phys Rev. B 70, 205125 (2004).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Sridhar, S.

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

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Tech. 47, 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef] [PubMed]

Swillo, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Taflove, A.

A. Taflove, Computational Electrodynamics—The Finite Difference Time-Domain Method (Artech House, Boston, 1995).

Talneau, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Tang, H.-T.

H.-T. Chien, H.-T. Tang, C.-H. Kuo, C.-C. Chen, and Z. Ye, “Directed diffraction without negative refraction,” Phys. Rev. B 70, 113101 (2004).
[CrossRef]

Thylen, L.

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, “Coupling between plane waves and Bloch waves in photonic crystals with negative refraction,” Phys. Rev. B 71, 045111 (2005).
[CrossRef]

Thylén, L.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, “Negative refraction at infrared wavelengths in a two-dimensional photonic crystal,” Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096–10099 (1998).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Vodo, P.

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

Wang, X.

X. Wang and K. Kempa, “Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs,” Phys. Rev. B 71, 085101 (2005).
[CrossRef]

X. Wang, Z. F. Ren, and K. Kempa, “Unrestricted superlensing in a triangular two-dimensional photonic crystal,” Opt. Express 12, 2919–2924 (2004).
[CrossRef] [PubMed]

Xiao, S.

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S. Xiao, M. Qiu, Z. Ruan, and S. He, “Influence of the surface termination to the point imaging by a photonic crystal slab with negative refraction,” Appl. Phys. Lett. 85, 4269–4271 (2004).
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Figures (10)

Fig. 1.
Fig. 1.

(a) Photonic band diagram (transverse magnetic modes) of the proposed PhC; (b) effective index of refraction of the second photonic band.

Fig. 2.
Fig. 2.

Scenario under study: a PhC slab with thickness L oriented so that the interfaces are along the ΓK direction. Slab terminations are carefully chosen to ensure the excitation of a surface mode. Several sets of electric field monitors are placed in the structure under analysis: lines A, B, C, D, E and F. The optical source is placed at z=-L and radiates upwards.

Fig. 3.
Fig. 3.

Electric field distribution for the scenario described in Fig. 2. Gaussian source with initial width 0.4λ and frequency a/λ=0.306. The PhC slab thickness is L=(11.5 3-0.4)a=19.52a. The snapshots show different time steps of an FDTD simulation.

Fig. 4.
Fig. 4.

Time-space evolution of the field intensity at the NIL output. (a) Longitudinal direction; (b) transversal direction.

Fig. 5.
Fig. 5.

(a) Longitudinal and (b) transversal profiles of the field intensity in the external focus.

Fig. 6.
Fig. 6.

(a) Longitudinal profile of the field intensity inside the NIL along line C. The intensity produced by a point source (blue solid curve) and a plane-like wave (black dashed curve) are compared. (b) Time-space evolution of the field intensity inside the NIL along the longitudinal direction.

Fig. 7.
Fig. 7.

(a) Transversal profile of the field intensity inside the NIL along line E. The intensity produced by a point source (blue solid curve) and a plane-like wave (black dashed curve) are compared. (b) Time-space evolution of the field intensity inside the NIL along the transversal direction.

Fig. 8.
Fig. 8.

Transversal profiles of the field intensity inside the NIL along lines D (black), E (blue) and F (red) for L=19.52a.

Fig. 9.
Fig. 9.

(a) Longitudinal and (b) transversal intensity patterns for the internal focus in the cases of a slab with dielectric (black curve) or a hole (blue curve) at its center. For the sake of comparison, the red curve shows the profiles of the external focus with the intensity double In order to get a better visual comparison. the longitudinal external pattern in (a) is represented inverted with respect to z=L/2.

Fig. 10.
Fig. 10.

Longitudinal intensity patterns for three different frequencies of the source: a/λ=0.296 (red), 0.306 (blue) and 0.32 (black). The vertical dotted line stands for the PhC-air output interface.

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