Abstract

We observe, by means of finite element calculations, that some photonic crystals produce negative refraction with almost circular isofrequency lines of their band diagram, so that a slab of this structure presents a large degree of isoplanatism and thus can behave like an imaging system. However, it has aberrations on comparison with a model of ideal lossless left-handed material within an effective medium theory. Further, we see that it does not produce subwavelength focusing. We discuss the limitations and requirements for such photonic crystal slabs to yield superresolved images of extended objects.

© 2007 Optical Society of America

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    [CrossRef]
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  4. A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
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  5. C. G. Parazzoli, R. B. Greegor, and K. Li, B. E. C. Koltenbach, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003).
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    [CrossRef] [PubMed]
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    [CrossRef]
  25. Z. Y. Li and L. L. Lin, "Evaluation of lensing in photonic crystal slabs exhibiting negative refraction," Phys. Rev. B 68, 245110 (2003).
    [CrossRef]
  26. X. Wang, Z. F. Ren and K. Kempa, "Improved superlensing in two-dimensional photonic crystals with a basis," Appl. Phys. Lett. 86, 061105 (2004).
    [CrossRef]
  27. R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis "Negative refraction and superlens behavior in a two-dimensional photonic crystal" Phys. Rev. B 71, 085106 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  36. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 18, 528 (1993).
    [CrossRef] [PubMed]
  37. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991)
    [CrossRef]

2006 (1)

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre and B. Gralak, "Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability," Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

2005 (4)

2004 (7)

M. Nieto-Vesperinas, "Problem of image superresolution with a negative-refractive-index slab," J. Opt. Soc. Am. A 21, 491 (2004).
[CrossRef]

J. L. Garcia-Pomar and M. Nieto-Vesperinas, "Transmission study of prisms and slabs of lossy negative index media," Opt. Express 12,2081 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2081>
[CrossRef] [PubMed]

X. Wang, Z. F. Ren and K. Kempa, "Improved superlensing in two-dimensional photonic crystals with a basis," Appl. Phys. Lett. 86, 061105 (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]

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]

R. Merlin, "Analytical solution of the almost-perfect-lens problem," Appl. Phys. Lett. 84, 1290 (2004).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

2003 (9)

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

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, and K. Li, B. E. C. Koltenbach, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

N.-C. Panoiu and R. M. Osgood, "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611 (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]

C. Luo, S. G. Johnson, J. D. Joannopoulos and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

D. N. Chigrin, S. Enoch C. M. Sotomayor-Torres and G. Tayeb, "Self-guiding in two-dimensional photonic crystals," Opt. Express 11, 1203 (2003). http://www.opticsexpress.org/abstract.cfm?uri=OE-11-10-1203>
[CrossRef] [PubMed]

2002 (3)

N. Garcia and M. Nieto-Vesperinas, "Is there an experimental verification of a negative index of refraction yet?," Opt. Lett. 27, 885 (2002).
[CrossRef]

N. Garcia and M. Nieto-Vesperinas, "Left-handed materials do not make a perfect lens," Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

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 (2)

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

R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811 (2001).
[CrossRef]

2000 (3)

B. Gralak, S. Enoch, G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012 (2000).
[CrossRef]

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 (2000)
[CrossRef]

1999 (2)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced non-linear phenomena," IEEE Trans. Microwave Theory Tech. MTT-47, 195 (1999).

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 (1999).
[CrossRef]

1993 (1)

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991)
[CrossRef]

1968 (1)

V. G. Veselago,"The electrodynamics of substances with simultanenous negative values of ∑ and μ," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Arjavalingam, G.

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]

Brock, J. B.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Brommer, K. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 18, 528 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991)
[CrossRef]

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]

Chigrin, D. N.

Chuang, I. L.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

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]

Decoopman, T.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre and B. Gralak, "Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability," Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

Derov, J. S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

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]

Enoch, S.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre and B. Gralak, "Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability," Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

B. Gralak, S. Enoch, G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012 (2000).
[CrossRef]

Etrich, C.

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]

Foteinopoulou, S.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis "Negative refraction and superlens behavior in a two-dimensional photonic crystal" Phys. Rev. B 71, 085106 (2005).
[CrossRef]

Garcia, N.

N. Garcia and M. Nieto-Vesperinas, "Is there an experimental verification of a negative index of refraction yet?," Opt. Lett. 27, 885 (2002).
[CrossRef]

N. Garcia and M. Nieto-Vesperinas, "Left-handed materials do not make a perfect lens," Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

Garcia-Pomar, J. L.

Gralak, B.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre and B. Gralak, "Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability," Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

B. Gralak, S. Enoch, G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012 (2000).
[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]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, and K. Li, B. E. C. Koltenbach, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

Guven, K.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis "Negative refraction and superlens behavior in a two-dimensional photonic crystal" Phys. Rev. B 71, 085106 (2005).
[CrossRef]

Halevi, P.

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 (1999).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced non-linear phenomena," IEEE Trans. Microwave Theory Tech. MTT-47, 195 (1999).

Houck, A. A.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

Iliew, R.

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

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]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 18, 528 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991)
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

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]

Kempa, K.

X. Wang, Z. F. Ren and K. Kempa, "Improved superlensing in two-dimensional photonic crystals with a basis," Appl. Phys. Lett. 86, 061105 (2004).
[CrossRef]

Koltenbach, B. E. C.

C. G. Parazzoli, R. B. Greegor, and K. Li, B. E. C. Koltenbach, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

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]

Lederer, F.

Li, K.

C. G. Parazzoli, R. B. Greegor, and K. Li, B. E. C. Koltenbach, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

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, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: 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, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

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]

Maystre, D.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre and B. Gralak, "Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability," Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

Meade, R. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 18, 528 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991)
[CrossRef]

Merlin, R.

R. Merlin, "Analytical solution of the almost-perfect-lens problem," Appl. Phys. Lett. 84, 1290 (2004).
[CrossRef]

Moussa, R.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis "Negative refraction and superlens behavior in a two-dimensional photonic crystal" Phys. Rev. B 71, 085106 (2005).
[CrossRef]

Narimanov, E. E.

Nieto-Vesperinas, M.

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 (2000)
[CrossRef]

Osgood, R. M.

N.-C. Panoiu and R. M. Osgood, "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611 (2003).
[CrossRef]

Ozbay, E.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis "Negative refraction and superlens behavior in a two-dimensional photonic crystal" Phys. Rev. B 71, 085106 (2005).
[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] [PubMed]

Panoiu, N.-C.

N.-C. Panoiu and R. M. Osgood, "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611 (2003).
[CrossRef]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, and K. Li, B. E. C. Koltenbach, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

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

Pendry, J. B.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

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 non-linear phenomena," IEEE Trans. Microwave Theory Tech. MTT-47, 195 (1999).

Podolskiy, V. A.

Ramakrishna, S. A.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Ramos-Mendieta, F.

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 (1999).
[CrossRef]

Rappe, A. M.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 18, 528 (1993).
[CrossRef] [PubMed]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991)
[CrossRef]

Ren, Z. F.

X. Wang, Z. F. Ren and K. Kempa, "Improved superlensing in two-dimensional photonic crystals with a basis," Appl. Phys. Lett. 86, 061105 (2004).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced non-linear phenomena," IEEE Trans. Microwave Theory Tech. MTT-47, 195 (1999).

Robertson, W. M.

Rosenbluth, M.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Ruppin, R.

R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811 (2001).
[CrossRef]

Schultz, S.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

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

Schurig, D.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

Shelby, R. A.

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

Smith, D. R.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

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

Sokoloff, J.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis "Negative refraction and superlens behavior in a two-dimensional photonic crystal" Phys. Rev. B 71, 085106 (2005).
[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] [PubMed]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals: 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 non-linear phenomena," IEEE Trans. Microwave Theory Tech. MTT-47, 195 (1999).

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]

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, and K. Li, B. E. C. Koltenbach, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

Tayeb, G.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre and B. Gralak, "Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability," Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

B. Gralak, S. Enoch, G. Tayeb, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012 (2000).
[CrossRef]

Tuttle, G.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis "Negative refraction and superlens behavior in a two-dimensional photonic crystal" Phys. Rev. B 71, 085106 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago,"The electrodynamics of substances with simultanenous negative values of ∑ and μ," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

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

Wang, X.

X. Wang, Z. F. Ren and K. Kempa, "Improved superlensing in two-dimensional photonic crystals with a basis," Appl. Phys. Lett. 86, 061105 (2004).
[CrossRef]

Ye, Z.

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]

Zhang, L.

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis "Negative refraction and superlens behavior in a two-dimensional photonic crystal" Phys. Rev. B 71, 085106 (2005).
[CrossRef]

Appl. Phys. Lett. (3)

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, "Limitations on subdiffraction imaging with a negative refractive index slab," Appl. Phys. Lett. 82, 1506 (2003).
[CrossRef]

R. Merlin, "Analytical solution of the almost-perfect-lens problem," Appl. Phys. Lett. 84, 1290 (2004).
[CrossRef]

X. Wang, Z. F. Ren and K. Kempa, "Improved superlensing in two-dimensional photonic crystals with a basis," Appl. Phys. Lett. 86, 061105 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced non-linear phenomena," IEEE Trans. Microwave Theory Tech. MTT-47, 195 (1999).

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

J. Phys.: Condens. Matter (1)

R. Ruppin, "Surface polaritons of a left-handed material slab," J. Phys.: Condens. Matter 13, 1811 (2001).
[CrossRef]

Nature (London) (1)

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

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. B (8)

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 (1999).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 (1991)
[CrossRef]

R. Moussa, S. Foteinopoulou, L. Zhang, G. Tuttle, K. Guven, E. Ozbay, and C. M. Soukoulis "Negative refraction and superlens behavior in a two-dimensional photonic crystal" Phys. Rev. B 71, 085106 (2005).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[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]

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

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 (2000)
[CrossRef]

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]

Phys. Rev. E (1)

N.-C. Panoiu and R. M. Osgood, "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611 (2003).
[CrossRef]

Phys. Rev. Lett. (8)

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

N. Garcia and M. Nieto-Vesperinas, "Left-handed materials do not make a perfect lens," Phys. Rev. Lett. 88, 207403 (2002).
[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. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell’s law," Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, and K. Li, B. E. C. Koltenbach, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, "Negative refraction and left-handed electromagnetism in microwave photonic crystals," Phys. Rev. Lett. 92, 127401 (2004).
[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]

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre and B. Gralak, "Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability," Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

Science (1)

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

Sov. Phys. Usp. (1)

V. G. Veselago,"The electrodynamics of substances with simultanenous negative values of ∑ and μ," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (3)

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

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1968).

A. L. Efros, C. Y. Li, and A. L. Pokrovsky, "Evanescent waves in photonic crystals and image of Veselago lens," cond-mat/0503494(2005)

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Figures (15)

Fig. 1.
Fig. 1.

(a) Geometry of the numerical simulation for the PC slab of air cylinders in a dielectric matrix with ε = 12.96. The wave source is at distance z 0 from the slab limiting interface. (b) Brillouin zone for the hexagonal PC and symmetry points.

Fig. 2.
Fig. 2.

(a)Band diagram, obtained using a plane wave expansion calculation, for the hexagonal lattice of air cylinders in a dielectric matrix with ε = 12.96. The red line corresponding to the range of frequencies used, cuts the second band in such a way that there is a circle-like isofrequency about the Γ point. The corresponding frequency surface gradient is negative and so is the group velocity. The light line (broken) is also shown. (b) Second band for ΓK (solid line) and ΓM (dashed line) directions, showing the differences, at used frequencies, of wavevector distances from the Γ point to the K and M points, (bottom inset), as well as the corresponding deformation of the corresponding isofrequency from a circle, (top inset) for λ = 3.36a.

Fig. 3.
Fig. 3.

Map of the modulus of the electric field Ey for a narrow slit which acts like point source (down) with a λ = 3.28a in front of a 2-D hexagonal photonic crystal. We observe a focus both inside and out the crystal. The outer focus is elongated as a consequence of aberrations. (White spots in the color distribution indicate that the value is out of the color scale on the right).

Fig. 4.
Fig. 4.

Modulus of the real part of the transfer function (i.e. Fourier transform of the image of a point source) produced by a hexagonal PC of air holes in a dielectric matrix with permittivity ε = 12.96, lattice constant a and radius r = 0.4a, at different wavelengths. We observe that their widths do not exceed the Rayleigh limit of resolution 1/λ.

Fig. 5.
Fig. 5.

Modulus of the real part of the transfer function (Fourier transform of the image of a point source) produced by a hexagonal PC of air holes in a dielectric matrix with permittivity ε = 12.96 for λ = 3.32a, at different distances z 0 and different thickness d = 2z 0 of the source from the slab. Their widths do not exceed those of the Rayleigh limit of resolution 1/λ, although the source is in near field.

Fig. 6.
Fig. 6.

Electric field amplitude distribution of an extended object wavefront for λ = 3.28a measured at a distance z 0 from the slab (red dashed line); which does not demand superresolution details. Its image obtained from the transfer function via by Fourier transform, as explained in the text, is shown in the green dotted line. The image obtained by propagation FE simulation (black solid line) is very similar to the latter.

Fig. 7.
Fig. 7.

Aberrations analyzed by means of a ray tracing for: (a) A PC illuminated by a point source with λ = 3.32a, where we have considered only the aberration due to the deformation of the isofrequency from a circle one, (namely, the surrounding medium has a refractive index that equals the averaged effective one of the crystal slab). (b) The same illuminated PC where we have also taken into account that the surrounding medium is air. This is the real situation of the FE simulation. We consider both the aberration caused by deformation in the isofrequency from a circle and that caused by difference between effective refractive index of the PC and the surrounding medium (air) (λ = 3.36a). (c) Same as (b) with the numeric simulation and λ = 3.32a; we observe agreement between ray tracing and FE simulation. This agreement is clear both in the position and depth of the focus obtained by both methods. (d) Distances ∆x (white symbols) and ∆y (black symbols) corresponding to the lateral and longitudinal aberration, respectively, for the case in which the configuration is that of Fig. (a)(circles and red line) and for the case in which is that of Fig. (b) (squares and blue line). These distances are referred to the caustic vertex in the paraxial focus.

Fig. 8.
Fig. 8.

(a)-(c) Map of the modulus |Ey | of the electric field for a slit emitting in front of left handed slab with n̂ = -1 + i0.001 for different distances z 0 in terms of the wavelength λ. (d) Modulus of the electric field measured on the exit plane of the slit, namely, at distance z 0 from the slab entrance interface. This magnitude is evaluated both with and without the presence of the LHM slab, both profiles are indistinguishable from each other.

Fig. 9.
Fig. 9.

Modulus of the real part of the transfer function (Fourier transform of the image of a point source) produced by a LHM with real part of the refractive index n 1 = -1 and imaginary part n 2 = 0.05 at different distances z 0 of the source from the slab. We observe that their widths exceed those limited by the Rayleigh limit of resolution 1/λ.

Fig. 10.
Fig. 10.

Electric field modulus |E| (normalized to the value in the exit of the slit) versus z coordinate for different distances z 0 from the slit to the slab. We observe an increasing of the modulus |E| on the interfaces and a suppression of the resolution in the focus along oz as z 0 decreases.

Fig. 11.
Fig. 11.

(a)-(c) Electric field amplitude Ey of an extended object containing subwavelength details (red solid line) and its image by a LHM slab for different distances z 0 and different thickness of the slab d = 2z 0. The image obtained via the transfer function is shown by the blue dashed line. The image obtained from the propagation simulation by the FE calculation is displayed by the black dotted line. (d) Electric field amplitude measured at distance z 0 from the slab entrance interface. This magnitude is evaluated both with and without the presence of the LHM slab (black solid line and red dashed line, respectively), both profiles are indistinguishable from each other except the slight differences in the tails.

Fig. 12.
Fig. 12.

(a) Total internal reflection at 45 degrees in a dielectric prism with n=3.5 below the photonic crystal slab. An evanescent wave is transmitted and incides on the crystal (b) Variation of the evanescent wave intensity along the depth (z-coordinate) of the crystal.

Fig. 13.
Fig. 13.

Condition for superresolution of a superlens with real part of the permittivity ε ≈ - 1 at a working frequency ωp /√2, ωp being the plasma frequency. Due to the fact that excited surface plasmons (green dashed line) have high value of the wavevector kx , the hyperbolic condition Eq. (8) in the evanescent zone (blue solid line) is satisfied for the wavevector kx of all evanescent components of the incident wavefront, since for high kx this condition becomes the asymptotic straight line kz = ikx (red dotted line) which corresponds to the flat zone of the dispersion relation (green dashed line)

Fig. 14.
Fig. 14.

Surface mode dispersion curve (red line) in the second band for TE polarization (Electric field parallel to the prisms). The surface mode is ”flat”, which implies that all those kx wavevectors at the the right of the light line included in the definition domain of this red segment are permitted in the surface at practically the same frequency of excitation.

Fig. 15.
Fig. 15.

(a) Map of the modulus of an extended object wavefront in the bottom inciding on a photonic crystal (b) Corresponding intensity of extended object wavefront (blue solid line) and its image by a crystal whose exit interface is cut such that a surface mode is either not excited (red dotted line) or excited (black dashed line) at the frequency ω = 0.345 × 2πc/a (i.e.λ = 2.898a)

Equations (10)

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

i ( x ) = o ( x′ ) P ( x x′ ) dx .
k z = k x 2 k 0 2 ,
k z = k′ x 2 k 0 2 n′ 2 ,
k z = k′ x 2 k 0 2 n′ 2 , = k 0 n s′ 2 1 =
k 0 i s 2 1 = k 0 s 2 + 1 ,
ε ( ω ) = 1 ω p 2 ω ( ω + i τ ) ωτ < < 1 1 ω p 2 ω 2
k x ( ω ) = ω c ε ( ω ) ε ( ω ) + 1 .
ω sp = ω p 2
k z = i k x ε ( ω ) ω 2 c 2
k z = i k x

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