Abstract

The left-handed behavior of a photonic-crystal flat lens with a graded index in a honeycomb lattice is proposed and theoretically studied. The performance of the flat superlens imaging of this structure has been demonstrated by finite-difference time-domain simulations. The full width at half-maximum of the image decreases to 62% compared to that of the image of a photonic-crystal slab without a graded index. The evanescent waves can be amplified and propagate to the far-field range. The image is not limited to be near the interface. The canalization effect of this structure is analyzed, and the tolerance of the edge cut of the graded-index structure is pretty good.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. 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).
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2010

2007

D. Luo, J. Ning, Q. Han, Z. Chen, L. Shang, and G. Fan “Research of superlensing in a honeycomb lattice photonic crystal,” J. Optoelectron. Adv. Mater. 9, 2308–2311 (2007).

2006

R. Gaji, R. Meisels, F. Kuchar, and K. Hinger, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73, 165310 (2006).
[CrossRef]

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

2005

Z. Tang, R. Peng, D. Fan, S. Wen, H. Zhang, and L. Qian, “Absolute left-handed behaviors in a triangular elliptical-rod photonic crystal,” Opt. Express 13, 9796–9803 (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]

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

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

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005).
[CrossRef]

2004

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

W. Park and J. Lee, “Mechanically tunable photonic crystal structure,” Appl. Phys. Lett. 85, 4845–4847 (2004).
[CrossRef]

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

2003

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

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901 (2003).
[CrossRef] [PubMed]

C. LuoM. lbanescu, G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 368–371(2003).
[CrossRef] [PubMed]

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

2002

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-negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[CrossRef]

2001

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

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]

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

1968

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

Belov, P. A.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005).
[CrossRef]

Chen, H.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Chen, K.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Chen, Z.

D. Luo, J. Ning, Q. Han, Z. Chen, L. Shang, and G. Fan “Research of superlensing in a honeycomb lattice photonic crystal,” J. Optoelectron. Adv. Mater. 9, 2308–2311 (2007).

Fan, D.

Fan, G.

D. Luo, J. Ning, Q. Han, Z. Chen, L. Shang, and G. Fan “Research of superlensing in a honeycomb lattice photonic crystal,” J. Optoelectron. Adv. Mater. 9, 2308–2311 (2007).

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]

Gaji, R.

R. Gaji, R. Meisels, F. Kuchar, and K. Hinger, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73, 165310 (2006).
[CrossRef]

Garcia, N.

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

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Grzegorczyk, T. M.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Han, Q.

D. Luo, J. Ning, Q. Han, Z. Chen, L. Shang, and G. Fan “Research of superlensing in a honeycomb lattice photonic crystal,” J. Optoelectron. Adv. Mater. 9, 2308–2311 (2007).

Hao, Y.

P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime,” Phys. Rev. B 73, 113110 (2006).
[CrossRef]

He, S.

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

Hinger, K.

R. Gaji, R. Meisels, F. Kuchar, and K. Hinger, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73, 165310 (2006).
[CrossRef]

Huang, K.

Huangfu, J.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Ikonen, P.

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005).
[CrossRef]

Joannopoulos, J. D.

C. LuoM. lbanescu, G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 368–371(2003).
[CrossRef] [PubMed]

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901 (2003).
[CrossRef] [PubMed]

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

Johnson, G.

C. LuoM. lbanescu, G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 368–371(2003).
[CrossRef] [PubMed]

Johnson, S. G.

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

Kang, X.

Kong, J. A.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Kuchar, F.

R. Gaji, R. Meisels, F. Kuchar, and K. Hinger, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73, 165310 (2006).
[CrossRef]

lbanescu, M.

C. LuoM. lbanescu, G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 368–371(2003).
[CrossRef] [PubMed]

Lee, J.

W. Park and J. Lee, “Mechanically tunable photonic crystal structure,” Appl. Phys. Lett. 85, 4845–4847 (2004).
[CrossRef]

Li, K.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Li, Y.

Li, Z.

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

Lin, L.

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

Lu, W. T.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Lu, Z.

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

Luo, C.

C. LuoM. lbanescu, G. Johnson, and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 368–371(2003).
[CrossRef] [PubMed]

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

Luo, D.

D. Luo, J. Ning, Q. Han, Z. Chen, L. Shang, and G. Fan “Research of superlensing in a honeycomb lattice photonic crystal,” J. Optoelectron. Adv. Mater. 9, 2308–2311 (2007).

Meisels, R.

R. Gaji, R. Meisels, F. Kuchar, and K. Hinger, “All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals,” Phys. Rev. B 73, 165310 (2006).
[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]

Nielsen, J. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Nieto-Vesperinas, M.

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

Ning, J.

D. Luo, J. Ning, Q. Han, Z. Chen, L. Shang, and G. Fan “Research of superlensing in a honeycomb lattice photonic crystal,” J. Optoelectron. Adv. Mater. 9, 2308–2311 (2007).

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]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Parimi, P. V.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Park, W.

W. Park and J. Lee, “Mechanically tunable photonic crystal structure,” Appl. Phys. Lett. 85, 4845–4847 (2004).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-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]

Peng, R.

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]

Qian, L.

Qiu, M.

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

Ran, L.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Reed, E. J.

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901 (2003).
[CrossRef] [PubMed]

Ruan, Z.

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

Schneider, G. J.

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

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]

Shang, L.

D. Luo, J. Ning, Q. Han, Z. Chen, L. Shang, and G. Fan “Research of superlensing in a honeycomb lattice photonic crystal,” J. Optoelectron. Adv. Mater. 9, 2308–2311 (2007).

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]

Shi, P.

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]

Simovski, C. R.

P. A. Belov, C. R. Simovski, and P. Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005).
[CrossRef]

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]

Soljacic, M.

E. J. Reed, M. Soljacic, and J. D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901 (2003).
[CrossRef] [PubMed]

Soukoulis, C. M.

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. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Tang, Z.

Tanielian, M. H.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Thompson, M. A.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Thylén, L.

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

Vetter, A. M.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Vier, D. C.

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

Vodo, P.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

Wen, S.

Wu, Qi

Qi Wu, “Negative refraction by photonic nanostructure,” Ph.D. dissertation (University of Colorado at Boulder, 2008) Chap. 6, pp. 171–192.

Xiao, S.

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

Zhang, H.

Zhang, X.

H. Chen, L. Ran, J. Huangfu, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Appl. Phys. Lett.

P. Vodo, P. V. Parimi, W. T. Lu, and S. Sridhar, “Focusing by planoconcave lens using negative refraction,” Appl. Phys. Lett. 86, 201108 (2005).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, J. A. Nielsen, M. A. Thompson, K. Li, A. M. Vetter, M. H. Tanielian, and D. C. Vier, “Performance of a negative index of refraction lens,” Appl. Phys. Lett. 84, 3232–3234 (2004).
[CrossRef]

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[CrossRef]

J. Optoelectron. Adv. Mater.

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Opt. Express

Phys. Rev. B

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

Phys. Rev. E

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram for the imaging system formed by the 2D PC slab. The PC slab consists of a honeycomb lattice of silicon rods (black rods) with a radius of 0.24 a in an air matrix.

Fig. 2
Fig. 2

Normalized average intensities over a period for the flat superlens. The object distance is d o = 3.26 a and the image distance is d i = 15.86 a .

Fig. 3
Fig. 3

(a) FWHM of the image versus the number of layers. (b) Distance between images and the right interface of the PC slab ( d i ) versus the number of layers. The object distance is d o = 3.26 a .

Fig. 4
Fig. 4

Average intensities over a period for the graded-index flat superlens. The object distance is d o = 3.26 a and the image distance is d i = 3.26 a .

Fig. 5
Fig. 5

Band structure of a PC in a honeycomb lattice with radius of rods equal to 0.24 a . The red dotted and blue dashed–dotted curves represent the light lines of refractive index n eff equal to 1 and 1.45, respectively.

Fig. 6
Fig. 6

(a) FWHM of image dots varies with the edge cut of the left and right interfaces. (b) Location of image dots varies with the edge cut of the left and right interfaces.

Fig. 7
Fig. 7

Average intensities over a period for the graded-index flat superlens. The PC slab is cut 0.08 a in the left interface and 0.16 a in the right interface. The object distance is d o = 3.26 a , and the image distance is d i = 2.46 a .

Fig. 8
Fig. 8

Transverse normalized field intensities of the images of a 2D PC slab without a graded index and with a graded index.

Equations (1)

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r n = r ( N n ) / N * ( r r 1 ) ,

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