Abstract

We demonstrate layered superlensing in two-dimensional photonic crystals structured by both square and triangular lattices. In virtue of equifrequency contour analysis and FDTD calculation, both near field and far field imaging are displayed. Layered superlensing consisting of only triangular lattice photonic crystal is also studied and it exhibits more flexibility than the single layer counterpart. That is, the objective distance can be changed freely while keeping the image distance constant and vice versa. Hence, farther field imaging is achieved.

© 2006 Optical Society of America

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  3. I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "BW media- media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett. 31, 129-133 (2001).
    [CrossRef]
  4. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  5. 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]
  6. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Technol. 47, 2075-2084 (1999).
    [CrossRef]
  7. L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," PIER 51, 249-279 (2005).
    [CrossRef]
  8. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  9. 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]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
    [CrossRef] [PubMed]
  13. 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]
  14. 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]
  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. 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]
  17. X. Zhang, "Image resolution depending on slab thickness and object distance in a two-dimensional photoniccrystal-based superlens," Phys. Rev. B 70, 195110 (2004).
    [CrossRef]
  18. X. Wang and K. Kempa, "Effects of disorder on subwavelength lensing in two-dimensional photonic crystal slabs," Phys. Rev. B 71, 085101 (2005).
    [CrossRef]
  19. A. Martinez and J. Marti, "Negative refraction in two-dimensional photonic crystals: Role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
    [CrossRef]
  20. A. Martinez and J. Marti, "Analysis of wave focusing inside a negative-index photonic-crystal slab," Opt. Express 13, 2858-2868 (2005).
    [CrossRef] [PubMed]
  21. C. Li, J. M. Holt, and A. L. Efros, "Far-field imaging by the Veselago lens made of a photonic crystal," J. Opt. Soc. Am. B 23, 490-497 (2006).
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    [CrossRef]
  26. K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
    [CrossRef]
  27. A. Taflove and S. C. Hagness, Computational Electrodynamics—the Finite-Difference Time-Domain Method (Artech House, Norwood, MA, 2000).
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    [CrossRef]

2006 (3)

2005 (4)

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

A. Martinez and J. Marti, "Negative refraction in two-dimensional photonic crystals: Role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
[CrossRef]

A. Martinez and J. Marti, "Analysis of wave focusing inside a negative-index photonic-crystal slab," Opt. Express 13, 2858-2868 (2005).
[CrossRef] [PubMed]

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," PIER 51, 249-279 (2005).
[CrossRef]

2004 (3)

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]

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]

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

2003 (4)

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, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a Negative Refractive Index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

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. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef] [PubMed]

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 (2)

R. W. Ziolkowski, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "BW media- media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett. 31, 129-133 (2001).
[CrossRef]

2000 (3)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

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 Theory Technol. 47, 2075-2084 (1999).
[CrossRef]

1996 (2)

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]

S. D. Gedney, "An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices," IEEE Trans. Antennas Propagat. 44, 1630-1639 (1996).
[CrossRef]

1991 (1)

M. Plihal, A. Shambrook, and A. A. Maradudin, "Two-dimensional photonic band structures," Optics Commun. 80, 3-4 (1991).
[CrossRef]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of and," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1966 (1)

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Aydin, K.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef] [PubMed]

Chen, H.

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," PIER 51, 249-279 (2005).
[CrossRef]

Cheng, K.

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," PIER 51, 249-279 (2005).
[CrossRef]

Cubukcu, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef] [PubMed]

De Raedt, H.

Economou, E. N.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a Negative Refractive Index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Efros, A. L.

Foteinopoulou, S.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a Negative Refractive Index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

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. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef] [PubMed]

Gedney, S. D.

S. D. Gedney, "An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices," IEEE Trans. Antennas Propagat. 44, 1630-1639 (1996).
[CrossRef]

Grzegorczyk, T. M.

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," PIER 51, 249-279 (2005).
[CrossRef]

He, S.

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 Theory Technol. 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]

Holt, J. M.

Huangfu, J.

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," PIER 51, 249-279 (2005).
[CrossRef]

Ilvonen, S.

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "BW media- media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett. 31, 129-133 (2001).
[CrossRef]

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]

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]

Kong, J. A.

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," PIER 51, 249-279 (2005).
[CrossRef]

Li, C.

Li, C. Y.

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]

Lindell, I. V.

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "BW media- media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett. 31, 129-133 (2001).
[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]

Maradudin, A. A.

M. Plihal, A. Shambrook, and A. A. Maradudin, "Two-dimensional photonic band structures," Optics Commun. 80, 3-4 (1991).
[CrossRef]

Marti, J.

A. Martinez and J. Marti, "Negative refraction in two-dimensional photonic crystals: Role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
[CrossRef]

A. Martinez and J. Marti, "Analysis of wave focusing inside a negative-index photonic-crystal slab," Opt. Express 13, 2858-2868 (2005).
[CrossRef] [PubMed]

Martinez, A.

A. Martinez and J. Marti, "Analysis of wave focusing inside a negative-index photonic-crystal slab," Opt. Express 13, 2858-2868 (2005).
[CrossRef] [PubMed]

A. Martinez and J. Marti, "Negative refraction in two-dimensional photonic crystals: Role of lattice orientation and interface termination," Phys. Rev. B 71, 235115 (2005).
[CrossRef]

Michielsen, K.

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Nikoskinen, K. I.

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "BW media- media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett. 31, 129-133 (2001).
[CrossRef]

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]

Ozbay, E.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef] [PubMed]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

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 Theory Technol. 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]

Plihal, M.

M. Plihal, A. Shambrook, and A. A. Maradudin, "Two-dimensional photonic band structures," Optics Commun. 80, 3-4 (1991).
[CrossRef]

Qiu, M.

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]

Ran, L.

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," PIER 51, 249-279 (2005).
[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 Theory Technol. 47, 2075-2084 (1999).
[CrossRef]

Ruan, Z.

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]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Shambrook, A.

M. Plihal, A. Shambrook, and A. A. Maradudin, "Two-dimensional photonic band structures," Optics Commun. 80, 3-4 (1991).
[CrossRef]

Shen, C.

Smith, D. R.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a Negative Refractive Index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

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. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, "Negative refraction by photonic crystals," Nature (London) 423, 604-605 (2003).
[CrossRef] [PubMed]

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 Theory Technol. 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]

Tretyakov, S. A.

I. V. Lindell, S. A. Tretyakov, K. I. Nikoskinen, and S. Ilvonen, "BW media- media with negative parameters, capable of supporting backward waves," Microwave Opt. Technol. Lett. 31, 129-133 (2001).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of and," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

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.

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]

Yee, K. S.

K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag. 14, 302-307 (1966).
[CrossRef]

Youngs, I.

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]

Zhang, X.

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Cheng, T. M. Grzegorczyk, and J. A. Kong, "Experimental study on several left-handed metamaterials," PIER 51, 249-279 (2005).
[CrossRef]

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

Ziolkowski, R. W.

R. W. Ziolkowski, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

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]

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Figures (4)

Fig. 1.
Fig. 1.

Calculated photonic band structures for (a) triangular 2D PC with air holes of radius r=0.4atri in dielectric matrix with ε=12.96 and (b) square 2D PC with dielectric rods in air, radius r=0.3asqua , ε=14. Frequencies for negative refraction are marked for (a) ω1 =0.306 and (b) ω2 =0.192.

Fig. 2.
Fig. 2.

Electric field distribution with frequency 0.306 *ωa/2πc for layered superlens structured by triangular lattice PC, varying the position of the two slabs. Geometric optics analysis are presented in the right column, wherein the PC is considered as an effective medium with n=-1.

Fig. 3.
Fig. 3.

Left: Equifrequency contour analysis of the refraction at the interface between the square lattice PC and triangular lattice PC whose normal are along the ΓΜ and ΓΚ directions. The incident (ki ) and refracted (kf ) wave vectors as well as the group velocity of incident wave (vgi ) and the refracted wave (vgf ) are shown. The dashed line represents the conservation of parallel component of wave vector. Right: Schematics representation of the refraction at the square-triangular lattice PC interface.

Fig. 4.
Fig. 4.

Electric field distribution of (a) square-triangular lattice layered PC slab with near field source, (b) square-triangular lattice layered PC slab with far field source, (c) triangular-square lattice layered PC slab with near field source, and (d) triangular-square lattice layered PC slab with far field source.

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