Abstract

A simple superlens formed by a one-dimensional dielectric photonic crystal is introduced. Off-axis subwavelength focusing is achieved and studied with the equifrequency contour analysis and finite-difference time-domain simulation. Besides its advantage of simplicity, the present superlens can give a spot size much smaller than that achieved by a slab of some high-dimensional photonic crystal of negative refraction. The properties of an on-axis image achieved by the combination of two slabs of the one-dimensional photonic crystal are also studied.

© 2008 Optical Society of America

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References

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of epsi 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. 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]
  4. 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]
  5. 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]
  6. S. He, Z. Ruan, L. Chen, and J. Shen, “Focusing properties of a photonic crystal slab with negative refraction,” Phys. Rev. B 70, 115113 (2004).
    [CrossRef]
  7. 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]
  8. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
    [CrossRef] [PubMed]
  9. H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
    [CrossRef]
  10. 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]
  11. S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, “Imaging properties of an elliptical-rod photonic-crystal slab lens,” Phys. Rev. B 72, 075101 (2005).
    [CrossRef]
  12. A. Taflove, Computational Electrodynamics--the Finite Difference Time-Domain Method (Artech, 1995).

2006

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[CrossRef]

2005

S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, “Imaging properties of an elliptical-rod photonic-crystal slab lens,” Phys. Rev. B 72, 075101 (2005).
[CrossRef]

2004

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]

S. He, Z. Ruan, L. Chen, and J. Shen, “Focusing properties of a photonic crystal slab with negative refraction,” Phys. Rev. B 70, 115113 (2004).
[CrossRef]

2003

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]

2002

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]

2000

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

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]

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]

1968

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

Appl. Phys. Lett.

H. Shin and S. Fan, “All-angle negative refraction and evanescent wave amplification using one-dimensional metallodielectric photonic crystals,” Appl. Phys. Lett. 89, 151102 (2006).
[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]

Phys. Rev. B

S. Feng, Z.-Y. Li, Z.-F. Feng, B.-Y. Cheng, and D.-Z. Zhang, “Imaging properties of an elliptical-rod photonic-crystal slab lens,” Phys. Rev. B 72, 075101 (2005).
[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, 10696-10705 (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]

S. He, Z. Ruan, L. Chen, and J. Shen, “Focusing properties of a photonic crystal slab with negative refraction,” Phys. Rev. B 70, 115113 (2004).
[CrossRef]

Phys. Rev. Lett.

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]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

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

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]

Sov. Phys. Usp.

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

Other

A. Taflove, Computational Electrodynamics--the Finite Difference Time-Domain Method (Artech, 1995).

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Figures (5)

Fig. 1
Fig. 1

(a) Projected band structure (TE polarization) for a 1D PhC. The horizontal line corresponds to the normalized frequency of 0.221. The inset shows the structure of the 1D PhC. (b) Equifrequency contours (EFCs) of the 1D PhC at the normalized frequency of 0.221. (c) Part of EFCs of band 1.

Fig. 2
Fig. 2

(a) Superlensing slab formed by terminating a 1D dielectric PhC. (b) Negatively (associated with point A ) and positively (associated with point B) refracted beams constructed from EFCs and conservation of k y . Bottom arrows indicate group-velocity directions. (c) Diagram for the principle of the present off-axis focusing.

Fig. 3
Fig. 3

Snapshots of the electric field ( E z ) for the PhC lens (indicated by the black solid lines) of thickness 2 a , 4 a , and 8 a when the point source is placed at x = 2 a , 3 a , 5 a in (a), (b), and (c), respectively.

Fig. 4
Fig. 4

Distribution of the electric field intensity at the transversal image plane when the surface termination angle ϕ varies. The thickness of the PhC slab is 4 a , and the point source is located at x = 3 a , y = 0 .

Fig. 5
Fig. 5

Snapshots of the electric field ( E z ) for a point source placed at x = 6 a , 8 a , 10 a , and 20 a in (a), (b), (c), and (d), respectively. The slab surfaces are indicated by the black solid lines, and the interface of the two slabs is marked by the dash-dotted line. (e) The distribution of the electric field intensity at the transversal image plane. The inset shows the on-axis superlens consisting of two slabs of the 1D PhC.

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