Abstract

In this paper we theoretically study the left-handed behaviors in a two-dimensional triangular photonic crystal made of elliptical rods in air. An absolute left-handed region is found in the second photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Typical left-handed behaviors such as negative refraction, flat superlensing and plano-concave lensing are demonstrated by the finite-difference time-domain simulations. These behaviors are also compared with the quasi-negative refraction and the resulted focusing effects in a square-lattice two-dimensional photonic crystal.

© 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. R. A. Shelby, D. R. Smith and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  3. Hongsheng Chen, Lixin Ran, Jiantao, Huangfu, Xianmin Zhang, Kangsheng Chen, Tomasz M. Grzegorczyk and Jin Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
    [CrossRef]
  4. Ertugrul Cubukcu, Koray Aydin, Ekmel Ozbay Stavroula Foteinopoulou and Costas M. Soukoulis, “Negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
    [CrossRef] [PubMed]
  5. Patanjali V. Parimi, Wentao T. Lu, Plarenta Vodo and Srinivas Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404 (2003).
    [CrossRef] [PubMed]
  6. N.Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science 302, 1537-1540 (2003).
    [CrossRef] [PubMed]
  7. Evan J.Reed, Marin Soljacic and John D. Joannopoulos, “Reversed Doppler effect in photonic crystals,” Phys. Rev. Lett. 91, 133901 (2003).
    [CrossRef] [PubMed]
  8. Chiyan Luo, Mihai lbanescu, G. Johnson and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 368-371 (2003).
    [CrossRef] [PubMed]
  9. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  10. 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]
  11. 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]
  12. Nicholas Fang, Hyesog Lee, Cheng Sun and Xiang Zhang, “Sub-diffraction-limited optical imaging with a sliver superlens,” Science 308, 534-537 (2005).
    [CrossRef] [PubMed]
  13. 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]
  14. S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional Photonic Crystals,” Phys. Rev. B 67, 235107 (2003).
    [CrossRef]
  15. Pavel A. Belov, Constantin R. Simovski and Pekka Ikonen, “Canalization of subwavelength images by electromagnetic crystals,” Phys. Rev. B 71, 193105 (2005).
    [CrossRef]
  16. Alejandro Martinez and Javier Marti, “Analysis of wave focusing inside a negative photonic-crystal slab,” Opt. Express 13, 2858-2868 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-2858">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-2858</a>.
    [CrossRef] [PubMed]
  17. Chiyan Luo, Steven G. Johnson, J. D. Joannopoulos and J. B. Pendry, “All-negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  18. Chao-Hsien Kuo and Zhen Ye, “Flat lens imaging does not need negative refraction,” cond-mat/0312288 (2004).
  19. Chao-Hsien Kuo and Zhen Ye, “Optical transmission of photonic crystal structures formed by dielectric crystals: Evidence for non-negative refraction,” Phys. Rev. E 70, 056608 (2004).
    [CrossRef]
  20. Hung-Ta Chien, Hui-Ting Tang, Chao-Hsien Kuo, Chii-Chang Chen and Zhen Ye, “Direct diffraction without negative refraction,” Phys. Rev. B 70, 113101 (2004).
    [CrossRef]
  21. Liang-Shan Chen, Chao-Hsien Kuo and Zhen Ye, “Guiding optical flows by Photonic Crystal slabs made of dielectric cylinders,” Phys. Rev. E 69, 066612 (2004).
    [CrossRef]
  22. Chao-Hsien Kuo and Zhen Ye, “Negative-refraction-like behavior revealed by arrays of dielectric cylinders,” Phys. Rev. E 70, 026608 (2004).
    [CrossRef]
  23. R. Moussa, S. Foteinopoulou, Lei 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]
  24. Shuai Feng, Zhi-Yuan Li, Zhi-Fang Feng, Bing-Ying Cheng and Dao-Zhong Zhang, “Imaging properties of an elliptical-rod photonic-crystal slab lens,” Phys. Rev. B 72, 075101 (2005).
    [CrossRef]
  25. A.Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House INC, Norwood, 1995).
  26. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1991).
    [CrossRef]
  27. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).
  28. Zhaolin Lu, Caihua Chen, Christopher A. Schuetz, Shouyuan Shi, Janusz A. Murakowski, Garrett J. Schneider and Dennis W. Prather “Subwavelength imaging by a flat cylindrical lens using optimized negative refraction,” Appl. Phys. Lett. 87, 091907 (2005).
    [CrossRef]
  29. Xianyu Ao and Sailing He, “Negative refraction of left-handed behavior in porous alumina with infiltrated sliver at an optical wavelength,” Appl. Phys. Lett. 87, 101112 (2005).
    [CrossRef]
  30. Sanshui Xiao, Min Qiu, Zhichao Ruan and Sailing He, “Influence of the surface termination to the point imaging by a photonic crystals slab with negative refraction,” Appl. Phys. Lett. 85, 4269-4271 (2004).
    [CrossRef]
  31. X. Wang, Z. F. Ren and K.Kempa, “Unrestricted superlensing in a triangular two-dimensional photonic crystal,” Opt. Express 12, 2919-2924 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-2919">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-13-2919</a>.
    [CrossRef] [PubMed]
  32. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou1 and C. M. Soukoulis, “Subwavelength Resolution in a Two-Dimensional Photonic-Crystal- Based Superlens,” Phys. Rev. Lett. 91, 207401 (2003).
    [CrossRef] [PubMed]
  33. Zhixiang Tang, Hao Zhang, Runwu Peng, Yunxia Ye, Lei Shen, Shuangchun Wen and Dianyuan Fan, “ Two degenerate anisotropic modes in the experimental photonic crystal slab lens,” submitted to Opt. Commun (2005).

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]

Zhaolin Lu, Caihua Chen, Christopher A. Schuetz, Shouyuan Shi, Janusz A. Murakowski, Garrett J. Schneider and Dennis W. Prather “Subwavelength imaging by a flat cylindrical lens using optimized negative refraction,” Appl. Phys. Lett. 87, 091907 (2005).
[CrossRef]

Xianyu Ao and Sailing He, “Negative refraction of left-handed behavior in porous alumina with infiltrated sliver at an optical wavelength,” Appl. Phys. Lett. 87, 101112 (2005).
[CrossRef]

Sanshui Xiao, Min Qiu, Zhichao Ruan and Sailing He, “Influence of the surface termination to the point imaging by a photonic crystals slab with negative refraction,” Appl. Phys. Lett. 85, 4269-4271 (2004).
[CrossRef]

cond-mat

Chao-Hsien Kuo and Zhen Ye, “Flat lens imaging does not need negative refraction,” cond-mat/0312288 (2004).

J. Comput. Phys.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185-200 (1991).
[CrossRef]

Nature

Ertugrul Cubukcu, Koray Aydin, Ekmel Ozbay Stavroula Foteinopoulou and Costas M. Soukoulis, “Negative refraction by photonic crystals,” Nature 423, 604-605 (2003).
[CrossRef] [PubMed]

Patanjali V. Parimi, Wentao T. Lu, Plarenta Vodo and Srinivas Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404 (2003).
[CrossRef] [PubMed]

Opt. Commun

Zhixiang Tang, Hao Zhang, Runwu Peng, Yunxia Ye, Lei Shen, Shuangchun Wen and Dianyuan Fan, “ Two degenerate anisotropic modes in the experimental photonic crystal slab lens,” submitted to Opt. Commun (2005).

Opt. Express

Phys. Rev. B

Hung-Ta Chien, Hui-Ting Tang, Chao-Hsien Kuo, Chii-Chang Chen and Zhen Ye, “Direct diffraction without negative refraction,” Phys. Rev. B 70, 113101 (2004).
[CrossRef]

R. Moussa, S. Foteinopoulou, Lei 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]

Shuai Feng, Zhi-Yuan Li, Zhi-Fang Feng, Bing-Ying Cheng and Dao-Zhong 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]

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

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

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

Phys. Rev. E

Chao-Hsien Kuo and Zhen Ye, “Optical transmission of photonic crystal structures formed by dielectric crystals: Evidence for non-negative refraction,” Phys. Rev. E 70, 056608 (2004).
[CrossRef]

Hongsheng Chen, Lixin Ran, Jiantao, Huangfu, Xianmin Zhang, Kangsheng Chen, Tomasz M. Grzegorczyk and Jin Au Kong, “Left-handed materials composed of only S-shaped resonators,” Phys. Rev. E 70, 057605 (2004).
[CrossRef]

Liang-Shan Chen, Chao-Hsien Kuo and Zhen Ye, “Guiding optical flows by Photonic Crystal slabs made of dielectric cylinders,” Phys. Rev. E 69, 066612 (2004).
[CrossRef]

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

Phys. Rev. Lett.

E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopolou1 and C. M. Soukoulis, “Subwavelength Resolution in a Two-Dimensional Photonic-Crystal- Based Superlens,” Phys. Rev. Lett. 91, 207401 (2003).
[CrossRef] [PubMed]

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

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

Science

Chiyan Luo, Mihai lbanescu, G. Johnson and J. D. Joannopoulos, “Cerenkov radiation in photonic crystals,” Science 299, 368-371 (2003).
[CrossRef] [PubMed]

N.Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science 302, 1537-1540 (2003).
[CrossRef] [PubMed]

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

Nicholas Fang, Hyesog Lee, Cheng Sun and Xiang Zhang, “Sub-diffraction-limited optical imaging with a sliver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Sov. Phys. Usp.

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

Other

A.Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House INC, Norwood, 1995).

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).

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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematics of a triangular of array elliptical rods in air. (b) The photonic band structure for the TM polarization.

Fig. 2.
Fig. 2.

Several EFCs of the lowest two bands for the TM polarization.

Fig. 3.
Fig. 3.

Effective index of the second band vs. the normalized frequency.

Fig. 4.
Fig. 4.

The calculated effective index neff (θ) at the optimal frequency ω 0= 0.313.

Fig. 5.
Fig. 5.

Negative refractions for two incident angles: (a) φ = 30° and (b) φ = 60°.

Fig. 6.
Fig. 6.

The propagation maps for the flat superlens. The object distance is do = 2.75a for (a) and do ′ = 4.75a for (b). (a1) and (b1) are the snapshots of the electric field. (a2) and (b2) display the corresponding normalized average intensities over a period.

Fig. 7.
Fig. 7.

The transverse normalized field intensities of the source and the images.

Fig. 8.
Fig. 8.

(a) Focusing by plano-concave lens. (b)Field maps of the incident point source and the emerging plane wave.

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