Abstract

A novel dual-negative-refraction (DNR) effect is studied in two types of normal two-dimensional photonic crystals (2DPCs) with hexagonal lattices. Systematical analyses of the band structures and equifrequency surfaces indicate that the DNR may be realized when the overlapping second and third bands with relatively flat shapes and only a slight separation are available at some frequencies close to the band’s peak of 2DPCs. Further simulations have not only confirmed the DNR and corresponding dual-imaging effects in normal 2DPCs with hexagonal lattices but also revealed some relative rules to the dual images. In particular, the thickness as well the cutoff value at terminations of PCs can strongly influence the performance of dual images and even determine whether the dual images would appear. Moreover, a relatively low working frequency is recommended to minimize the distortion degree of dual images.

© 2012 Optical Society of America

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Y. J. Huang, W. T. Lu, and S. Sridhar, Phys. Rev. A 76, 013824 (2007).
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R. Zhou, X. S. Chen, and W. Lu, Phys. Rev. E 74, 016610 (2006).
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C. Y. Qiu, X. D. Zhang, and Z. Y. Liu, Phys. Rev. B 71, 054302 (2005).
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R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
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N. Fabre, L. Lalouat, B. Cluzel, X. Méique, D. Lippens, F. D. Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef]

Dios, Z.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Doan, M. T.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Dokmeci, M. R.

Dong, G. Y.

Fabre, N.

N. Fabre, L. Lalouat, B. Cluzel, X. Méique, D. Lippens, F. D. Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef]

Fornel, F. D.

N. Fabre, L. Lalouat, B. Cluzel, X. Méique, D. Lippens, F. D. Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef]

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R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, Phys. Rev. B 73, 165310 (2006).
[CrossRef]

Gralak, B.

Gu, B.

He, S. L.

S. S. Xiao, M. Qiu, Z. C. Ruan, and S. L. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

Hingerl, K.

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, Phys. Rev. B 73, 165310 (2006).
[CrossRef]

Huang, Y. J.

Jia, W.

H. Wu, L. Y. Jiang, W. Jia, and X. Y. Li, J. Opt. 13, 095103 (2011).
[CrossRef]

Jiang, L. Y.

H. Wu, L. Y. Jiang, W. Jia, and X. Y. Li, J. Opt. 13, 095103 (2011).
[CrossRef]

Joannopoulos, J. D.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Johnson, S. G.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Jugessur, A. S.

Kang, M.

Kaufman, L. J.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Kirk, A. G.

Kuchar, F.

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, Phys. Rev. B 73, 165310 (2006).
[CrossRef]

Lalouat, L.

N. Fabre, L. Lalouat, B. Cluzel, X. Méique, D. Lippens, F. D. Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef]

Li, S. M.

Li, X. Y.

H. Wu, L. Y. Jiang, W. Jia, and X. Y. Li, J. Opt. 13, 095103 (2011).
[CrossRef]

Li, Y. N.

Li, Z. Y.

Z. Y. Li and L. L. Lin, Phys. Rev. B 68, 245110 (2003).
[CrossRef]

Lin, L. L.

Z. Y. Li and L. L. Lin, Phys. Rev. B 68, 245110 (2003).
[CrossRef]

Lippens, D.

N. Fabre, L. Lalouat, B. Cluzel, X. Méique, D. Lippens, F. D. Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef]

Liu, K.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Liu, Z. Y.

C. Y. Qiu, X. D. Zhang, and Z. Y. Liu, Phys. Rev. B 71, 054302 (2005).
[CrossRef]

Lu, W.

R. Zhou, X. S. Chen, and W. Lu, Phys. Rev. E 74, 016610 (2006).
[CrossRef]

Lu, W. T.

Luo, C. Y.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Méique, X.

N. Fabre, L. Lalouat, B. Cluzel, X. Méique, D. Lippens, F. D. Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef]

Meisels, R.

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, Phys. Rev. B 73, 165310 (2006).
[CrossRef]

Mulot, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Osgood, R. M.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Panoiu, N. C.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Pendry, J. B.

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Perry, C. H.

Pierre, R.

Qiu, C. Y.

C. Y. Qiu, X. D. Zhang, and Z. Y. Liu, Phys. Rev. B 71, 054302 (2005).
[CrossRef]

Qiu, M.

S. S. Xiao, M. Qiu, Z. C. Ruan, and S. L. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Ruan, Z. C.

S. S. Xiao, M. Qiu, Z. C. Ruan, and S. L. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

Selvarasah, S.

Smigaj, W.

Sridhar, S.

Sun, G. L.

Swillo, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Talneau, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Tayeb, G.

Thylén, L.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Vanbésien, O.

N. Fabre, L. Lalouat, B. Cluzel, X. Méique, D. Lippens, F. D. Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef]

Veselago, V. G.

V. G. Veselago, Phys. Usp. 10, 509 (1968).
[CrossRef]

Wang, H. T.

Wong, C. W.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Wu, H.

H. Wu, L. Y. Jiang, W. Jia, and X. Y. Li, J. Opt. 13, 095103 (2011).
[CrossRef]

Xiao, S. S.

S. S. Xiao, M. Qiu, Z. C. Ruan, and S. L. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

Yang, X. L.

Yu, M. B.

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

Zhang, X. D.

C. Y. Qiu, X. D. Zhang, and Z. Y. Liu, Phys. Rev. B 71, 054302 (2005).
[CrossRef]

Zhou, J.

Zhou, R.

R. Zhou, X. S. Chen, and W. Lu, Phys. Rev. E 74, 016610 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

S. S. Xiao, M. Qiu, Z. C. Ruan, and S. L. He, Appl. Phys. Lett. 85, 4269 (2004).
[CrossRef]

J. Opt. (1)

H. Wu, L. Y. Jiang, W. Jia, and X. Y. Li, J. Opt. 13, 095103 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. A (1)

Y. J. Huang, W. T. Lu, and S. Sridhar, Phys. Rev. A 76, 013824 (2007).
[CrossRef]

Phys. Rev. B (4)

C. Y. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Z. Y. Li and L. L. Lin, Phys. Rev. B 68, 245110 (2003).
[CrossRef]

R. Gajić, R. Meisels, F. Kuchar, and K. Hingerl, Phys. Rev. B 73, 165310 (2006).
[CrossRef]

C. Y. Qiu, X. D. Zhang, and Z. Y. Liu, Phys. Rev. B 71, 054302 (2005).
[CrossRef]

Phys. Rev. E (1)

R. Zhou, X. S. Chen, and W. Lu, Phys. Rev. E 74, 016610 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

R. Chatterjee, N. C. Panoiu, K. Liu, Z. Dios, M. B. Yu, M. T. Doan, L. J. Kaufman, R. M. Osgood, and C. W. Wong, Phys. Rev. Lett. 100, 187401 (2008).
[CrossRef]

N. Fabre, L. Lalouat, B. Cluzel, X. Méique, D. Lippens, F. D. Fornel, and O. Vanbésien, Phys. Rev. Lett. 101, 073901 (2008).
[CrossRef]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef]

Phys. Usp. (1)

V. G. Veselago, Phys. Usp. 10, 509 (1968).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

TM band structures (the lowest four bands) and band surfaces (only the second and third bands) of the (a1), (a2) triangular-lattice and (b1), (b2) honeycomb-lattice 2DPCs. The upper and lower insets show the schematic diagram and corresponding first Brillouin zone with three high-symmetry lattice points of 2DPCs, respectively.

Fig. 2.
Fig. 2.

Comparison plots of EFSs for the TM2 and TM3 bands in the (a1) triangular-lattice 2DPC and (b1) honeycomb-lattice 2DPC; the combined EFSs of TM2 and TM3 bands for the (a2) triangular-lattice 2DPC and (b2) honeycomb-lattice 2DPC at frequency 0.332×2πc/a and 0.19×2πc/a, respectively. The arrows in (a2) and (b2) represent the wave vectors for different incident and refractive waves.

Fig. 3.
Fig. 3.

FDTD simulations of the refraction behavior of incident waves for the (a1), (a2) triangular-lattice 2DPC and (b1), (b2) honeycomb-lattice 2DPC when working frequency is 0.332×2πc/a and 0.19×2πc/a, respectively.

Fig. 4.
Fig. 4.

(a1), (b1) Reflectivity at the input surface versus cutoff of PC terminations. FDTD simulations of the dual-imaging effect for (a2) the 7-layer triangular-lattice 2DPC when cutoff=0.04a and (b2) the 16-layer honeycomb-lattice 2DPC when cutoff=0.36a. The insets show the cross-sectional distribution of normalized intensity along the horizontal direction for dual images.

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