Abstract

Positive–negative refraction based on overlapping bands in a two-dimensional square lattice photonic crystal was studied by theoretical analysis and numerical simulation. An incident beam launching into this photonic crystal under certain conditions will excite simultaneously the negative refracted mode at the second band and the positive refracted mode at the third band, which overlaps with the second band. This positive–negative refraction effect can be manipulated by adjusting the incident angle. This special mechanism of positive–negative refraction can be used to realize beam splitting with more design flexibilities and more excellent properties.

© 2008 Optical Society of America

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

2005 (2)

2004 (5)

Y. Luo, W. Zhang, Y. Huang, J. Zhao, and J. Peng, “Wide-angle beam splitting by use of positive-negative refraction in photonic crystals,” Opt. Lett. 29, 2920-2922 (2004).
[CrossRef]

S. Shi, A. Sharkawy, C. Chen, D. M. Pustai, and D. W. Prather, “Dispersion-based beam splitter in photonic crystals,” Opt. Lett. 27, 617-619 (2004).
[CrossRef]

S. Shi, C. Chen, and D. W. Prather, “Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers,” J. Opt. Soc. Am. A 21, 1769-1775 (2004).
[CrossRef]

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical analysis of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

2003 (1)

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

2002 (2)

2001 (1)

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 (3)

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]

B. Gralak, S. Enoch, and G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012-1020 (2000).
[CrossRef]

1999 (1)

M. Thèvenot, A. Reineix, and B. Jecko, “FDTD approach for modeling PBG structures,” J. Opt. A, Pure Appl. Opt. 1, 495-500 (1999).
[CrossRef]

1996 (1)

J. Fang and Z. Wu, “Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media,” IEEE Trans. Microwave Theory Tech. 44, 2216-2222 (1996).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

1968 (1)

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

Ao, X.

Asakawa, K.

Carlsson, N.

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Chen, C.

S. Shi, C. Chen, and D. W. Prather, “Plane-wave expansion method for calculating band structure of photonic crystal slabs with perfectly matched layers,” J. Opt. Soc. Am. A 21, 1769-1775 (2004).
[CrossRef]

S. Shi, A. Sharkawy, C. Chen, D. M. Pustai, and D. W. Prather, “Dispersion-based beam splitter in photonic crystals,” Opt. Lett. 27, 617-619 (2004).
[CrossRef]

Derov, J. S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Enoch, S.

Fang, J.

J. Fang and Z. Wu, “Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media,” IEEE Trans. Microwave Theory Tech. 44, 2216-2222 (1996).
[CrossRef]

Gralak, B.

Griol, A.

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical analysis of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

He, S.

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Huang, Y.

Ikeda, N.

Inoue, K.

Jecko, B.

M. Thèvenot, A. Reineix, and B. Jecko, “FDTD approach for modeling PBG structures,” J. Opt. A, Pure Appl. Opt. 1, 495-500 (1999).
[CrossRef]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Kawai, N.

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Luo, C.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Luo, Y.

Martí, J.

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical analysis of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

Martínez, A.

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical analysis of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

Míguez, H.

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical analysis of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[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]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

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

Peng, J.

Prather, D. W.

Pustai, D. M.

S. Shi, A. Sharkawy, C. Chen, D. M. Pustai, and D. W. Prather, “Dispersion-based beam splitter in photonic crystals,” Opt. Lett. 27, 617-619 (2004).
[CrossRef]

Reineix, A.

M. Thèvenot, A. Reineix, and B. Jecko, “FDTD approach for modeling PBG structures,” J. Opt. A, Pure Appl. Opt. 1, 495-500 (1999).
[CrossRef]

Ruan, Z.

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]

Sharkawy, A.

S. Shi, A. Sharkawy, C. Chen, D. M. Pustai, and D. W. Prather, “Dispersion-based beam splitter in photonic crystals,” Opt. Lett. 27, 617-619 (2004).
[CrossRef]

A. Sharkawy, S. Shi, and D. W. Prather, “Heterostructure photonic crystals: theory and applications,” Appl. Opt. 41, 7245-7253 (2002).
[CrossRef] [PubMed]

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, S.

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]

Sokoloff, J.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Sugimoto, Y.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

Tayeb, G.

Thèvenot, M.

M. Thèvenot, A. Reineix, and B. Jecko, “FDTD approach for modeling PBG structures,” J. Opt. A, Pure Appl. Opt. 1, 495-500 (1999).
[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]

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Wu, Z.

J. Fang and Z. Wu, “Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media,” IEEE Trans. Microwave Theory Tech. 44, 2216-2222 (1996).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Zhang, W.

Zhao, J.

Appl. Opt. (1)

IEEE Trans. Microwave Theory Tech. (1)

J. Fang and Z. Wu, “Generalized perfectly matched layer for the absorption of propagating and evanescent waves in lossless and lossy media,” IEEE Trans. Microwave Theory Tech. 44, 2216-2222 (1996).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

M. Thèvenot, A. Reineix, and B. Jecko, “FDTD approach for modeling PBG structures,” J. Opt. A, Pure Appl. Opt. 1, 495-500 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Lett. (5)

Phys. Rev. B (3)

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]

A. Martínez, H. Míguez, A. Griol, and J. Martí, “Experimental and theoretical analysis of the self-focusing of light by a photonic crystal lens,” Phys. Rev. B 69, 165119 (2004).
[CrossRef]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “Subwavelength imaging in photonic crystals,” Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Phys. Rev. Lett. (4)

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

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

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Science (1)

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

Sov. Phys. Usp. (1)

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

Other (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, 2000).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the 2D PhC with square lattice circular dielectric rods in air. The input interface and the output interface are in the Γ M direction. The black arrow I represents the incident beam with an incident angle θ in .

Fig. 2
Fig. 2

(a) Lowest four bands of this PhC for TM polarization. The normalized frequency ω a ( 2 π c ) = 0.38 is marked specially. (b) EFCs of the second band. (c) EFCs of the third band. Solid curves, dashed curves, and dotted curves denote the EFCs with normalized frequency 0.365, 0.380, and 0.400, respectively, in both (b) and (c).

Fig. 3
Fig. 3

(a) Illustrates reflection and refraction at the input interface. (b) and (c) Illustrate reflection and refraction for positive and negative refracted beams at the output interface, respectively. The black solid arrow I and gray arrow I denote the incident beam and its reflected beam, the hollow arrows R p , R n , R p , and R p denote positive and negative refracted beams and their reflected beams, and the gray arrows T p and T n denote transmitted beams for positive and negative refracted beams, respectively. Gray curves, black solid curves, and dashed curves denote the EFCs with normalized frequency 0.380 in air, the second and third band in PhC, respectively. The dashed lines denote the conservation requirement of the tangential component of the wave vector.

Fig. 4
Fig. 4

Instantaneous distribution of the electric field E obtained by numerical simulation. The incident light with normalized frequency ω a ( 2 π c ) equivalent to 0.38 launches onto the PhC containing 23 layers of rods with an incident angle θ in equivalent to 20°. All of the arrows and corresponding marks are the same as that in Fig. 3.

Fig. 5
Fig. 5

Distribution of power density of transmitted beams at the output interface. (a)–(c) Correspond to the incident angle θ in equivalent to 15°, 20°, and 25°, respectively. The power density of the transmitted beam is normalized by that of the incident beam.

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