Abstract

We examine quasiperiodic multilayers arranged in m-bonacci sequences, which combine ordinary positive-index materials and dispersive metamaterials with negative index in a certain frequency range. When the volume-averaged refractive index of the nonperiodic multilayer equals zero, the structure does not propagate light radiation and exhibits a forbidden band. We identify some analytical expressions to determine the upper and lower limits of the above zero-average refractive-index bandgap. We recognize that these limits are not explicitly dependent on the geometrical parameters of the stack of layers.

© 2009 Optical Society of America

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References

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  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).
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    [CrossRef]

2009

2007

J. A. Monsoriu, R. A. Depine, and E. Silvestre, J. Eur. Opt. Soc. Rapid Publ. 2, 07002 (2007).
[CrossRef]

2006

2004

J. Li, D. Zhao, and Z. Liu, Phys. Lett. A 332, 461 (2004).
[CrossRef]

2003

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Brueck, S. R. J.

Chan, C. T.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Chen, H.

Depine, R. A.

E. Silvestre, R. A. Depine, M. L. Martínez-Ricci, and J. A. Monsoriu, J. Opt. Soc. Am. B 26, 581 (2009).
[CrossRef]

J. A. Monsoriu, R. A. Depine, and E. Silvestre, J. Eur. Opt. Soc. Rapid Publ. 2, 07002 (2007).
[CrossRef]

Huangfu, J.

Joannopoulos, J. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Kong, J. A.

Li, J.

J. Li, D. Zhao, and Z. Liu, Phys. Lett. A 332, 461 (2004).
[CrossRef]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Liu, Z.

J. Li, D. Zhao, and Z. Liu, Phys. Lett. A 332, 461 (2004).
[CrossRef]

Maciá, E.

E. Maciá, Rep. Prog. Phys. 69, 397 (2006).
[CrossRef]

Martínez-Ricci, M. L.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Monsoriu, J. A.

E. Silvestre, R. A. Depine, M. L. Martínez-Ricci, and J. A. Monsoriu, J. Opt. Soc. Am. B 26, 581 (2009).
[CrossRef]

J. A. Monsoriu, R. A. Depine, and E. Silvestre, J. Eur. Opt. Soc. Rapid Publ. 2, 07002 (2007).
[CrossRef]

Osgood, R. M.

Panoiu, N. C.

Ran, L.

Shen, L.

Sheng, P.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Silvestre, E.

E. Silvestre, R. A. Depine, M. L. Martínez-Ricci, and J. A. Monsoriu, J. Opt. Soc. Am. B 26, 581 (2009).
[CrossRef]

J. A. Monsoriu, R. A. Depine, and E. Silvestre, J. Eur. Opt. Soc. Rapid Publ. 2, 07002 (2007).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

Yuan, Y.

Zhang, S.

Zhao, D.

J. Li, D. Zhao, and Z. Liu, Phys. Lett. A 332, 461 (2004).
[CrossRef]

Zhou, L.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

J. Eur. Opt. Soc. Rapid Publ.

J. A. Monsoriu, R. A. Depine, and E. Silvestre, J. Eur. Opt. Soc. Rapid Publ. 2, 07002 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Phys. Lett. A

J. Li, D. Zhao, and Z. Liu, Phys. Lett. A 332, 461 (2004).
[CrossRef]

Phys. Rev. Lett.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef] [PubMed]

Rep. Prog. Phys.

E. Maciá, Rep. Prog. Phys. 69, 397 (2006).
[CrossRef]

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 2008).

N.Engheta and R.W.Ziolkowski, eds., Metamaterials: Physics and Engineering Explorations (Wiley-IEEE, 2006).

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Figures (2)

Fig. 1
Fig. 1

(a) Frequency behavior of the constitutive parameters corresponding to the MM layer. (b) Fibonacci and (c) Tribonacci photonic spectra at normal incidence for different generation levels.

Fig. 2
Fig. 2

Photonic spectrum as a function of the incident angle for (a) the Fibonacci MM multilayer with level number S = 10 and (b) the Tribonacci MM multilayer with level number S = 8 .

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

μ ¯ = 0 , ( ω c ) 2 ϵ ¯ + k x 2 μ 1 ¯ = 0 ( TE ) ,
ϵ ¯ = 0 , ( ω c ) 2 μ ¯ + k x 2 ϵ 1 ¯ = 0 ( TM ) ,
μ ¯ = 0 , ϵ ¯ = 0 ,
ϵ A ( ν ) = 1 + 5 2 ν 2 0.9 2 + 10 2 ν 2 11.5 2 ,
μ A ( ν ) = 1 3 2 ν 2 0.902 2 ,
Φ ¯ S = τ S Φ A d A + Φ B d B τ S d A + d B ,

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