Abstract

The origin of frequency gaps in the dispersion relation of periodic, quasi-periodic, and random photonic structures consisting of different arrangements of dielectric cylinders has been investigated. For TM polarization it was found that the formation and properties of gaps are strongly affected by Mie resonances of a single cylinder. Both the spectral position and size depend on the properties of this single scatterer. In contrast, for TE polarization no correlation between the scattering properties and bandgap formation was found, as Mie resonances are spectrally not well separated. For the inverted structure consisting of air cylinders in a dielectric material, the frequency gaps depend on the spatial arrangement of the cylinders because no pronounced Mie resonances exist in this case.

© 2006 Optical Society of America

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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]
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    [CrossRef]
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    [CrossRef]
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2005 (1)

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

2003 (1)

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2003).
[CrossRef]

2000 (1)

M. E. Zorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberger, and M. C. Netti, Nature 404, 740 (2000).
[CrossRef]

1998 (2)

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

1994 (1)

1987 (2)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

M. Kohmoto, B. Sutherland, and K. Iguchi, Phys. Rev. Lett. 58, 2436 (1987).
[CrossRef] [PubMed]

1986 (1)

D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986).
[CrossRef]

1984 (1)

D. Levine and P. J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984).
[CrossRef]

Baumberger, J. J.

M. E. Zorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberger, and M. C. Netti, Nature 404, 740 (2000).
[CrossRef]

Capolino, F.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Chan, C. T.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[CrossRef]

Chan, Y. S.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[CrossRef]

Charlton, M. D. B.

M. E. Zorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberger, and M. C. Netti, Nature 404, 740 (2000).
[CrossRef]

Della Villa, A.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Economou, E. N.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

Enoch, S.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Felbacq, D.

Galdi, V.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Hase, M.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2003).
[CrossRef]

Iguchi, K.

M. Kohmoto, B. Sutherland, and K. Iguchi, Phys. Rev. Lett. 58, 2436 (1987).
[CrossRef] [PubMed]

Kohmoto, M.

M. Kohmoto, B. Sutherland, and K. Iguchi, Phys. Rev. Lett. 58, 2436 (1987).
[CrossRef] [PubMed]

Kurokawa, Y.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2003).
[CrossRef]

Levine, D.

D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986).
[CrossRef]

D. Levine and P. J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984).
[CrossRef]

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

Liu, Z. Y.

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[CrossRef]

Maystre, D.

Miyazaki, H.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2003).
[CrossRef]

Miyazaki, H. T.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2003).
[CrossRef]

Netti, M. C.

M. E. Zorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberger, and M. C. Netti, Nature 404, 740 (2000).
[CrossRef]

Parker, G. J.

M. E. Zorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberger, and M. C. Netti, Nature 404, 740 (2000).
[CrossRef]

Pierro, V.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Shinya, N.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2003).
[CrossRef]

Sigalas, M. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

Soukoulis, C. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

Steinhardt, P. J.

D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986).
[CrossRef]

D. Levine and P. J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984).
[CrossRef]

Sutherland, B.

M. Kohmoto, B. Sutherland, and K. Iguchi, Phys. Rev. Lett. 58, 2436 (1987).
[CrossRef] [PubMed]

Tayeb, G.

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

D. Felbacq, G. Tayeb, and D. Maystre, J. Opt. Soc. Am. A 11, 2526 (1994).
[CrossRef]

van Hulst, H. C.

H. C. van Hulst, Light Scattering by Small Particles (Wiley, 1957).

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Zorob, M. E.

M. E. Zorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberger, and M. C. Netti, Nature 404, 740 (2000).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nature (1)

M. E. Zorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberger, and M. C. Netti, Nature 404, 740 (2000).
[CrossRef]

Phys. Rev. B (2)

D. Levine and P. J. Steinhardt, Phys. Rev. B 34, 596 (1986).
[CrossRef]

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2003).
[CrossRef]

Phys. Rev. Lett. (6)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 81, 1405 (1998).
[CrossRef]

M. Kohmoto, B. Sutherland, and K. Iguchi, Phys. Rev. Lett. 58, 2436 (1987).
[CrossRef] [PubMed]

D. Levine and P. J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984).
[CrossRef]

A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, Phys. Rev. Lett. 94, 183903 (2005).
[CrossRef] [PubMed]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, Phys. Rev. Lett. 80, 956 (1998).
[CrossRef]

Other (1)

H. C. van Hulst, Light Scattering by Small Particles (Wiley, 1957).

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Figures (4)

Fig. 1
Fig. 1

Layouts of (a) fivefold and (b) sevenfold QPC (b). The frequency-dependent LDOS for a line source inside a QPC with different symmetries is shown in (c) and for a random structure with and without constraints the minimum center-to-center distance in (d).

Fig. 2
Fig. 2

Upper and lower bounds of the bandgap as a function of the radius of the cylinders (at ϵ 2 = 13 ) in (a) and as a function of the dielectric constant of the cylinders (at R = 0.2 a ) in (b) for TM polarization.

Fig. 3
Fig. 3

SCS of a cylinder with R = 0.2 a and ϵ 2 = 13 in (a) for TM and (c) for TE polarization. The amplitude around the cylinder in the inset in (a) for TM polarization is shown at f TM = 0.3 a λ 1 for the first gap and at f TM = 0.55 a λ 1 for the second gap. The amplitudes in the insets in (c) are shown at frequencies shortly after the resonances at f TE = 0.55 a λ 1 for the first gap and at f TE = 0.82 a λ 1 for the second gap. In (b) the amplitudes of the first three Mie coefficients for the same cylinder are shown for TM- and in (d) for TE-polarized light.

Fig. 4
Fig. 4

LDOS of a line source from inside a finite structure (air cylinders in ε 1 = 13 , R = 0.3 a ) for different structure sizes: (a) triangular PC, (b) fivefold QPC.

Equations (2)

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u Inc ( r , θ ) = m = ( i ) m J m ( ε 1 k 0 r ) e i m θ ,
a m = ε 1 J m ( ε 2 k 0 R ) J m ( ε 1 k 0 R ) ε 2 J m ( ε 2 k 0 R ) J m ( ε 1 k 0 R ) ε 1 J m ( ε 2 k 0 R ) H m ( ε 1 k 0 R ) ε 2 J m ( ε 2 k 0 R ) H m ( ε 1 k 0 R ) .

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