Abstract

We investigated the optical properties of a circular photonic crystal (CPC) for which the distance between lattices was systematically distributed. The transmission spectra of CPC composed of alumina cylinders were examined in the frequency region from 0 to 20 GHz. We show that photonic gaps are obtained not only in CPCs but also in phase-shifted CPCs. The isotropic photonic gaps are evidenced by changes in the incident angle of a millimeter wave.

© 2004 Optical Society of America

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2002

2001

M. A. van Eijkelenborg, M. C. J. Large, A. Argyros, J. Zagari, S. Manos, N. A. Issa, I. Bassett, S. Fleming, R. C. McPhedran, C. M. de Sterke, and N. A. P. Nicorovici, Opt. Express 9, 319 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2001). Their model, however, is unique in that they do not assume any periodic lattice as a starting mother lattice.
[CrossRef]

2000

J. Xu, J. Song, C. Li, and K. Ueda, Opt. Commun. 182, 343 (2000).
[CrossRef]

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

S. David, A. Chelnokov, and J.-M. Lourtioz, Opt. Lett. 25, 1001 (2000).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 61, 13458 (2000).
[CrossRef]

1998

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

1996

T. F. Krauss, R. M. De La Rue, and S. Brand, Nature 383, 699 (1996).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

1988

1987

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

1979

K. Ohtaka, Phys. Rev. B 19, 5057 (1979).
[CrossRef]

Argyros, A.

Bassett, I.

Baumberg, J. J.

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

Botten, L. C.

Brand, S.

T. F. Krauss, R. M. De La Rue, and S. Brand, Nature 383, 699 (1996).
[CrossRef]

Bur, J.

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. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, and M. C. Netti, Nature 404, 740 (2000).
[CrossRef] [PubMed]

Chelnokov, A.

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Cheng, B.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Chow, E.

David, S.

De La Rue, R. M.

T. F. Krauss, R. M. De La Rue, and S. Brand, Nature 383, 699 (1996).
[CrossRef]

de Sterke, C. M.

Economou, E. N.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 61, 13458 (2000).
[CrossRef]

Fan, S.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Fleming, S.

Hase, M.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2001). Their model, however, is unique in that they do not assume any periodic lattice as a starting mother lattice.
[CrossRef]

Issa, N. A.

Jin, C.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Joannopoulos, J. D.

S. Y. Lin, E. Chow, J. Bur, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 27, 1400 (2002).
[CrossRef]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, New York, 1995).

Johnson, S. G.

Köhler, S.

Krauss, T. F.

T. F. Krauss, R. M. De La Rue, and S. Brand, Nature 383, 699 (1996).
[CrossRef]

Kuhlmey, B. T.

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Kurokawa, Y.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2001). Their model, however, is unique in that they do not assume any periodic lattice as a starting mother lattice.
[CrossRef]

Large, M. C. J.

Li, C.

J. Xu, J. Song, C. Li, and K. Ueda, Opt. Commun. 182, 343 (2000).
[CrossRef]

Li, Z.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 61, 13458 (2000).
[CrossRef]

Lin, S. Y.

Liu, Z. Y.

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

Lourtioz, J.-M.

Manos, S.

Maystre, D.

McPhedran, R. C.

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, New York, 1995).

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Meng, X.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Miyazaki, H.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2001). Their model, however, is unique in that they do not assume any periodic lattice as a starting mother lattice.
[CrossRef]

Miyazaki, H. T.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2001). Their model, however, is unique in that they do not assume any periodic lattice as a starting mother lattice.
[CrossRef]

Netti, M. C.

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

Nicorovici, N. A. P.

Ohtaka, K.

K. Ohtaka, Phys. Rev. B 19, 5057 (1979).
[CrossRef]

Parker, G. J.

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

Reversez, G.

Shinya, N.

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2001). Their model, however, is unique in that they do not assume any periodic lattice as a starting mother lattice.
[CrossRef]

Sigalas, M. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 61, 13458 (2000).
[CrossRef]

Song, J.

J. Xu, J. Song, C. Li, and K. Ueda, Opt. Commun. 182, 343 (2000).
[CrossRef]

Soukoulis, C. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 61, 13458 (2000).
[CrossRef]

Ueda, K.

J. Xu, J. Song, C. Li, and K. Ueda, Opt. Commun. 182, 343 (2000).
[CrossRef]

van Eijkelenborg, M. A.

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

White, T. P.

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, New York, 1995).

Xu, J.

J. Xu, J. Song, C. Li, and K. Ueda, Opt. Commun. 182, 343 (2000).
[CrossRef]

Yablonovitch, E.

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

Yousif, H. A.

Zagari, J.

Zhang, D.

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

Zoorob, M. E.

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

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

T. F. Krauss, R. M. De La Rue, and S. Brand, Nature 383, 699 (1996).
[CrossRef]

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

Opt. Commun.

J. Xu, J. Song, C. Li, and K. Ueda, Opt. Commun. 182, 343 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, Phys. Rev. B 61, 13458 (2000).
[CrossRef]

C. Jin, X. Meng, B. Cheng, Z. Li, and D. Zhang, Phys. Rev. B 63, 195107 (2001).
[CrossRef]

H. Miyazaki, M. Hase, H. T. Miyazaki, Y. Kurokawa, and N. Shinya, Phys. Rev. B 67, 235109 (2001). Their model, however, is unique in that they do not assume any periodic lattice as a starting mother lattice.
[CrossRef]

K. Ohtaka, Phys. Rev. B 19, 5057 (1979).
[CrossRef]

Phys. Rev. Lett.

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

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

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, Phys. Rev. Lett. 77, 3787 (1996).
[CrossRef] [PubMed]

Other

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, New York, 1995).

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Figures (3)

Fig. 1
Fig. 1

Actual sample configurations and numbers of cylinders for (a) the phase-shifted small CPC (small-Δθ CPC) and (b) the phase-shifted large CPC (large-Δθ CPC). The line at the bottom in (a) and the short line in the center of (b) indicate the places where the calculated and experimental spectra (Fig. 3 below) of electric field intensity were obtained.

Fig. 2
Fig. 2

(a) Schematic of the experimental setup. The electric field intensity in a CPC is measured with a probe antenna. A millimeter wave was generated from a Hewlett-Packard 8510C vector network analysis system and irradiated from a rectangular horn antenna. The wave intensity emitted from the horn antenna was measured in the horizontal plane and is shown in the inset.

Fig. 3
Fig. 3

(a) Experimental spectra of electric field intensity obtained in the CPC and the Δθ CPC. The direction of the incident wave is parallel to the y axis. Each spectrum was displaced by -20 dB. A decrease in electric field intensity caused by the presence of a photonic gap was observed in the frequency region as predicted by the theoretical calculation. The depth of the drop for the calculated spectrum is normalized to the drop for the experimental spectrum. (b) Frequencies of the upper and the lower band edges of the photonic gap as a function of rotation angle ϕ of the CPC and of the Δθ CPC. Angle ϕ=0° when the direction of propagation of the millimeter wave is parallel to the y axis. The spectra were measured at the center of the CPC or the Δθ CPC.

Equations (1)

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x=dN sin2mπ6N+ΔθN,y=dN cos2mπ6N+ΔθN,

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