Abstract

We propose three dimensionless approximate expressions to predict the thickness filling factor, gap center, and gap width of the maximum omnidirectional gap (MODG) for various refractive indices in one-dimensional photonic crystals. These expressions are simple and do not include trigonometric or inverse trigonometric functions. It is easy to obtain the MODG from given refractive indices but also to estimate the refractive indices from the MODG based on the results.

© 2011 Optical Society of America

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2010

2009

2008

W. J. Hsueh, C. T. Chen, and C. H. Chen, Phys. Rev. A 78, 013836 (2008).
[CrossRef]

2005

2003

2002

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, Appl. Phys. Lett. 80, 4291 (2002).
[CrossRef]

2001

2000

J. Lekner, J. Opt. A 2, 349 (2000).
[CrossRef]

1999

1998

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Alagappan, G.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Chen, C. H.

W. J. Hsueh, C. T. Chen, and C. H. Chen, Phys. Rev. A 78, 013836 (2008).
[CrossRef]

Chen, C. T.

W. J. Hsueh, C. T. Chen, and C. H. Chen, Phys. Rev. A 78, 013836 (2008).
[CrossRef]

Chigrin, D. N.

Cho, W.

Clement, T. J.

DeCorby, R. G.

Deopura, M.

Dwivedi, P. K.

Fan, S.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Fan, Y. L.

Fink, Y.

Gaponenko, S. V.

Gessmann, Th.

Gill, W. N.

Han, P.

Hsueh, W. J.

W. J. Hsueh, S. J. Wun, and T. H. Yu, J. Opt. Soc. Am. B 27, 1092 (2010).
[CrossRef]

W. J. Hsueh, C. T. Chen, and C. H. Chen, Phys. Rev. A 78, 013836 (2008).
[CrossRef]

Hu, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, Appl. Phys. Lett. 80, 4291 (2002).
[CrossRef]

Jia, W.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, Appl. Phys. Lett. 80, 4291 (2002).
[CrossRef]

Jiang, Z. M.

Joannopoulos, J. D.

Lavrinenko, A. V.

Lekner, J.

J. Lekner, J. Opt. A 2, 349 (2000).
[CrossRef]

Li, Y.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, Appl. Phys. Lett. 80, 4291 (2002).
[CrossRef]

Liu, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, Appl. Phys. Lett. 80, 4291 (2002).
[CrossRef]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Moore, R. A.

Nguyen, H. T.

Ojha, M.

Perova, T. S.

Plawsky, J. L.

Schubert, E. F.

Southwell, W. H.

Temelkuran, B.

Thomas, E. L.

B. Temelkuran, E. L. Thomas, J. D. Joannopoulos, and Y. Fink, Opt. Lett. 26, 1370 (2001).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

Tolmachev, V. A.

Ullal, C. K.

Wang, H.

Wang, X.

D. T. Zhao, H. Zhou, Z. M. Jiang, Y. L. Fan, and X. Wang, Opt. Lett. 28, 843 (2003).
[CrossRef] [PubMed]

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, Appl. Phys. Lett. 80, 4291 (2002).
[CrossRef]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, Opt. Lett. 23, 1573 (1998).
[CrossRef]

Wu, P.

Wun, S. J.

Xi, J.-Q.

Xu, C.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, Appl. Phys. Lett. 80, 4291 (2002).
[CrossRef]

Yarotsky, D. A.

Yu, T. H.

Zhao, D. T.

Zhou, H.

Zi, J.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, Appl. Phys. Lett. 80, 4291 (2002).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, Appl. Phys. Lett. 80, 4291 (2002).
[CrossRef]

J. Lightwave Technol.

J. Opt. A

J. Lekner, J. Opt. A 2, 349 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. A

W. J. Hsueh, C. T. Chen, and C. H. Chen, Phys. Rev. A 78, 013836 (2008).
[CrossRef]

Science

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, Science 282, 1679 (1998).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Sketch of the gap center and gap width of the gap hole in region (0,0) for the NI and TMG states and the MODG.

Fig. 2
Fig. 2

(a) FFM of the MODG versus n B / ( n A + n B ) , (b) coefficients a F and b F of the present formulas versus n A 2 , and (c) error of the calculated FFM. In (a), the thick solid and dotted curves correspond to the exact and the present methods, denoted by symbols E- and H-, respectively. The numbers following E- and H- are the n A values. In (c), the thick solid and dashed curves correspond to the present method and [2], denoted by H- and F-, respectively. The circles, rectangles and others on the curves present the results located at n B = 3.0 and 5.0.

Fig. 3
Fig. 3

(a) Calculated CFM versus ( n A + n B ) / ( 4 n A n B ) , (b) coefficient Δ Ω versus n A 2 , and (c) error of the calculated results for binary PhCs. The parameters and notations are the same as in Fig. 2.

Fig. 4
Fig. 4

(a) Exact and calculated GWM versus ( n B n A ) / ( π n A n B ) and (b) error of the calculated results. The parameters and notations are the same as in Fig. 2.

Equations (5)

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

F c ( Omni ) = n B ( n A + n B ) + Δ F S , Ω c ( Omni ) = n A + n B 4 n A n B + Δ Ω ,
Δ F = a F n A 2 + b F ,
Δ Ω = a Ω n A 2 + b Ω .
GW c ( Omni ) = Ω c ( NI ) Ω c ( TMG ) + 0.5 ( GW c ( NI ) + GW c ( TMG ) ) + Δ S ,
GW c ( Omni ) = n B n A π n A n B ( 1 + Δ W S ) + Δ W O ,

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