Abstract

A systematic study of the omnidirectional reflection range of one-dimensional photonic crystals with a staggered structure is presented, based on numerical simulations performed with the well-known transfer-matrix method without any simplifying assumptions. We determined that the excellent performance of the crystals extends the range of omnidirectional reflection. We redefined the structure by employing two structural parameters and found that they play different roles in bandgap broadening, which is useful for practical design. The relations between the omnidirectional reflection range and the two structural parameters are presented in detail.

© 2003 Optical Society of America

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S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[CrossRef] [PubMed]

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

2001 (4)

J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
[CrossRef]

M. Deopura, C. K. Ullal, B. Temelkuran, and Y. Fink, “Dielectric omnidirectional visible reflector,” Opt. Lett. 26, 1197–1199 (2001).
[CrossRef]

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lim, and J. C. Lee, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals,” Appl. Phys. Lett. 79, 15–17 (2001).
[CrossRef]

D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
[CrossRef]

2000 (4)

J. Lekner, “Omnidirectional reflection by multilayer dielectric mirrors,” J. Opt. A: Pure Appl. Opt. 2, 349–352 (2000).
[CrossRef]

E. Cojocaru, “Omnidirectional reflection from Solc-type anisotropic periodic dielectric structures,” Appl. Opt. 39, 6441–6447 (2000).
[CrossRef]

I. Abdulhalim, “Reflective phase-only modulation using one-dimensional photonic crystals,” J. Opt. A: Pure Appl. Opt. 2, L9–L11 (2000).
[CrossRef]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419 (2000).
[CrossRef] [PubMed]

1999 (6)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
[CrossRef]

W. H. Southwell, “Omnidirectional mirror design with quarter-wave dielectric stacks,” Appl. Opt. 38, 5464–5467 (1999).
[CrossRef]

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).
[CrossRef]

H. Li, G. Gu, H. Chen, and S. Zhu, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
[CrossRef]

1998 (5)

E. Yablonovitch, “Engineered omnidirectional external-reflectivity spectra from one-dimensional layered interference filters,” Opt. Lett. 23, 1648–1649 (1998).
[CrossRef]

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73, 2084–2086 (1998).
[CrossRef]

J. P. Dowling, “Mirror on the wall: you’re omnidirectional after all,” Science 282, 1841–1842 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

1997 (2)

1995 (2)

A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, and R. Szipocs, “Sub-10-fs mirror-dispersion-controlled Ti:sapphire laser,” Opt. Lett. 20, 602–604 (1995).
[CrossRef] [PubMed]

D. Zhang, Z. Li, W. Hu, and B. Cheng, “Broadband optical reflector—an application of light localization in one dimension,” Appl. Phys. Lett. 67, 2431–2432 (1995).
[CrossRef]

1994 (1)

1989 (1)

1987 (2)

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

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

1966 (2)

Abdulhalim, I.

D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
[CrossRef]

I. Abdulhalim, “Reflective phase-only modulation using one-dimensional photonic crystals,” J. Opt. A: Pure Appl. Opt. 2, L9–L11 (2000).
[CrossRef]

Alfano, R. R.

Baumeister, P. W.

Chen, C.

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Chen, H.

H. Li, G. Gu, H. Chen, and S. Zhu, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
[CrossRef]

Cheng, B.

D. Zhang, Z. Li, W. Hu, and B. Cheng, “Broadband optical reflector—an application of light localization in one dimension,” Appl. Phys. Lett. 67, 2431–2432 (1995).
[CrossRef]

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
[CrossRef]

Cojocaru, E.

Deopura, M.

Dobrowolski, J. A.

Dowling, J. P.

J. P. Dowling, “Mirror on the wall: you’re omnidirectional after all,” Science 282, 1841–1842 (1998).
[CrossRef]

Fan, S.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419 (2000).
[CrossRef] [PubMed]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

Fang, H.

J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
[CrossRef]

Ferencz, K.

Fink, Y.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[CrossRef] [PubMed]

M. Deopura, C. K. Ullal, B. Temelkuran, and Y. Fink, “Dielectric omnidirectional visible reflector,” Opt. Lett. 26, 1197–1199 (2001).
[CrossRef]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419 (2000).
[CrossRef] [PubMed]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
[CrossRef]

Gu, G.

H. Li, G. Gu, H. Chen, and S. Zhu, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
[CrossRef]

Ha, Y. K.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lim, and J. C. Lee, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals,” Appl. Phys. Lett. 79, 15–17 (2001).
[CrossRef]

Hart, S. D.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[CrossRef] [PubMed]

Haus, H. A.

Heavens, O. S.

Heine, C.

Hu, W.

D. Zhang, Z. Li, W. Hu, and B. Cheng, “Broadband optical reflector—an application of light localization in one dimension,” Appl. Phys. Lett. 67, 2431–2432 (1995).
[CrossRef]

Hu, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Ibanescu, M.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419 (2000).
[CrossRef] [PubMed]

Jia, W.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Joannopoulos, J. D.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419 (2000).
[CrossRef] [PubMed]

Y. Fink, D. J. Ripin, S. Fan, C. Chen, J. D. Joannopoulos, and E. L. Thomas, “Guiding optical light in air using an all-dielectric structure,” J. Lightwave Technol. 17, 2039–2041 (1999).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef] [PubMed]

Kärtner, F. X.

Kee, C. S.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lim, and J. C. Lee, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals,” Appl. Phys. Lett. 79, 15–17 (2001).
[CrossRef]

Keller, U.

Kim, J. E.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lim, and J. C. Lee, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals,” Appl. Phys. Lett. 79, 15–17 (2001).
[CrossRef]

Krausz, F.

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
[CrossRef]

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “All-dielectric one-dimensional periodic structures for total omnidirectional reflection and partial spontaneous emission control,” J. Lightwave Technol. 17, 2018–2024 (1999).
[CrossRef]

Lee, J. C.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lim, and J. C. Lee, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals,” Appl. Phys. Lett. 79, 15–17 (2001).
[CrossRef]

Lekner, J.

J. Lekner, “Omnidirectional reflection by multilayer dielectric mirrors,” J. Opt. A: Pure Appl. Opt. 2, 349–352 (2000).
[CrossRef]

Lenzner, M.

Li, H.

H. Li, G. Gu, H. Chen, and S. Zhu, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
[CrossRef]

Li, Y.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Li, Z.

D. Zhang, Z. Li, W. Hu, and B. Cheng, “Broadband optical reflector—an application of light localization in one dimension,” Appl. Phys. Lett. 67, 2431–2432 (1995).
[CrossRef]

Liddell, H. M.

Lim, H.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lim, and J. C. Lee, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals,” Appl. Phys. Lett. 79, 15–17 (2001).
[CrossRef]

Lin, Z.

J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
[CrossRef]

Liu, X.

X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
[CrossRef]

Lusk, D.

D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
[CrossRef]

Maskaly, G. R.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[CrossRef] [PubMed]

Matuschek, N.

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

Morf, R.

Park, H. Y.

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lim, and J. C. Lee, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals,” Appl. Phys. Lett. 79, 15–17 (2001).
[CrossRef]

Placido, F.

D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
[CrossRef]

Porpov, K. V.

Prideaux, P. H.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[CrossRef] [PubMed]

Ripin, D. J.

Roberts, P. J.

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Scheuer, V.

Schibli, T.

Southwell, W. H.

Spielmann, C.

Spielmann, Ch.

Stingl, A.

Sullivan, B. T.

Szipocs, R.

Temelkuran, B.

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
[CrossRef] [PubMed]

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Appl. Opt. (6)

Appl. Phys. A (1)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional reflection from a one-dimensional dielectric lattice,” Appl. Phys. A 68, 25–28 (1999).
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Appl. Phys. Lett. (5)

J. Zi, J. Wan, and C. Zhang, “Large frequency range of negligible transmission in one-dimensional photonic quantum well structures,” Appl. Phys. Lett. 73, 2084–2086 (1998).
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H. Li, G. Gu, H. Chen, and S. Zhu, “Disordered dielectric high reflectors with broadband from visible to infrared,” Appl. Phys. Lett. 74, 3260–3262 (1999).
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[CrossRef]

Y. K. Ha, Y. C. Yang, J. E. Kim, H. Y. Park, C. S. Kee, H. Lim, and J. C. Lee, “Tunable omnidirectional reflection bands and defect modes of a one-dimensional photonic band gap structure with liquid crystals,” Appl. Phys. Lett. 79, 15–17 (2001).
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X. Wang, X. Hu, Y. Li, W. Jia, C. Xu, X. Liu, and J. Zi, “Enlargement of omnidirectional total reflection frequency range in one-dimensional photonic crystals by using photonic heterostructures,” Appl. Phys. Lett. 80, 4291–4293 (2002).
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J. Lightwave Technol. (2)

J. Opt. A: Pure Appl. Opt. (2)

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J. Phys. D (1)

J. Xu, H. Fang, and Z. Lin, “Expanding high reflection range in a dielectric multilayer reflector by disorder and inhomogeneity,” J. Phys. D 34, 445–449 (2001).
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Opt. Commun. (2)

D. Lusk, I. Abdulhalim, and F. Placido, “Omnidirectional reflection from Fibonacci quasi-periodic one-dimensional photonic crystal,” Opt. Commun. 198, 273–279 (2001).
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P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgaps and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
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Opt. Lett. (6)

Phys. Rev. Lett. (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
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S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
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Science (4)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282, 1679–1682 (1998).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415–419 (2000).
[CrossRef] [PubMed]

S. D. Hart, G. R. Maskaly, B. Temelkuran, P. H. Prideaux, J. D. Joannopoulos, and Y. Fink, “External reflection from omnidirectional dielectric mirror fibers,” Science 296, 510–513 (2002).
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Z. Knittl, Optics of Thin Films (Wiley, New York, 1976).

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Figures (6)

Fig. 1
Fig. 1

Three examples of a staggered structure: (a) single-staggered structure with kl=0.6 and m=10; (b) double-staggered structure with kh=kl=0.6 and m=10; (c) double-staggered structure with kh=0.6, kl=0.2, and m=10.

Fig. 2
Fig. 2

Numerical results of the ODR range of a single-staggered structure as a function of number of cells m for kl=0.1, 0.3, 0.5, 0.7, and 0.9. The case of kl=0 corresponds to a periodic structure.

Fig. 3
Fig. 3

Reflective spectra at three incident angles of a single-staggered structure with m=90 for (a) kl=0.5 and (b) kl=0.7. Two lines and the corresponding frequency in each figure denote the range with reflectance higher than 99% for all incident angles and polarizations.

Fig. 4
Fig. 4

Upper edge of the bandgap at normal incidence as a function of a staggered parameter for m=80, 90, and 100.

Fig. 5
Fig. 5

Dependence of the ODR range of a single-staggered structure on structural parameters: (a) number of cells and (b) the staggered parameter. The width of the ODR range as a function of the staggered parameter is shown in (c).

Fig. 6
Fig. 6

Dependence of the ODR range of a degenerate double-staggered structure on structural parameters: (a) number of cells and (b) the staggered parameter. The width of the ODR range as a function of staggered parameter is shown in (c).

Equations (10)

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

H(i)=c(2i-1)H(1),L(i)=c(2i)L(1),
c(i)=1+d(i-1),
H(i)=a(i)H˜,L(i)=b(i)L˜,
a(i)=1+kh2 i-1m-1-1,
b(i)=1+kl2 i-1m-1-1,
H(i)=H0,L(i)=b(i)L0,
b(i)=1+kl2 i-1m-1-1.
H(i)=a(i)H0,L(i)=a(i)L0,
a(i)=1+k2 i-1m-1-1.
H(i)H(i)+L(i)=H0H0+L0,

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