Abstract

General conditions for obtaining omnidirectional bandgaps (OBG) were derived based on consideration of the permeability of the material. It was found that the OBG is a universal property of a special kind of photonic crystal (PC) comprising two alternate layers with different wave impedances and with the same product of permittivity and permeability (not only the refractive index). Moreover, for this kind of PC, the OBG can be broadened by decreasing the refractive index of the ambient medium and/or increasing the ratio between the wave impedances of the components of the PC.

© 2006 Optical Society of America

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  1. E. Yablonovitch, 'Inhibited spontaneous emission in solid-state physics and electronics,' Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, 'Large omnidirectional band gaps in metallodielectric photonic crystals,' Phys. Rev. B 54, 11245-11251 (1996).
    [CrossRef]
  4. K. Busch and S. John, 'Photonic band gap formation in certain self-organizing systems,' Phys. Rev. E 58, 3896-3908 (1998).
    [CrossRef]
  5. R. Biswas, M. M. Sigalas, K.-M. Ho, and S.-Y. Lin, 'Three-dimensional photonic band gaps in modified simple cubic lattices,' Phys. Rev. B 65, 205121 (2002).
    [CrossRef]
  6. D. C. Meisel, M. Wegener, and K. Busch, 'Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetries and complete photonic band gaps,' Phys. Rev. B 70, 165104 (2004).
    [CrossRef]
  7. 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]
  8. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, 'Complete band gaps in one-dimensional left-handed periodic structures,' Phys. Rev. Lett. 95, 193903-4 (2005).
    [CrossRef]
  9. K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, 'Creating 'defects' in photonic crystals by controlling polarizations,' Phys. Lett. A 325, 415-419 (2004).
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    [CrossRef]
  12. 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. LT17, 2039-2041 (1999).
    [CrossRef]
  13. M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, 'An all-dielectric coaxial waveguide,' Science 289, 415-420 (2000).
    [CrossRef] [PubMed]
  14. 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, 510-514 (2002).
    [CrossRef] [PubMed]
  15. B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, 'Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,' Nature 420, 650-653 (2002).
    [CrossRef] [PubMed]
  16. C. S. Kee, J. E. Kim, and H. Y. Park, 'Omnidirectional reflection bands of one-dimensional magnetic photonic crystals,' J. Opt. A 6, 1086-1088 (2004).
    [CrossRef]
  17. J. B. Pendry, 'Negative refraction makes a perfect lens,' Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  18. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, 'Experimental demonstration of near-infrared negative-index metamaterials,' Phys. Rev. Lett. 95, 137404 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  20. M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Chap. 1.
  21. C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
    [CrossRef]
  22. L. Wu, S. He, and L. Chen, 'On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,' http://www.arxiv:physics/0211007 (2002).
  23. L. Wang, H. Chen, and S. Zhu, 'Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,' Phys. Rev. B 70, 245102 (2004).
    [CrossRef]
  24. Fransisco Villa and J. A. Gaspar-Armenta, 'Electromagnetic surface waves: photonic crystal-photonic crystal interface,' Opt. Commun. 223, 109-115 (2003).
    [CrossRef]
  25. J. J. Vera, 'Some properties of multi-layer films with periodic structure,' Opt. Acta 11, 315-331 (1964).
    [CrossRef]

2005 (3)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, 'Complete band gaps in one-dimensional left-handed periodic structures,' Phys. Rev. Lett. 95, 193903-4 (2005).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, 'Experimental demonstration of near-infrared negative-index metamaterials,' Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, 'Nanofabricated media with negative permeability at visible frequencies,' Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

2004 (4)

L. Wang, H. Chen, and S. Zhu, 'Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,' Phys. Rev. B 70, 245102 (2004).
[CrossRef]

K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, 'Creating 'defects' in photonic crystals by controlling polarizations,' Phys. Lett. A 325, 415-419 (2004).
[CrossRef]

D. C. Meisel, M. Wegener, and K. Busch, 'Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetries and complete photonic band gaps,' Phys. Rev. B 70, 165104 (2004).
[CrossRef]

C. S. Kee, J. E. Kim, and H. Y. Park, 'Omnidirectional reflection bands of one-dimensional magnetic photonic crystals,' J. Opt. A 6, 1086-1088 (2004).
[CrossRef]

2003 (1)

Fransisco Villa and J. A. Gaspar-Armenta, 'Electromagnetic surface waves: photonic crystal-photonic crystal interface,' Opt. Commun. 223, 109-115 (2003).
[CrossRef]

2002 (3)

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, 510-514 (2002).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, 'Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,' Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

R. Biswas, M. M. Sigalas, K.-M. Ho, and S.-Y. Lin, 'Three-dimensional photonic band gaps in modified simple cubic lattices,' Phys. Rev. B 65, 205121 (2002).
[CrossRef]

2000 (2)

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, 'An all-dielectric coaxial waveguide,' Science 289, 415-420 (2000).
[CrossRef] [PubMed]

J. B. Pendry, 'Negative refraction makes a perfect lens,' Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999 (3)

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]

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. LT17, 2039-2041 (1999).
[CrossRef]

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

1998 (3)

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]

K. Busch and S. John, 'Photonic band gap formation in certain self-organizing systems,' Phys. Rev. E 58, 3896-3908 (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]

1996 (1)

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, 'Large omnidirectional band gaps in metallodielectric photonic crystals,' Phys. Rev. B 54, 11245-11251 (1996).
[CrossRef]

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]

1964 (1)

J. J. Vera, 'Some properties of multi-layer films with periodic structure,' Opt. Acta 11, 315-331 (1964).
[CrossRef]

Benoit, G.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, 'Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,' Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Biswas, R.

R. Biswas, M. M. Sigalas, K.-M. Ho, and S.-Y. Lin, 'Three-dimensional photonic band gaps in modified simple cubic lattices,' Phys. Rev. B 65, 205121 (2002).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Chap. 1.

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, 'Experimental demonstration of near-infrared negative-index metamaterials,' Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Busch, K.

D. C. Meisel, M. Wegener, and K. Busch, 'Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetries and complete photonic band gaps,' Phys. Rev. B 70, 165104 (2004).
[CrossRef]

K. Busch and S. John, 'Photonic band gap formation in certain self-organizing systems,' Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

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. LT17, 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.

L. Wang, H. Chen, and S. Zhu, 'Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,' Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Chen, L.

L. Wu, S. He, and L. Chen, 'On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,' http://www.arxiv:physics/0211007 (2002).

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]

Fan, S.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, 'An all-dielectric coaxial waveguide,' Science 289, 415-420 (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. LT17, 2039-2041 (1999).
[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]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, 'Large omnidirectional band gaps in metallodielectric photonic crystals,' Phys. Rev. B 54, 11245-11251 (1996).
[CrossRef]

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, 'Experimental demonstration of near-infrared negative-index metamaterials,' Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Fink, Y.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, 'Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,' Nature 420, 650-653 (2002).
[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, 510-514 (2002).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, 'An all-dielectric coaxial waveguide,' Science 289, 415-420 (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. LT17, 2039-2041 (1999).
[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]

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, 'Nanofabricated media with negative permeability at visible frequencies,' Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

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]

Gaspar-Armenta, J. A.

Fransisco Villa and J. A. Gaspar-Armenta, 'Electromagnetic surface waves: photonic crystal-photonic crystal interface,' Opt. Commun. 223, 109-115 (2003).
[CrossRef]

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, 'Nanofabricated media with negative permeability at visible frequencies,' Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, 'Nanofabricated media with negative permeability at visible frequencies,' Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Grigorenko, A. N.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, 'Nanofabricated media with negative permeability at visible frequencies,' Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Hart, S. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, 'Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,' Nature 420, 650-653 (2002).
[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, 510-514 (2002).
[CrossRef] [PubMed]

He, S.

L. Wu, S. He, and L. Chen, 'On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,' http://www.arxiv:physics/0211007 (2002).

Ho, K.-M.

R. Biswas, M. M. Sigalas, K.-M. Ho, and S.-Y. Lin, 'Three-dimensional photonic band gaps in modified simple cubic lattices,' Phys. Rev. B 65, 205121 (2002).
[CrossRef]

Ibanescu, M.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, 'An all-dielectric coaxial waveguide,' Science 289, 415-420 (2000).
[CrossRef] [PubMed]

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, 510-514 (2002).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, 'Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,' Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, 'An all-dielectric coaxial waveguide,' Science 289, 415-420 (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. LT17, 2039-2041 (1999).
[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]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, 'Large omnidirectional band gaps in metallodielectric photonic crystals,' Phys. Rev. B 54, 11245-11251 (1996).
[CrossRef]

John, S.

K. Busch and S. John, 'Photonic band gap formation in certain self-organizing systems,' Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

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

Kee, C. S.

C. S. Kee, J. E. Kim, and H. Y. Park, 'Omnidirectional reflection bands of one-dimensional magnetic photonic crystals,' J. Opt. A 6, 1086-1088 (2004).
[CrossRef]

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Khrushchev, I. Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, 'Nanofabricated media with negative permeability at visible frequencies,' Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Kim, E. J.

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Kim, J. E.

C. S. Kee, J. E. Kim, and H. Y. Park, 'Omnidirectional reflection bands of one-dimensional magnetic photonic crystals,' J. Opt. A 6, 1086-1088 (2004).
[CrossRef]

Kim, S. J.

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, 'Complete band gaps in one-dimensional left-handed periodic structures,' Phys. Rev. Lett. 95, 193903-4 (2005).
[CrossRef]

Kwon, Y. S.

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

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]

Li, R.

K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, 'Creating 'defects' in photonic crystals by controlling polarizations,' Phys. Lett. A 325, 415-419 (2004).
[CrossRef]

Lim, H.

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Lin, S.-Y.

R. Biswas, M. M. Sigalas, K.-M. Ho, and S.-Y. Lin, 'Three-dimensional photonic band gaps in modified simple cubic lattices,' Phys. Rev. B 65, 205121 (2002).
[CrossRef]

Liu, D.

K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, 'Creating 'defects' in photonic crystals by controlling polarizations,' Phys. Lett. A 325, 415-419 (2004).
[CrossRef]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, 'Experimental demonstration of near-infrared negative-index metamaterials,' Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

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, 510-514 (2002).
[CrossRef] [PubMed]

Meisel, D. C.

D. C. Meisel, M. Wegener, and K. Busch, 'Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetries and complete photonic band gaps,' Phys. Rev. B 70, 165104 (2004).
[CrossRef]

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]

Myung, N. H.

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, 'Experimental demonstration of near-infrared negative-index metamaterials,' Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, 'Experimental demonstration of near-infrared negative-index metamaterials,' Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Park, H. Y.

C. S. Kee, J. E. Kim, and H. Y. Park, 'Omnidirectional reflection bands of one-dimensional magnetic photonic crystals,' J. Opt. A 6, 1086-1088 (2004).
[CrossRef]

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Pendry, J. B.

J. B. Pendry, 'Negative refraction makes a perfect lens,' Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Petrovic, J.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, 'Nanofabricated media with negative permeability at visible frequencies,' Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

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, 510-514 (2002).
[CrossRef] [PubMed]

Ren, K.

K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, 'Creating 'defects' in photonic crystals by controlling polarizations,' Phys. Lett. A 325, 415-419 (2004).
[CrossRef]

Ren, X.

K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, 'Creating 'defects' in photonic crystals by controlling polarizations,' Phys. Lett. A 325, 415-419 (2004).
[CrossRef]

Ripin, D. J.

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. LT17, 2039-2041 (1999).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, 'Complete band gaps in one-dimensional left-handed periodic structures,' Phys. Rev. Lett. 95, 193903-4 (2005).
[CrossRef]

Shin, S. Y.

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Sigalas, M. M.

R. Biswas, M. M. Sigalas, K.-M. Ho, and S.-Y. Lin, 'Three-dimensional photonic band gaps in modified simple cubic lattices,' Phys. Rev. B 65, 205121 (2002).
[CrossRef]

Song, H. C.

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, 'Complete band gaps in one-dimensional left-handed periodic structures,' Phys. Rev. Lett. 95, 193903-4 (2005).
[CrossRef]

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, 510-514 (2002).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, 'Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,' Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Thomas, E. L.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, 'An all-dielectric coaxial waveguide,' Science 289, 415-420 (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. LT17, 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]

Vera, J. J.

J. J. Vera, 'Some properties of multi-layer films with periodic structure,' Opt. Acta 11, 315-331 (1964).
[CrossRef]

Villa, Fransisco

Fransisco Villa and J. A. Gaspar-Armenta, 'Electromagnetic surface waves: photonic crystal-photonic crystal interface,' Opt. Commun. 223, 109-115 (2003).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, 'Large omnidirectional band gaps in metallodielectric photonic crystals,' Phys. Rev. B 54, 11245-11251 (1996).
[CrossRef]

Wang, L.

L. Wang, H. Chen, and S. Zhu, 'Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,' Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Wegener, M.

D. C. Meisel, M. Wegener, and K. Busch, 'Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetries and complete photonic band gaps,' Phys. Rev. B 70, 165104 (2004).
[CrossRef]

Winn, J. N.

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]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Chap. 1.

Wu, L.

L. Wu, S. He, and L. Chen, 'On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,' http://www.arxiv:physics/0211007 (2002).

Yablonovitch, E.

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

Yarotsky, D. A.

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]

Zhang, S.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, 'Experimental demonstration of near-infrared negative-index metamaterials,' Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Zhang, Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, 'Nanofabricated media with negative permeability at visible frequencies,' Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

Zhou, J.

K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, 'Creating 'defects' in photonic crystals by controlling polarizations,' Phys. Lett. A 325, 415-419 (2004).
[CrossRef]

Zhu, S.

L. Wang, H. Chen, and S. Zhu, 'Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,' Phys. Rev. B 70, 245102 (2004).
[CrossRef]

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).
[CrossRef]

J. Lightwave Technol. (1)

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. LT17, 2039-2041 (1999).
[CrossRef]

J. Opt. A (1)

C. S. Kee, J. E. Kim, and H. Y. Park, 'Omnidirectional reflection bands of one-dimensional magnetic photonic crystals,' J. Opt. A 6, 1086-1088 (2004).
[CrossRef]

Nature (2)

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, 'Nanofabricated media with negative permeability at visible frequencies,' Nature 438, 335-338 (2005).
[CrossRef] [PubMed]

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, 'Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,' Nature 420, 650-653 (2002).
[CrossRef] [PubMed]

Opt. Acta (1)

J. J. Vera, 'Some properties of multi-layer films with periodic structure,' Opt. Acta 11, 315-331 (1964).
[CrossRef]

Opt. Commun. (1)

Fransisco Villa and J. A. Gaspar-Armenta, 'Electromagnetic surface waves: photonic crystal-photonic crystal interface,' Opt. Commun. 223, 109-115 (2003).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

K. Ren, X. Ren, R. Li, J. Zhou, and D. Liu, 'Creating 'defects' in photonic crystals by controlling polarizations,' Phys. Lett. A 325, 415-419 (2004).
[CrossRef]

Phys. Rev. B (4)

R. Biswas, M. M. Sigalas, K.-M. Ho, and S.-Y. Lin, 'Three-dimensional photonic band gaps in modified simple cubic lattices,' Phys. Rev. B 65, 205121 (2002).
[CrossRef]

D. C. Meisel, M. Wegener, and K. Busch, 'Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: symmetries and complete photonic band gaps,' Phys. Rev. B 70, 165104 (2004).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, 'Large omnidirectional band gaps in metallodielectric photonic crystals,' Phys. Rev. B 54, 11245-11251 (1996).
[CrossRef]

L. Wang, H. Chen, and S. Zhu, 'Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,' Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Phys. Rev. E (2)

C. S. Kee, E. J. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, 'Essential parameter in the formation of photonic band gaps,' Phys. Rev. E 59, 4695-4698 (1999).
[CrossRef]

K. Busch and S. John, 'Photonic band gap formation in certain self-organizing systems,' Phys. Rev. E 58, 3896-3908 (1998).
[CrossRef]

Phys. Rev. Lett. (5)

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]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, 'Complete band gaps in one-dimensional left-handed periodic structures,' Phys. Rev. Lett. 95, 193903-4 (2005).
[CrossRef]

J. B. Pendry, 'Negative refraction makes a perfect lens,' Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, 'Experimental demonstration of near-infrared negative-index metamaterials,' Phys. Rev. Lett. 95, 137404 (2005).
[CrossRef] [PubMed]

Science (3)

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, 'An all-dielectric coaxial waveguide,' Science 289, 415-420 (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, 510-514 (2002).
[CrossRef] [PubMed]

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]

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Chap. 1.

L. Wu, S. He, and L. Chen, 'On unusual narrow transmission bands for a multi-layered periodic structure containing left-handed materials,' http://www.arxiv:physics/0211007 (2002).

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Figures (2)

Fig. 1
Fig. 1

Schematic representation of finite magnetic multilayered periodic structures; and E and H are the electric and magnetic fields, respectively.

Fig. 2
Fig. 2

Photonic bandgaps as a function of the incident angle for multilayered structures with different parameters. (a) ϵ a = 4 , μ a = 1 , ϵ b = 1 , μ b = 4 , ϵ 0 = 1 , μ 0 = 1 . (b) ϵ a = 4 , μ a = 1 , ϵ b = 1 , μ b = 4 , ϵ 0 = 0.5 , μ 0 = 0.5 . (c) ϵ a = 4 , μ a = 1 , ϵ b = 0.5 , μ b = 8 , ϵ 0 = 0.5 , μ 0 = 0.5 . The gray areas depict the OBGs.

Equations (8)

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

r TE = ϵ a μ a cos ( θ a ) ϵ b μ b cos ( θ b ) ϵ a μ a cos ( θ a ) + ϵ b μ b cos ( θ b ) ,
r TM = ϵ b μ b cos ( θ a ) ϵ a μ a cos ( θ b ) ϵ b μ b cos ( θ a ) + ϵ a μ a cos ( θ b ) ,
tan θ B TE = μ b a ( μ b a ϵ b a ) ϵ b a μ b a 1 ,
tan θ B TM = ϵ b a ( ϵ b a μ b a ) ϵ b a μ b a 1 ,
θ a max = arcsin ( ϵ a μ 0 ϵ a μ a ) < min ( θ B TE , θ B TM ) .
cos β a cos β b [ ( p b p a + p a p b ) sin β a sin β b ] 2 + 1 = 0 ,
p j = { 1 ϵ 0 μ 0 ( ϵ j μ j ) sin 2 θ 0 Z j , TE Z j 1 ϵ 0 μ 0 ( ϵ j μ j ) sin 2 θ 0 , TM } , j = a , b ,
cos 2 β [ ( Z a Z b + Z b Z a ) sin 2 β ] 2 + 1 = 0 .

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