Abstract

Characterization of omnidirectional bandgaps in the multiple frequency ranges of one-dimensional photonic crystals based on gap map diagrams is proposed. In the gap map, there is one maximum range of the omnidirectional gap in each region, which is divided by the half-wave lines. The occurrence of the maximum range of the omnidirectional gap can be obtained by the characteristics of these gap map diagrams, including the zero-gap points, the occurrence of midgaps, and the frequency ranges of midgaps, for normal and grazing incidences with transverse-electric and transverse-magnetic polarizations. Moreover, concise empirical schemes are proposed to approximately determine the center and gap width of the maximum omnidirectional gaps in multiple frequency ranges.

© 2010 Optical Society of America

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  1. 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]
  2. E. Yablonovitch, “Engineered omnidirectional external-reflectivity spectra from one-dimensional layered interference filters,” Opt. Lett. 23, 1648–1649 (1998).
    [CrossRef]
  3. 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]
  4. R. G. DeCorby, H. T. Nguyen, P. K. Dwivedi, and T. J. Clement, “Planar omnidirectional reflectors in chalcogenide glass and polymer,” Opt. Express 13, 6228–6233 (2005).
    [CrossRef] [PubMed]
  5. J. Lekner, “Omnidirectional reflection by multilayer dielectric mirrors,” J. Opt. A, Pure Appl. Opt. 2, 349–352 (2000).
    [CrossRef]
  6. M. Deopura, C. K. Ullal, B. Temelkuran, and Y. Fink, “Dielectric omnidirectional visible reflector,” Opt. Lett. 26, 1197–1199 (2001).
    [CrossRef]
  7. B. Temelkuran, E. L. Thomas, J. D. Joannopoulos, and Y. Fink, “Low-loss infrared dielectric material system for broadband dual-range omnidirectional reflectivity,” Opt. Lett. 26, 1370–1372 (2001).
    [CrossRef]
  8. I. Nusinsky and A. A. Hardy, “Omnidirectional reflection in several frequency ranges of one-dimensional photonic crystals,” Appl. Opt. 46, 3510–3517 (2007).
    [CrossRef] [PubMed]
  9. 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]
  10. Y. Xiang, X. Dai, S. Wen, and D. Fan, “Enlargement of zero averaged refractive index gaps in the photonic heterostructures containing negative-index materials,” Phys. Rev. E 76, 056604 (2007).
    [CrossRef]
  11. G. Alagappan and P. Wu, “Geometrically distributed one-dimensional photonic crystals for light-reflection in all angles,” Opt. Express 17, 11550–11557 (2009).
    [CrossRef] [PubMed]
  12. P. Han and H. Wang, “Criterion of omnidirectional reflection in a one-dimensional photonic heterostructure,” J. Opt. Soc. Am. B 22, 1571–1575 (2005).
    [CrossRef]
  13. 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]
  14. V. A. Tolmachev, T. S. Perova, and R. A. Moore, “Method of construction of composite one-dimensional photonic crystal with extended photonic band gaps,” Opt. Express 13, 8433–8441 (2005).
    [CrossRef] [PubMed]
  15. 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]
  16. 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]
  17. A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
    [CrossRef]
  18. S. Fan, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
    [CrossRef]
  19. 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 (2005).
    [CrossRef] [PubMed]
  20. W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
    [CrossRef]
  21. D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
    [CrossRef]
  22. J. A. Gaspar-Armenta and F. Villa, “Band-structure properties of one-dimensional photonic crystals under the formalism of equivalent systems,” J. Opt. Soc. Am. B 21, 405–412 (2004).
    [CrossRef]
  23. I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006).
    [CrossRef]
  24. W. J. Hsueh and J. C. Lin, “Numerical stable method for the analysis of Bloch waves in a general one-dimensional photonic crystal cavity,” J. Opt. Soc. Am. B 24, 2249–2258 (2007).
    [CrossRef]
  25. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1988).

2009

2008

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
[CrossRef]

2007

2006

I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006).
[CrossRef]

2005

R. G. DeCorby, H. T. Nguyen, P. K. Dwivedi, and T. J. Clement, “Planar omnidirectional reflectors in chalcogenide glass and polymer,” Opt. Express 13, 6228–6233 (2005).
[CrossRef] [PubMed]

A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
[CrossRef]

S. Fan, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

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 (2005).
[CrossRef] [PubMed]

P. Han and H. Wang, “Criterion of omnidirectional reflection in a one-dimensional photonic heterostructure,” J. Opt. Soc. Am. B 22, 1571–1575 (2005).
[CrossRef]

V. A. Tolmachev, T. S. Perova, and R. A. Moore, “Method of construction of composite one-dimensional photonic crystal with extended photonic band gaps,” Opt. Express 13, 8433–8441 (2005).
[CrossRef] [PubMed]

2004

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

J. A. Gaspar-Armenta and F. Villa, “Band-structure properties of one-dimensional photonic crystals under the formalism of equivalent systems,” J. Opt. Soc. Am. B 21, 405–412 (2004).
[CrossRef]

2002

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

2000

J. Lekner, “Omnidirectional reflection by multilayer dielectric mirrors,” J. Opt. A, Pure Appl. Opt. 2, 349–352 (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

1998

Akjou, A.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Alagappan, G.

Bria, D.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Chen, C.

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, C. H.

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
[CrossRef]

Chen, C. T.

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
[CrossRef]

Chigrin, D. N.

Clement, T. J.

Dai, X.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Enlargement of zero averaged refractive index gaps in the photonic heterostructures containing negative-index materials,” Phys. Rev. E 76, 056604 (2007).
[CrossRef]

DeCorby, R. G.

Deopura, M.

Djafari-Rouhani, B.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Dobrzynski, L.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Dwivedi, P. K.

Efros, A. L.

A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
[CrossRef]

El Boudouti, E. H.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Elson, J. M.

S. Fan, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

Fan, D.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Enlargement of zero averaged refractive index gaps in the photonic heterostructures containing negative-index materials,” Phys. Rev. E 76, 056604 (2007).
[CrossRef]

Fan, S.

S. Fan, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[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, 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]

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]

B. Temelkuran, E. L. Thomas, J. D. Joannopoulos, and Y. Fink, “Low-loss infrared dielectric material system for broadband dual-range omnidirectional reflectivity,” Opt. Lett. 26, 1370–1372 (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]

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]

Gaponenko, S. V.

Gaspar-Armenta, J. A.

Golubev, V. G.

A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
[CrossRef]

Han, P.

Hardy, A. A.

I. Nusinsky and A. A. Hardy, “Omnidirectional reflection in several frequency ranges of one-dimensional photonic crystals,” Appl. Opt. 46, 3510–3517 (2007).
[CrossRef] [PubMed]

I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006).
[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]

Hsueh, W. J.

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
[CrossRef]

W. J. Hsueh and J. C. Lin, “Numerical stable method for the analysis of Bloch waves in a general one-dimensional photonic crystal cavity,” J. Opt. Soc. Am. B 24, 2249–2258 (2007).
[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]

B. Temelkuran, E. L. Thomas, J. D. Joannopoulos, and Y. Fink, “Low-loss infrared dielectric material system for broadband dual-range omnidirectional reflectivity,” Opt. Lett. 26, 1370–1372 (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]

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]

Kamaev, V.

A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
[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 (2005).
[CrossRef] [PubMed]

Kurdyukov, D. A.

A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
[CrossRef]

Lavrinenko, A. V.

Lekner, J.

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

Li, C. Y.

A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
[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]

Lin, J. C.

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]

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]

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]

Moore, R. A.

Nguyen, H. T.

Nougaoui, A.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Nusinsky, I.

I. Nusinsky and A. A. Hardy, “Omnidirectional reflection in several frequency ranges of one-dimensional photonic crystals,” Appl. Opt. 46, 3510–3517 (2007).
[CrossRef] [PubMed]

I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006).
[CrossRef]

Overfelt, P. L.

S. Fan, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

Perova, T. S.

Pokrovsky, A. L.

A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
[CrossRef]

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]

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 (2005).
[CrossRef] [PubMed]

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 (2005).
[CrossRef] [PubMed]

Temelkuran, B.

Thomas, E. L.

B. Temelkuran, E. L. Thomas, J. D. Joannopoulos, and Y. Fink, “Low-loss infrared dielectric material system for broadband dual-range omnidirectional reflectivity,” Opt. Lett. 26, 1370–1372 (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, 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]

Tolmachev, V. A.

Ullal, C. K.

Vardeny, Z. V.

A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
[CrossRef]

Vigneron, J. P.

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Villa, F.

Wang, H.

Wang, 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]

Wen, S.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Enlargement of zero averaged refractive index gaps in the photonic heterostructures containing negative-index materials,” Phys. Rev. E 76, 056604 (2007).
[CrossRef]

Winn, J. N.

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]

Wu, P.

Xiang, Y.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Enlargement of zero averaged refractive index gaps in the photonic heterostructures containing negative-index materials,” Phys. Rev. E 76, 056604 (2007).
[CrossRef]

Xu, C.

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]

Yablonovitch, E.

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1988).

Yarotsky, D. A.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1988).

Zi, J.

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]

Appl. Opt.

Appl. Phys. Lett.

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]

J. Lightwave Technol.

J. Opt. A, Pure Appl. Opt.

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

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Phys. Rev. A

W. J. Hsueh, C. T. Chen, and C. H. Chen, “Omnidirectional band gap in Fibonacci photonic crystal with metamaterials using a band-edge formalism,” Phys. Rev. A 78, 013836 (2008).
[CrossRef]

Phys. Rev. B

A. L. Pokrovsky, V. Kamaev, C. Y. Li, Z. V. Vardeny, A. L. Efros, D. A. Kurdyukov, and V. G. Golubev, “Theoretical and experimental studies of metal-infiltrated opals,” Phys. Rev. B 71, 165114 (2005).
[CrossRef]

S. Fan, J. M. Elson, and P. L. Overfelt, “Transparent photonic band in metallodielectric nanostructures,” Phys. Rev. B 72, 085117 (2005).
[CrossRef]

I. Nusinsky and A. A. Hardy, “Band-gap analysis of one-dimensional photonic crystals and conditions for gap closing,” Phys. Rev. B 73, 125104 (2006).
[CrossRef]

Phys. Rev. E

D. Bria, B. Djafari-Rouhani, A. Akjou, L. Dobrzynski, J. P. Vigneron, E. H. El Boudouti, and A. Nougaoui, “Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials,” Phys. Rev. E 69, 066613 (2004).
[CrossRef]

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Enlargement of zero averaged refractive index gaps in the photonic heterostructures containing negative-index materials,” Phys. Rev. E 76, 056604 (2007).
[CrossRef]

Phys. Rev. Lett.

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 (2005).
[CrossRef] [PubMed]

Science

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).
[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

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1988).

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Figures (7)

Fig. 1
Fig. 1

The gap maps for (a) TE1 and TM1 modes, and (b) NI and TM1 modes in the PC with n A = 2.0 , n B = 4.0 . In (a), the gray areas correspond to the overlap of the bandgaps between the TE1 and TM1 modes. The thick solid and dashed lines (red) correspond to the half-wave lines for both of the TM1 and TE1 modes. The thin solid lines correspond to gap edges for the TE1 (green) and TM1 (black) modes. In (b), the gray areas correspond to the overlap of the bandgaps between the NI and TM1 modes. The thick solid and dashed lines correspond to half-wave lines for both of the TM1 (blue) and NI (red) modes. The thin solid lines correspond to gap edges for the NI (green) and TM1 (black) modes.

Fig. 2
Fig. 2

(a) Existence condition for the midgap and the maximum gap in some regions for the TM1 mode versus the ratio n B / n A for the PC with n A = 2.0 . (b) Center of the frequency range of each midgap and maximum gap. (c) Gap width of each midgap and maximum gap. The dashed and thin solid lines correspond to the midgap and the maximum gap, respectively. The numbers p and q in parentheses ( p , q ) correspond to the gap in region ( p , q ) . It is noted that the dashed lines for regions (0,0), (1,1), and (2,2) in (a) and (c) overlap.

Fig. 3
Fig. 3

Sketch of the relation between the maximum gap in region ( p , q ) for the ODG and the midgaps for the NI, TM1, and ODR modes. The triangle (blue) and open circle (red) mark the centers of the maximum gap and the midgap, respectively, of the ODR mode. The rectangles mark the centers of the midgaps for the NI and TM1 modes.

Fig. 4
Fig. 4

(a) Existence condition of the midgap and maximum gap in some regions for the ODR mode. (b) Center of the frequency range of each midgap and the maximum gap. The dashed and thin solid lines correspond to the midgap and the maximum gap, respectively. The rectangles and circles mark the critical points for the midgap and the ODGs, respectively. It is noted that the dashed lines for regions (0,0), (1,1), and (2,2) in (a) overlap. The parameters and notations are the same as in Fig. 3.

Fig. 5
Fig. 5

The midgap width and maximum gap in some regions for the ODR mode. The thin solid lines correspond to the gap width of the MODG. The dashed and dotted lines correspond to the midgap width calculated by Eqs. (12, 13), respectively. The circles mark the critical points for the existence of the ODGs. The rectangles and crosses mark the approximated critical points determined by Eqs. (12, 13), respectively.

Fig. 6
Fig. 6

Difference between the calculated and the exact values of the MODG in region (0,0). The solid line corresponds to the quarter wave stack. The dotted and dashed lines correspond to the approximated methods based on the quarter wave stack [3, 5] and Eq. (13), respectively.

Fig. 7
Fig. 7

Contour of the calculated and exact gap widths of the MODG in region (2,2) relative to the center frequency. The ranges of the refractive indices in the PCs are n A < 2.5 and n B / n A < 3 . The thin solid lines correspond to the exact MODG. The dashed and dotted lines correspond to the gap width ratio calculated by Eqs. (12, 13), respectively.

Equations (17)

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J e = 0 ,     for   e = 1 , 1 ,
J e = cos   k A d A   cos   k B d B Λ   sin   k A d A   sin   k B d B e ,
J e F = 0.
k 0 ( n A 2 n e 2 ) 1 / 2 d A = p π ,
k 0 ( n B 2 n e 2 ) 1 / 2 d B = q π ,
F p , q = ( 1 + q p n f , A n f , B ) 1 ,
Ω p , q = 0.5 ( p n f , A 1 + q n f , B 1 ) ,
F p , q , c = ( 1 + q + 0.5 p + 0.5 n f , A n f , B ) 1 ,
Ω p , q , c = 0.5 [ ( p + 0.5 ) n f , A 1 + ( q + 0.5 ) n f , B 1 ] .
G W p , q , c = 2 ϕ A Ω p , q , c ( p + 0.5 ) π .
cos ( p q p + 0.5 ϕ A ) ( 1 Λ ¯ ) cos ( p + q + 1 p + 0.5 ϕ A ) ( 1 + Λ ¯ ) + 2 = 0 ,
G W p , q , c = ϕ A π ( n f , A 1 + q + 0.5 p + 0.5 n f , B 1 ) .
G W p , p , c = n f , A 1 + n f , B 1 π sin 1 Λ ¯ 1 Λ ¯ + 1 .
F p , q , c ( Omni ) = 0.5 { [ 1 + q + 0.5 p + 0.5 α 1 ] 1 + [ 1 + q + 0.5 p + 0.5 α 2 ] 1 } ,
Ω p , q , c ( Omni ) = 0.25 [ α A ( p + 0.5 ) + α B ( q + 0.5 ) ] ,
G W p , q , d ( Omni ) = Ω p , q , c ( NI ) Ω p , q , c ( TM 1 ) + 0.5 ( G W p , q , c ( NI ) + G W p , q , c ( TM 1 ) ) .
G W p , q , c ( Omni ) = Ω p , q , c ( NI ) Ω p , q , c ( TM 1 ) + 0.5 ( G W p , q , c ( NI ) + G W p , q , c ( TM 1 ) ) + Δ S p , q ,

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