Abstract

We systematically investigate the criterion of omnidirectional reflection in one-dimensional photonic heterostructures and show that the photonic heterostructures can extend not only the frequency range of omnidirectional reflection but also the range of materials; that is, the refractive-index contrast between the composites can be much lower than those required in single periodic structures. This idea is of immense practical importance and can be extended to other structures whose underlying physics are the same as those of a photonic heterostructure, such as a staggered structure and some types of quasi-period structure.

© 2005 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]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional dielectric mirror fibers," Opt. Lett. 23, 1573-1575 (1998).
    [CrossRef]
  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]
  5. 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: Mater. Sci. Process. 68, 25-28 (1999).
    [CrossRef]
  6. 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]
  7. 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]
  8. 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]
  9. M. Deopura, C. K. Ullal, B. Temelkuran, and Y. Fink, "Dielectric omnidirectional visible reflector," Opt. Lett. 26, 1197-1199 (2001).
    [CrossRef]
  10. P. Han and H. Z. Wang, "Extension of omnidirectional reflection range in one-dimensional photonic crystals with a staggered structure," J. Opt. Soc. Am. B 20, 1996-2001 (2003).
    [CrossRef]
  11. J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
    [CrossRef]
  12. W. H. Southwell, "Omnidirectional mirror design with quarter-wave dielectric stacks," Appl. Opt. 38, 5464-5467 (1999).
    [CrossRef]
  13. Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, "Silicon-based photonic crystal heterostructure," Appl. Phys. Lett. 79, 3395-3397 (2001).
    [CrossRef]
  14. 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]
  15. B. Huang, P. Gu, and L. Yang, "Construction of one-dimensional photonic crystals based on the incident angle domain," Phys. Rev. E 68, 046601-5 (2003).
    [CrossRef]
  16. J. Lekner, "Omnidirectional reflection by multilayer dielectric mirrors," J. Opt. A, Pure Appl. Opt. 2, 349-352 (2000).
    [CrossRef]
  17. H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, 1986), pp. 177-179.
  18. K. Sakoda, Optical Properties of Photonic Crystals (Spring-Verlag, 2001), pp. 21-22.

2003 (3)

B. Huang, P. Gu, and L. Yang, "Construction of one-dimensional photonic crystals based on the incident angle domain," Phys. Rev. E 68, 046601-5 (2003).
[CrossRef]

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[CrossRef]

P. Han and H. Z. Wang, "Extension of omnidirectional reflection range in one-dimensional photonic crystals with a staggered structure," J. Opt. Soc. Am. B 20, 1996-2001 (2003).
[CrossRef]

2002 (2)

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 (2)

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, "Silicon-based photonic crystal heterostructure," Appl. Phys. Lett. 79, 3395-3397 (2001).
[CrossRef]

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

2000 (2)

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 (3)

1998 (2)

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional dielectric mirror fibers," 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]

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]

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]

Chigrin, D. N.

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]

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: Mater. Sci. Process. 68, 25-28 (1999).
[CrossRef]

Deopura, M.

Dong, J. W.

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[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]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional dielectric mirror fibers," 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]

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]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional dielectric mirror fibers," 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.

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]

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: Mater. Sci. Process. 68, 25-28 (1999).
[CrossRef]

Gu, P.

B. Huang, P. Gu, and L. Yang, "Construction of one-dimensional photonic crystals based on the incident angle domain," Phys. Rev. E 68, 046601-5 (2003).
[CrossRef]

Han, P.

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[CrossRef]

P. Han and H. Z. Wang, "Extension of omnidirectional reflection range in one-dimensional photonic crystals with a staggered structure," J. Opt. Soc. Am. B 20, 1996-2001 (2003).
[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]

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]

Huang, B.

B. Huang, P. Gu, and L. Yang, "Construction of one-dimensional photonic crystals based on the incident angle domain," Phys. Rev. E 68, 046601-5 (2003).
[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]

Jiang, Z. M.

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, "Silicon-based photonic crystal heterostructure," Appl. Phys. Lett. 79, 3395-3397 (2001).
[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]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional dielectric mirror fibers," 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]

John, S.

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

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: Mater. Sci. Process. 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]

Lekner, J.

J. Lekner, "Omnidirectional reflection by multilayer dielectric mirrors," J. Opt. A, Pure Appl. Opt. 2, 349-352 (2000).
[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]

Liu, J.

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, "Silicon-based photonic crystal heterostructure," Appl. Phys. Lett. 79, 3395-3397 (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]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, 1986), pp. 177-179.

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]

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]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Spring-Verlag, 2001), pp. 21-22.

Shi, B.

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, "Silicon-based photonic crystal heterostructure," Appl. Phys. Lett. 79, 3395-3397 (2001).
[CrossRef]

Southwell, W. H.

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]

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

Thomas, E. L.

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]

Ullal, C. K.

Wang, H. Z.

P. Han and H. Z. Wang, "Extension of omnidirectional reflection range in one-dimensional photonic crystals with a staggered structure," J. Opt. Soc. Am. B 20, 1996-2001 (2003).
[CrossRef]

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[CrossRef]

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]

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, "Silicon-based photonic crystal heterostructure," Appl. Phys. Lett. 79, 3395-3397 (2001).
[CrossRef]

Winn, J. N.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional dielectric mirror fibers," 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]

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.

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

Yang, L.

B. Huang, P. Gu, and L. Yang, "Construction of one-dimensional photonic crystals based on the incident angle domain," Phys. Rev. E 68, 046601-5 (2003).
[CrossRef]

Yarotsky, D. A.

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]

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: Mater. Sci. Process. 68, 25-28 (1999).
[CrossRef]

Zhao, D. T.

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, "Silicon-based photonic crystal heterostructure," Appl. Phys. Lett. 79, 3395-3397 (2001).
[CrossRef]

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. (1)

Appl. Phys. A: Mater. Sci. Process. (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: Mater. Sci. Process. 68, 25-28 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

Z. M. Jiang, B. Shi, D. T. Zhao, J. Liu, and X. Wang, "Silicon-based photonic crystal heterostructure," Appl. Phys. Lett. 79, 3395-3397 (2001).
[CrossRef]

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]

Chin. Phys. Lett. (1)

J. W. Dong, P. Han, and H. Z. Wang, "Broad omnidirectional reflection band forming using the combination of Fibonacci quasi-periodic and periodic one-dimensional photonic crystals," Chin. Phys. Lett. 20, 1963-1965 (2003).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

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

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Phys. Rev. E (1)

B. Huang, P. Gu, and L. Yang, "Construction of one-dimensional photonic crystals based on the incident angle domain," Phys. Rev. E 68, 046601-5 (2003).
[CrossRef]

Phys. Rev. Lett. (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]

Science (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]

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]

Other (2)

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, 1986), pp. 177-179.

K. Sakoda, Optical Properties of Photonic Crystals (Spring-Verlag, 2001), pp. 21-22.

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Figures (7)

Fig. 1
Fig. 1

Schematic of the 1-D PCs consisting of alternating dielectric layers of two materials with high and low refractive indices n h and n l and layer thicknesses d h and d l , respectively.

Fig. 2
Fig. 2

(A) Stop-band edges of a periodic structure as a function of incident angle. (B), (C), (D) The reflective spectra of the structure at three different incident angles. The solid curves correspond to p polarizations, and the dashed curves correspond to s polarizations. The frequency axis is normalized to the band center at normal incidence. The structural parameters are n 0 = 1 , n sub = 2.4 , n l = 1.7 , n h = 3.4 , and n h d h = n l d l (quarter-wave stacks at normal incidence); the number of units is 10.

Fig. 3
Fig. 3

Schematic of a photonic heterostructure S 1 + S 2 . It should be mentioned that the lattice constants of the two PCs are different.

Fig. 4
Fig. 4

(A) p-polarization stop-band edges of S 1 (dashed curves) and S 2 = 1.397 ( S 1 ) (solid curves) as a function of incident angle. (B), (C), (D) The reflective spectra of the heterostructure Air ( S 1 ) 10 ( S 2 ) 10 Sub . Only the spectra of p polarization are shown. The structural parameters are the same with those of Fig. 2.

Fig. 5
Fig. 5

(A) p-polarization stop-band edges of the periodic structure S 1 . (B), (C), (D) The reflective spectra of S 1 at three different incident angles. Only spectra of p polarization are shown. The structural parameters are n 0 = 1 , n sub = 2.0 , n l = 1.7 , n h = 2.2 , and n h d h = n l d l ; the number of units is 25. The dashed–dotted line denotes that there is no ODR in this structure.

Fig. 6
Fig. 6

(A) p-polarization stop-band edges of the periodic structure S 1 (dashed curves) and S 2 = 1.108 ( S 1 ) (solid curves). (B), (C), (D) The reflective spectra of the heterostructure Air ( S 1 ) 25 ( S 2 ) 25 Sub at three different incident angles. Only spectra of p polarization are shown. The structural parameters are the same with those of Fig. 5.

Fig. 7
Fig. 7

Boundary of ODR for a heterostructure composed of a number of sub-PCs. The lowest dashed curve gives the limit determined by a Brewster window.

Equations (10)

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

ω ± = 2 c D h + D l ( π 2 ± ϕ ± ) ,
D h , l = d h , l ( n h , l 2 n 0 2 sin 2 θ ) 1 2 ,
ϕ ± = arcsin ( x 1 x + 1 ) x 1 4 x ( D h D l D h + D l ) 2 [ π 2 ± arcsin ( x 1 x + 1 ) ] 2 + O ( D h D l D h + D l ) 4 ,
x = { ( n h 2 n 0 2 sin 2 θ n l 2 n 0 2 sin 2 θ ) 1 2 for a p wave ( n h n l ) 2 × ( n h 2 n 0 2 sin 2 θ n l 2 n 0 2 sin 2 θ ) 1 2 for an s wave } .
S 2 = f ( S 1 ) ,
ω 2 ± ( θ ) = 1 f ω 1 ± ( θ ) ,
f R = ω 1 + ( 90 ° ) ω 1 ( 90 ° ) .
ω 1 + ( 0 ° ) ω num ( 90 ° ) ,
ω 1 + ( 0 ° ) ω 1 ( 90 ° ) R num .
n l sin ( tan 1 n h n l ) > n 0 .

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