Abstract

The lowest (main) and high-order Mie resonances and the Bragg-like multiple scattering of electromagnetic (EM) waves are determined as three mechanisms of formation and frequency position of two opaque bands, with narrow peaks in one of the bands in the transmission spectra of 2D photonic crystals composed of dielectric cylinders arranged parallel to the EM wave’s electric vector in the square lattice. The main Mie resonance in a single cylinder defines the frequency position of the main gap whose formation results from the Bragg-like scattering. An additional gap with narrow transmission peaks opens in the spectrum of a cylinder layer and becomes pronounced with the number of layers. It is argued that higher-order Mie resonances are responsible for the transmission peaks within the additional band of a perfect crystal. It is shown that 2D photonic crystals with a filling factor ranging from 3% to 20% at a fixed crystal period may be a good zero approximation to study wave transmission through a localizing 2D dense random medium slab.

© 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]
  2. S. John, 'Strong localization of photons in certain disordered dielectric superlattices,' Phys. Rev. Lett. 58, 2486-2489 (1987).
    [CrossRef] [PubMed]
  3. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, 'Donor and acceptor modes in photonic band structure,' Phys. Rev. Lett. 67, 3380-3383 (1991).
    [CrossRef] [PubMed]
  4. M. Sigalas, C. M. Soukoulis, E. M. Economou, C. T. Chan, and K. M. Ho, 'Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,' Phys. Rev. B 48, 14121-14126 (1993).
    [CrossRef]
  5. N. Garcia and A. Z. Genack, 'Anomalous photon diffusion at the threshold of the Anderson localization transition,' Phys. Rev. Lett. 66, 1850-1853 (1991).
    [CrossRef] [PubMed]
  6. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, 'Anderson localization of light,' Nature 390, 671-673 (1997).
    [CrossRef]
  7. A. A. Chabanov and A. Z. Genack, 'Photon localization in resonant media,' Phys. Rev. Lett. 87, 153901 (2001).
    [CrossRef] [PubMed]
  8. K. T. Compton, 'Some properties of resonance radiation and excited atoms,' Philos. Mag. 45, 750-760 (1923).
  9. E. A. Milne, 'The diffusion of imprisoned radiation through a gas,' J. Lond. Math. Soc. 1, 40-51 (1926).
    [CrossRef]
  10. E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Tight-binding parametrization for photonic band gap materials,' Phys. Rev. Lett. 81, 1405-1408 (1998).
    [CrossRef]
  11. M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, 'Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,' Phys. Rev. B 64, 195113 (2001).
    [CrossRef]
  12. Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface,' in Progress in Electromagnetic Research, J.A.Kong, ed. (EMW, 1999), Vol. 24, pp. 39-75.
    [CrossRef]
  13. Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface (summary),' J. Electromagn. Waves Appl. 13, 1335-1337 (1999).
    [CrossRef]
  14. C. Barnes and J. B. Pendry, 'Multiple scattering of waves in random media: a transfer matrix approach,' Proc. R. Soc. London, Ser. A 435, 185-196 (1991).
    [CrossRef]
  15. M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, 1964).
  16. E. Centeno, B. Guizal, and D. Felbacq, 'Multiplexing and demultiplexing with photonic crystals,' J. Opt. A, Pure Appl. Opt. 1, L10-L13 (1999).
    [CrossRef]
  17. C. A. Condat, and T. R. Kirkpatrick, 'Localization of acoustic waves,' in Scattering and Localization of Classical Waves in Random Media, P.Sheng, ed. (World Scientific, 1990).
  18. E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,' Phys. Rev. B 61, 13458-13464 (2000).
    [CrossRef]
  19. D. Sornette, 'Anderson localization and wave absorption,' J. Stat. Phys. 56, 669-680 (1989).
    [CrossRef]

2001 (2)

A. A. Chabanov and A. Z. Genack, 'Photon localization in resonant media,' Phys. Rev. Lett. 87, 153901 (2001).
[CrossRef] [PubMed]

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, 'Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,' Phys. Rev. B 64, 195113 (2001).
[CrossRef]

2000 (1)

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,' Phys. Rev. B 61, 13458-13464 (2000).
[CrossRef]

1999 (2)

E. Centeno, B. Guizal, and D. Felbacq, 'Multiplexing and demultiplexing with photonic crystals,' J. Opt. A, Pure Appl. Opt. 1, L10-L13 (1999).
[CrossRef]

Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface (summary),' J. Electromagn. Waves Appl. 13, 1335-1337 (1999).
[CrossRef]

1998 (1)

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Tight-binding parametrization for photonic band gap materials,' Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

1997 (1)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, 'Anderson localization of light,' Nature 390, 671-673 (1997).
[CrossRef]

1993 (1)

M. Sigalas, C. M. Soukoulis, E. M. Economou, C. T. Chan, and K. M. Ho, 'Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,' Phys. Rev. B 48, 14121-14126 (1993).
[CrossRef]

1991 (3)

N. Garcia and A. Z. Genack, 'Anomalous photon diffusion at the threshold of the Anderson localization transition,' Phys. Rev. Lett. 66, 1850-1853 (1991).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, 'Donor and acceptor modes in photonic band structure,' Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

C. Barnes and J. B. Pendry, 'Multiple scattering of waves in random media: a transfer matrix approach,' Proc. R. Soc. London, Ser. A 435, 185-196 (1991).
[CrossRef]

1989 (1)

D. Sornette, 'Anderson localization and wave absorption,' J. Stat. Phys. 56, 669-680 (1989).
[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]

1926 (1)

E. A. Milne, 'The diffusion of imprisoned radiation through a gas,' J. Lond. Math. Soc. 1, 40-51 (1926).
[CrossRef]

1923 (1)

K. T. Compton, 'Some properties of resonance radiation and excited atoms,' Philos. Mag. 45, 750-760 (1923).

Barabanenkov, M. Yu.

Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface (summary),' J. Electromagn. Waves Appl. 13, 1335-1337 (1999).
[CrossRef]

Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface,' in Progress in Electromagnetic Research, J.A.Kong, ed. (EMW, 1999), Vol. 24, pp. 39-75.
[CrossRef]

Barabanenkov, Yu. N.

Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface (summary),' J. Electromagn. Waves Appl. 13, 1335-1337 (1999).
[CrossRef]

Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface,' in Progress in Electromagnetic Research, J.A.Kong, ed. (EMW, 1999), Vol. 24, pp. 39-75.
[CrossRef]

Barnes, C.

C. Barnes and J. B. Pendry, 'Multiple scattering of waves in random media: a transfer matrix approach,' Proc. R. Soc. London, Ser. A 435, 185-196 (1991).
[CrossRef]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, 'Anderson localization of light,' Nature 390, 671-673 (1997).
[CrossRef]

Bayindir, M.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, 'Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,' Phys. Rev. B 64, 195113 (2001).
[CrossRef]

Brommer, K. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, 'Donor and acceptor modes in photonic band structure,' Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

Bulu, I.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, 'Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,' Phys. Rev. B 64, 195113 (2001).
[CrossRef]

Centeno, E.

E. Centeno, B. Guizal, and D. Felbacq, 'Multiplexing and demultiplexing with photonic crystals,' J. Opt. A, Pure Appl. Opt. 1, L10-L13 (1999).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov and A. Z. Genack, 'Photon localization in resonant media,' Phys. Rev. Lett. 87, 153901 (2001).
[CrossRef] [PubMed]

Chan, C. T.

M. Sigalas, C. M. Soukoulis, E. M. Economou, C. T. Chan, and K. M. Ho, 'Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,' Phys. Rev. B 48, 14121-14126 (1993).
[CrossRef]

Compton, K. T.

K. T. Compton, 'Some properties of resonance radiation and excited atoms,' Philos. Mag. 45, 750-760 (1923).

Condat, C. A.

C. A. Condat, and T. R. Kirkpatrick, 'Localization of acoustic waves,' in Scattering and Localization of Classical Waves in Random Media, P.Sheng, ed. (World Scientific, 1990).

Cubukcu, E.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, 'Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,' Phys. Rev. B 64, 195113 (2001).
[CrossRef]

Economou, E. M.

M. Sigalas, C. M. Soukoulis, E. M. Economou, C. T. Chan, and K. M. Ho, 'Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,' Phys. Rev. B 48, 14121-14126 (1993).
[CrossRef]

Economou, E. N.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,' Phys. Rev. B 61, 13458-13464 (2000).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Tight-binding parametrization for photonic band gap materials,' Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

Felbacq, D.

E. Centeno, B. Guizal, and D. Felbacq, 'Multiplexing and demultiplexing with photonic crystals,' J. Opt. A, Pure Appl. Opt. 1, L10-L13 (1999).
[CrossRef]

Garcia, N.

N. Garcia and A. Z. Genack, 'Anomalous photon diffusion at the threshold of the Anderson localization transition,' Phys. Rev. Lett. 66, 1850-1853 (1991).
[CrossRef] [PubMed]

Genack, A. Z.

A. A. Chabanov and A. Z. Genack, 'Photon localization in resonant media,' Phys. Rev. Lett. 87, 153901 (2001).
[CrossRef] [PubMed]

N. Garcia and A. Z. Genack, 'Anomalous photon diffusion at the threshold of the Anderson localization transition,' Phys. Rev. Lett. 66, 1850-1853 (1991).
[CrossRef] [PubMed]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, 'Donor and acceptor modes in photonic band structure,' Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

Goldberger, M. L.

M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, 1964).

Guizal, B.

E. Centeno, B. Guizal, and D. Felbacq, 'Multiplexing and demultiplexing with photonic crystals,' J. Opt. A, Pure Appl. Opt. 1, L10-L13 (1999).
[CrossRef]

Ho, K. M.

M. Sigalas, C. M. Soukoulis, E. M. Economou, C. T. Chan, and K. M. Ho, 'Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,' Phys. Rev. B 48, 14121-14126 (1993).
[CrossRef]

Joannopoulos, J. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, 'Donor and acceptor modes in photonic band structure,' Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

John, S.

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

Kirkpatrick, T. R.

C. A. Condat, and T. R. Kirkpatrick, 'Localization of acoustic waves,' in Scattering and Localization of Classical Waves in Random Media, P.Sheng, ed. (World Scientific, 1990).

Kouznetsov, V. L.

Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface (summary),' J. Electromagn. Waves Appl. 13, 1335-1337 (1999).
[CrossRef]

Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface,' in Progress in Electromagnetic Research, J.A.Kong, ed. (EMW, 1999), Vol. 24, pp. 39-75.
[CrossRef]

Lagendijk, A.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, 'Anderson localization of light,' Nature 390, 671-673 (1997).
[CrossRef]

Lidorikis, E.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,' Phys. Rev. B 61, 13458-13464 (2000).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Tight-binding parametrization for photonic band gap materials,' Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

Meade, R. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, 'Donor and acceptor modes in photonic band structure,' Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

Milne, E. A.

E. A. Milne, 'The diffusion of imprisoned radiation through a gas,' J. Lond. Math. Soc. 1, 40-51 (1926).
[CrossRef]

Ozbay, E.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, 'Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,' Phys. Rev. B 64, 195113 (2001).
[CrossRef]

Pendry, J. B.

C. Barnes and J. B. Pendry, 'Multiple scattering of waves in random media: a transfer matrix approach,' Proc. R. Soc. London, Ser. A 435, 185-196 (1991).
[CrossRef]

Rappe, A. M.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, 'Donor and acceptor modes in photonic band structure,' Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, 'Anderson localization of light,' Nature 390, 671-673 (1997).
[CrossRef]

Sigalas, M.

M. Sigalas, C. M. Soukoulis, E. M. Economou, C. T. Chan, and K. M. Ho, 'Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,' Phys. Rev. B 48, 14121-14126 (1993).
[CrossRef]

Sigalas, M. M.

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,' Phys. Rev. B 61, 13458-13464 (2000).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Tight-binding parametrization for photonic band gap materials,' Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

Sornette, D.

D. Sornette, 'Anderson localization and wave absorption,' J. Stat. Phys. 56, 669-680 (1989).
[CrossRef]

Soukoulis, C. M.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, 'Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,' Phys. Rev. B 64, 195113 (2001).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,' Phys. Rev. B 61, 13458-13464 (2000).
[CrossRef]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Tight-binding parametrization for photonic band gap materials,' Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

M. Sigalas, C. M. Soukoulis, E. M. Economou, C. T. Chan, and K. M. Ho, 'Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,' Phys. Rev. B 48, 14121-14126 (1993).
[CrossRef]

Tut, T.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, 'Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,' Phys. Rev. B 64, 195113 (2001).
[CrossRef]

Watson, K. M.

M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, 1964).

Wiersma, D. S.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, 'Anderson localization of light,' Nature 390, 671-673 (1997).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, 'Donor and acceptor modes in photonic band structure,' Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

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

J. Electromagn. Waves Appl. (1)

Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface (summary),' J. Electromagn. Waves Appl. 13, 1335-1337 (1999).
[CrossRef]

J. Lond. Math. Soc. (1)

E. A. Milne, 'The diffusion of imprisoned radiation through a gas,' J. Lond. Math. Soc. 1, 40-51 (1926).
[CrossRef]

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

E. Centeno, B. Guizal, and D. Felbacq, 'Multiplexing and demultiplexing with photonic crystals,' J. Opt. A, Pure Appl. Opt. 1, L10-L13 (1999).
[CrossRef]

J. Stat. Phys. (1)

D. Sornette, 'Anderson localization and wave absorption,' J. Stat. Phys. 56, 669-680 (1989).
[CrossRef]

Nature (1)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, 'Anderson localization of light,' Nature 390, 671-673 (1997).
[CrossRef]

Philos. Mag. (1)

K. T. Compton, 'Some properties of resonance radiation and excited atoms,' Philos. Mag. 45, 750-760 (1923).

Phys. Rev. B (3)

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Gap deformation and classical wave localization in disordered two-dimensional photonic-band-gap materials,' Phys. Rev. B 61, 13458-13464 (2000).
[CrossRef]

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, 'Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,' Phys. Rev. B 64, 195113 (2001).
[CrossRef]

M. Sigalas, C. M. Soukoulis, E. M. Economou, C. T. Chan, and K. M. Ho, 'Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,' Phys. Rev. B 48, 14121-14126 (1993).
[CrossRef]

Phys. Rev. Lett. (6)

N. Garcia and A. Z. Genack, 'Anomalous photon diffusion at the threshold of the Anderson localization transition,' Phys. Rev. Lett. 66, 1850-1853 (1991).
[CrossRef] [PubMed]

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]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, 'Donor and acceptor modes in photonic band structure,' Phys. Rev. Lett. 67, 3380-3383 (1991).
[CrossRef] [PubMed]

A. A. Chabanov and A. Z. Genack, 'Photon localization in resonant media,' Phys. Rev. Lett. 87, 153901 (2001).
[CrossRef] [PubMed]

E. Lidorikis, M. M. Sigalas, E. N. Economou, and C. M. Soukoulis, 'Tight-binding parametrization for photonic band gap materials,' Phys. Rev. Lett. 81, 1405-1408 (1998).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

C. Barnes and J. B. Pendry, 'Multiple scattering of waves in random media: a transfer matrix approach,' Proc. R. Soc. London, Ser. A 435, 185-196 (1991).
[CrossRef]

Other (3)

M. L. Goldberger and K. M. Watson, Collision Theory (Wiley, 1964).

Yu. N. Barabanenkov, V. L. Kouznetsov, and M. Yu. Barabanenkov, 'Transfer relations for electromagnetic wave scattering from periodic dielectric one-dimensional interface,' in Progress in Electromagnetic Research, J.A.Kong, ed. (EMW, 1999), Vol. 24, pp. 39-75.
[CrossRef]

C. A. Condat, and T. R. Kirkpatrick, 'Localization of acoustic waves,' in Scattering and Localization of Classical Waves in Random Media, P.Sheng, ed. (World Scientific, 1990).

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Figures (5)

Fig. 1
Fig. 1

Schematic showing an x z plane of the 2D photonic crystal slab with slices and splits. The wave vector k 0 and the magnetic vector H 0 are perpendicular and the electric vector E 0 is parallel to the y axis, i.e., to the axis of the rods.

Fig. 2
Fig. 2

Calculated relative power of EM radiation transmitted through N = 18 layers of cylinders arranged in a square lattice with a period Λ (solid curves) and (a) an equal slab of randomly positioned cylinders (open circles) ( T l o c , see Fig. 5) versus the wavelength of the EM waves assuming wave normal incidence, ϵ b a c = 1 , ϵ = ( 2.9 ) 2 , arbitrary units for the wavelength λ, period Λ = 4 , and radius (a) ρ = 0.6 , (after Ref. [16]), (b) ρ = 0.5 , (c) ρ = 0.4 . Total scattering cross sections on a unit length of an infinitely long cylinder (dashed curves) are calculated by Eq. (38) of Ref. [17]. Solid and open triangles (see Fig. 4) and solid circles with numbers mark some specific wavelengths.

Fig. 3
Fig. 3

(a) Edges (open triangles and inverse triangles), the middle (open circles), and the width (open squares) of the main photonic gap and the peak (marked by zero in Fig. 2) of the monopole resonance scattering on a single cylinder (solid circles) as a function of the radius of cylinders arranged in a square lattice (18 layers of cylinders) with the fixed period Λ = 4 . The effective radius of cylinders is defined by ρ e f f = ρ [ S ( λ ) π ρ 2 ] 1 2 . (b) The depth of the main gap as a function of wavelength mismatch Δ λ of the monopole resonance in a single cylinder λ monopole [see solid circles in (a)] and the middle of the gap [see open circles in (a)].

Fig. 4
Fig. 4

Transmission of N = 1 (see the inset), (a) N = 2 , and (b) N = 4 layers of the cylinders versus the wavelength of the EM waves, assuming wave normal incidence, ϵ b a c = 1 , ϵ = ( 2.9 ) 2 , radius ρ = 0.6 , and period Λ = 4 (after Ref. [16]). Inverse triangles and solid circles with numbers mark some specific wavelengths.

Fig. 5
Fig. 5

(a) Calculated relative power of EM radiation transmitted through the photonic structure described in Fig. 2 versus the number of cylinder layers for the wavelengths λ = 4.9 (solid circles) and 11.15 (open circles); the exponential power scaling approximation for the wavelengths λ = 4.9 (solid triangles and squares) and 11.15 (open triangles and squares) in the form (according to Ref. [19]) T l o c = ( e N ) 2 exp ( N N 0 ) , if ξ > L , otherwise ( a N ) exp ( N N 0 ) , is depicted with the parameters described below. (b) The dependence of the elastic mean free path e (curve 1), the localization length ξ, N 0 = ξ Λ (curve 2), and the parameter a (curve 3) on the wavelength of EM radiation are calculated according to Ref. [17].

Equations (3)

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d R d z i ( σ R + R σ ) = a F ( z ) + a F ( z ) R + R a F ( z ) + R a F ( z ) R ,
T d z i T σ = T a F ( z ) + T a F ( z ) R
Π z ( z = ρ ) = μ k μ z T μ 0 ( k 0 x ; ρ ) 2 = Π z ( z = ρ + L ) = k 0 z + μ k μ z + R μ 0 ( k 0 x ; ρ ) 2 ,

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