Abstract

The electromagnetic field distribution inside a one-dimensional random photonic lattice has been studied by using the transfer matrix method. We have considered incident waves at frequencies both within and outside the photonic bandgap. It is shown that in the vicinity of a Bragg remnant frequency, a random photonic lattice manifests a local maximum of the field intensity ensemble average inside the structure. The width of this maximum is much larger than a unit cell of the lattice.

© 1998 Optical Society of America

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References

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  1. J. B. Pendry, “Symmetry and transport of waves in 1-D disordered systems,” Adv. Phys. 43, 461–542 (1994).
    [CrossRef]
  2. C. M. Soukoulis, ed., Photonic Band Gaps and Localization Vol. 308 of NATO ASI series: Series B, Physics (Plenum, New York, 1993); M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991); K. M. Leung, Y. F. Lin, “Photon band structures: The plane-wave method,” Phys. Rev. B 41, 10188–10190 (1990).
    [CrossRef]
  3. J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209 (1993); P. M. Bell, J. B. Pendry, L. Martı́n-Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun.85, 306 (1995); J. B. Pendry, P. M. Bell, “Transfer matrix techniques for Electromagnetic Waves,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO ASI Series: Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 203–228.
    [CrossRef]
  4. V. Kuzmiak, A. A. Maradudin, F. Pincemin, “Photonic band structure of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
    [CrossRef]
  5. S. A. Bulgakov, M. Nieto-Vesperinas, “Competition of different scattering mechanisms in a one-dimensional random photonic lattice,” J. Opt. Soc. Am. A 13, 500–508 (1996).
    [CrossRef]
  6. H. G. Algul, M. Khazhinsky, A. R. McGurn, J. Kapenga, “Impurity modes from impurity clusters in photonic band structures,” J. Phys. Condens. Matter 7, 447–462 (1995).
    [CrossRef]
  7. K. M. Leung, “Defect modes in photonic band structures: a Green’s function approach using vector Wannier functions,” J. Opt. Soc. Am. B 10, 303–306 (1993).
    [CrossRef]
  8. D. Yeh, A. Yariv, C. S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977); P. Yeh, A. Yariv, “Bragg reflection waveguide,” Opt. Commun. 19, 427–430 (1976).
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    [CrossRef]
  10. A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical system that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
    [CrossRef]
  11. S. A. Bulgakov, M. Nieto-Vesperinas, “Interaction of different scattering mechanisms in a one-dimensional random photonic lattice,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO ASI Series: Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 691–702; S. A. Bulgakov, M. Nieto-Vesperinas, “Frequency properties of random photonic lattices,” Waves Random Media 7, 183–192 (1997).
    [CrossRef]
  12. S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, E. N. Economou, “Photonic band gaps in periodic dielectric structures: Relation to the single-scatterer MIE resonances,” in Photonic Band Gaps and Localization, C. M. Soukoulis, ed., Vol. 308 of NATO ASI Series: Series B, Physics (Plenum, New York, 1993), pp. 289–297.
    [CrossRef]
  13. C. Martijn de Sterke, R. C. McPhedran, “Bragg remnants in stratified random media,” Phys. Rev. B 47, 7780–7787 (1993).
    [CrossRef]
  14. E. N. Economou, C. M. Soukoulis, M. H. Cohen, “Localization for correlated binary-alloy disorder,” Phys. Rev. B 37, 4399–4407 (1988).
    [CrossRef]
  15. P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, New York, 1995).
  16. Nian-hua Liu, “Defect modes of stratified dielectric media,” Phys. Rev. B 55, 4097–4101 (1997).
    [CrossRef]
  17. Z. Daozhong, H. Wei, Z. Youlong, Z. Zhaolin, C. Bingying, Y. Guozhen, “Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,” Phys. Rev. B 50, 9810–9814 (1994).
    [CrossRef]
  18. J. P. Desideri, D. Sornette, “Band edge localization and spatial textures of surface acoustic waves in weakly disordered 1-D superlattices,” Europhys. Lett. 23, 165–170 (1993).
    [CrossRef]

1997

Nian-hua Liu, “Defect modes of stratified dielectric media,” Phys. Rev. B 55, 4097–4101 (1997).
[CrossRef]

1996

1995

H. G. Algul, M. Khazhinsky, A. R. McGurn, J. Kapenga, “Impurity modes from impurity clusters in photonic band structures,” J. Phys. Condens. Matter 7, 447–462 (1995).
[CrossRef]

1994

Z. Daozhong, H. Wei, Z. Youlong, Z. Zhaolin, C. Bingying, Y. Guozhen, “Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,” Phys. Rev. B 50, 9810–9814 (1994).
[CrossRef]

J. B. Pendry, “Symmetry and transport of waves in 1-D disordered systems,” Adv. Phys. 43, 461–542 (1994).
[CrossRef]

V. Kuzmiak, A. A. Maradudin, F. Pincemin, “Photonic band structure of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
[CrossRef]

1993

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209 (1993); P. M. Bell, J. B. Pendry, L. Martı́n-Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun.85, 306 (1995); J. B. Pendry, P. M. Bell, “Transfer matrix techniques for Electromagnetic Waves,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO ASI Series: Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 203–228.
[CrossRef]

J. P. Desideri, D. Sornette, “Band edge localization and spatial textures of surface acoustic waves in weakly disordered 1-D superlattices,” Europhys. Lett. 23, 165–170 (1993).
[CrossRef]

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical system that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
[CrossRef]

C. Martijn de Sterke, R. C. McPhedran, “Bragg remnants in stratified random media,” Phys. Rev. B 47, 7780–7787 (1993).
[CrossRef]

K. M. Leung, “Defect modes in photonic band structures: a Green’s function approach using vector Wannier functions,” J. Opt. Soc. Am. B 10, 303–306 (1993).
[CrossRef]

1991

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, S. L. McCall, “Microwave localization by two-dimensional random scattering,” Nature (London) 354, 53–55 (1991);D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structures and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993); D. R. Smith, S. Schultz, S. L. McCall, P. M. Platzmann, “Defect studies in a two-dimensional periodic photonic lattice,” J. Mod. Opt. 41, 395–404 (1994).
[CrossRef]

1988

E. N. Economou, C. M. Soukoulis, M. H. Cohen, “Localization for correlated binary-alloy disorder,” Phys. Rev. B 37, 4399–4407 (1988).
[CrossRef]

1977

Algul, H. G.

H. G. Algul, M. Khazhinsky, A. R. McGurn, J. Kapenga, “Impurity modes from impurity clusters in photonic band structures,” J. Phys. Condens. Matter 7, 447–462 (1995).
[CrossRef]

Armstrong, J. P.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, S. L. McCall, “Microwave localization by two-dimensional random scattering,” Nature (London) 354, 53–55 (1991);D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structures and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993); D. R. Smith, S. Schultz, S. L. McCall, P. M. Platzmann, “Defect studies in a two-dimensional periodic photonic lattice,” J. Mod. Opt. 41, 395–404 (1994).
[CrossRef]

Bingying, C.

Z. Daozhong, H. Wei, Z. Youlong, Z. Zhaolin, C. Bingying, Y. Guozhen, “Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,” Phys. Rev. B 50, 9810–9814 (1994).
[CrossRef]

Bulgakov, S. A.

S. A. Bulgakov, M. Nieto-Vesperinas, “Competition of different scattering mechanisms in a one-dimensional random photonic lattice,” J. Opt. Soc. Am. A 13, 500–508 (1996).
[CrossRef]

S. A. Bulgakov, M. Nieto-Vesperinas, “Interaction of different scattering mechanisms in a one-dimensional random photonic lattice,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO ASI Series: Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 691–702; S. A. Bulgakov, M. Nieto-Vesperinas, “Frequency properties of random photonic lattices,” Waves Random Media 7, 183–192 (1997).
[CrossRef]

Chan, C. T.

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, E. N. Economou, “Photonic band gaps in periodic dielectric structures: Relation to the single-scatterer MIE resonances,” in Photonic Band Gaps and Localization, C. M. Soukoulis, ed., Vol. 308 of NATO ASI Series: Series B, Physics (Plenum, New York, 1993), pp. 289–297.
[CrossRef]

Christensen, K. T.

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical system that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
[CrossRef]

Cohen, M. H.

E. N. Economou, C. M. Soukoulis, M. H. Cohen, “Localization for correlated binary-alloy disorder,” Phys. Rev. B 37, 4399–4407 (1988).
[CrossRef]

Dalichaouch, R.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, S. L. McCall, “Microwave localization by two-dimensional random scattering,” Nature (London) 354, 53–55 (1991);D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structures and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993); D. R. Smith, S. Schultz, S. L. McCall, P. M. Platzmann, “Defect studies in a two-dimensional periodic photonic lattice,” J. Mod. Opt. 41, 395–404 (1994).
[CrossRef]

Daozhong, Z.

Z. Daozhong, H. Wei, Z. Youlong, Z. Zhaolin, C. Bingying, Y. Guozhen, “Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,” Phys. Rev. B 50, 9810–9814 (1994).
[CrossRef]

Datta, S.

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, E. N. Economou, “Photonic band gaps in periodic dielectric structures: Relation to the single-scatterer MIE resonances,” in Photonic Band Gaps and Localization, C. M. Soukoulis, ed., Vol. 308 of NATO ASI Series: Series B, Physics (Plenum, New York, 1993), pp. 289–297.
[CrossRef]

Desideri, J. P.

J. P. Desideri, D. Sornette, “Band edge localization and spatial textures of surface acoustic waves in weakly disordered 1-D superlattices,” Europhys. Lett. 23, 165–170 (1993).
[CrossRef]

Economou, E. N.

E. N. Economou, C. M. Soukoulis, M. H. Cohen, “Localization for correlated binary-alloy disorder,” Phys. Rev. B 37, 4399–4407 (1988).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, E. N. Economou, “Photonic band gaps in periodic dielectric structures: Relation to the single-scatterer MIE resonances,” in Photonic Band Gaps and Localization, C. M. Soukoulis, ed., Vol. 308 of NATO ASI Series: Series B, Physics (Plenum, New York, 1993), pp. 289–297.
[CrossRef]

Guozhen, Y.

Z. Daozhong, H. Wei, Z. Youlong, Z. Zhaolin, C. Bingying, Y. Guozhen, “Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,” Phys. Rev. B 50, 9810–9814 (1994).
[CrossRef]

Ho, K. M.

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, E. N. Economou, “Photonic band gaps in periodic dielectric structures: Relation to the single-scatterer MIE resonances,” in Photonic Band Gaps and Localization, C. M. Soukoulis, ed., Vol. 308 of NATO ASI Series: Series B, Physics (Plenum, New York, 1993), pp. 289–297.
[CrossRef]

Hong, C. S.

Kapenga, J.

H. G. Algul, M. Khazhinsky, A. R. McGurn, J. Kapenga, “Impurity modes from impurity clusters in photonic band structures,” J. Phys. Condens. Matter 7, 447–462 (1995).
[CrossRef]

Khazhinsky, M.

H. G. Algul, M. Khazhinsky, A. R. McGurn, J. Kapenga, “Impurity modes from impurity clusters in photonic band structures,” J. Phys. Condens. Matter 7, 447–462 (1995).
[CrossRef]

Kuzmiak, V.

V. Kuzmiak, A. A. Maradudin, F. Pincemin, “Photonic band structure of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
[CrossRef]

Leung, K. M.

Liu, Nian-hua

Nian-hua Liu, “Defect modes of stratified dielectric media,” Phys. Rev. B 55, 4097–4101 (1997).
[CrossRef]

Maradudin, A. A.

V. Kuzmiak, A. A. Maradudin, F. Pincemin, “Photonic band structure of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
[CrossRef]

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical system that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
[CrossRef]

Martijn de Sterke, C.

C. Martijn de Sterke, R. C. McPhedran, “Bragg remnants in stratified random media,” Phys. Rev. B 47, 7780–7787 (1993).
[CrossRef]

McCall, S. L.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, S. L. McCall, “Microwave localization by two-dimensional random scattering,” Nature (London) 354, 53–55 (1991);D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structures and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993); D. R. Smith, S. Schultz, S. L. McCall, P. M. Platzmann, “Defect studies in a two-dimensional periodic photonic lattice,” J. Mod. Opt. 41, 395–404 (1994).
[CrossRef]

McGurn, A. R.

H. G. Algul, M. Khazhinsky, A. R. McGurn, J. Kapenga, “Impurity modes from impurity clusters in photonic band structures,” J. Phys. Condens. Matter 7, 447–462 (1995).
[CrossRef]

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical system that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
[CrossRef]

McPhedran, R. C.

C. Martijn de Sterke, R. C. McPhedran, “Bragg remnants in stratified random media,” Phys. Rev. B 47, 7780–7787 (1993).
[CrossRef]

Mueller, F. M.

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical system that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
[CrossRef]

Nieto-Vesperinas, M.

S. A. Bulgakov, M. Nieto-Vesperinas, “Competition of different scattering mechanisms in a one-dimensional random photonic lattice,” J. Opt. Soc. Am. A 13, 500–508 (1996).
[CrossRef]

S. A. Bulgakov, M. Nieto-Vesperinas, “Interaction of different scattering mechanisms in a one-dimensional random photonic lattice,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO ASI Series: Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 691–702; S. A. Bulgakov, M. Nieto-Vesperinas, “Frequency properties of random photonic lattices,” Waves Random Media 7, 183–192 (1997).
[CrossRef]

Pendry, J. B.

J. B. Pendry, “Symmetry and transport of waves in 1-D disordered systems,” Adv. Phys. 43, 461–542 (1994).
[CrossRef]

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209 (1993); P. M. Bell, J. B. Pendry, L. Martı́n-Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun.85, 306 (1995); J. B. Pendry, P. M. Bell, “Transfer matrix techniques for Electromagnetic Waves,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO ASI Series: Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 203–228.
[CrossRef]

Pincemin, F.

V. Kuzmiak, A. A. Maradudin, F. Pincemin, “Photonic band structure of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
[CrossRef]

Platzman, P. M.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, S. L. McCall, “Microwave localization by two-dimensional random scattering,” Nature (London) 354, 53–55 (1991);D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structures and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993); D. R. Smith, S. Schultz, S. L. McCall, P. M. Platzmann, “Defect studies in a two-dimensional periodic photonic lattice,” J. Mod. Opt. 41, 395–404 (1994).
[CrossRef]

Schultz, S.

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, S. L. McCall, “Microwave localization by two-dimensional random scattering,” Nature (London) 354, 53–55 (1991);D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structures and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993); D. R. Smith, S. Schultz, S. L. McCall, P. M. Platzmann, “Defect studies in a two-dimensional periodic photonic lattice,” J. Mod. Opt. 41, 395–404 (1994).
[CrossRef]

Sheng, P.

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, New York, 1995).

Sornette, D.

J. P. Desideri, D. Sornette, “Band edge localization and spatial textures of surface acoustic waves in weakly disordered 1-D superlattices,” Europhys. Lett. 23, 165–170 (1993).
[CrossRef]

Soukoulis, C. M.

E. N. Economou, C. M. Soukoulis, M. H. Cohen, “Localization for correlated binary-alloy disorder,” Phys. Rev. B 37, 4399–4407 (1988).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, E. N. Economou, “Photonic band gaps in periodic dielectric structures: Relation to the single-scatterer MIE resonances,” in Photonic Band Gaps and Localization, C. M. Soukoulis, ed., Vol. 308 of NATO ASI Series: Series B, Physics (Plenum, New York, 1993), pp. 289–297.
[CrossRef]

Wei, H.

Z. Daozhong, H. Wei, Z. Youlong, Z. Zhaolin, C. Bingying, Y. Guozhen, “Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,” Phys. Rev. B 50, 9810–9814 (1994).
[CrossRef]

Yariv, A.

Yeh, D.

Youlong, Z.

Z. Daozhong, H. Wei, Z. Youlong, Z. Zhaolin, C. Bingying, Y. Guozhen, “Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,” Phys. Rev. B 50, 9810–9814 (1994).
[CrossRef]

Zhaolin, Z.

Z. Daozhong, H. Wei, Z. Youlong, Z. Zhaolin, C. Bingying, Y. Guozhen, “Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,” Phys. Rev. B 50, 9810–9814 (1994).
[CrossRef]

Adv. Phys.

J. B. Pendry, “Symmetry and transport of waves in 1-D disordered systems,” Adv. Phys. 43, 461–542 (1994).
[CrossRef]

Europhys. Lett.

J. P. Desideri, D. Sornette, “Band edge localization and spatial textures of surface acoustic waves in weakly disordered 1-D superlattices,” Europhys. Lett. 23, 165–170 (1993).
[CrossRef]

J. Mod. Opt.

J. B. Pendry, “Photonic band structures,” J. Mod. Opt. 41, 209 (1993); P. M. Bell, J. B. Pendry, L. Martı́n-Moreno, A. J. Ward, “A program for calculating photonic band structures and transmission coefficients of complex structures,” Comput. Phys. Commun.85, 306 (1995); J. B. Pendry, P. M. Bell, “Transfer matrix techniques for Electromagnetic Waves,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO ASI Series: Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 203–228.
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

J. Phys. Condens. Matter

H. G. Algul, M. Khazhinsky, A. R. McGurn, J. Kapenga, “Impurity modes from impurity clusters in photonic band structures,” J. Phys. Condens. Matter 7, 447–462 (1995).
[CrossRef]

Nature (London)

R. Dalichaouch, J. P. Armstrong, S. Schultz, P. M. Platzman, S. L. McCall, “Microwave localization by two-dimensional random scattering,” Nature (London) 354, 53–55 (1991);D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structures and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993); D. R. Smith, S. Schultz, S. L. McCall, P. M. Platzmann, “Defect studies in a two-dimensional periodic photonic lattice,” J. Mod. Opt. 41, 395–404 (1994).
[CrossRef]

Phys. Rev. B

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical system that are periodic on average,” Phys. Rev. B 47, 13120–13125 (1993).
[CrossRef]

C. Martijn de Sterke, R. C. McPhedran, “Bragg remnants in stratified random media,” Phys. Rev. B 47, 7780–7787 (1993).
[CrossRef]

E. N. Economou, C. M. Soukoulis, M. H. Cohen, “Localization for correlated binary-alloy disorder,” Phys. Rev. B 37, 4399–4407 (1988).
[CrossRef]

Nian-hua Liu, “Defect modes of stratified dielectric media,” Phys. Rev. B 55, 4097–4101 (1997).
[CrossRef]

Z. Daozhong, H. Wei, Z. Youlong, Z. Zhaolin, C. Bingying, Y. Guozhen, “Experimental verification of light localization for disordered multilayers in the visible-infrared spectrum,” Phys. Rev. B 50, 9810–9814 (1994).
[CrossRef]

V. Kuzmiak, A. A. Maradudin, F. Pincemin, “Photonic band structure of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835–16844 (1994).
[CrossRef]

Other

C. M. Soukoulis, ed., Photonic Band Gaps and Localization Vol. 308 of NATO ASI series: Series B, Physics (Plenum, New York, 1993); M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991); K. M. Leung, Y. F. Lin, “Photon band structures: The plane-wave method,” Phys. Rev. B 41, 10188–10190 (1990).
[CrossRef]

P. Sheng, Introduction to Wave Scattering, Localization and Mesoscopic Phenomena (Academic, New York, 1995).

S. A. Bulgakov, M. Nieto-Vesperinas, “Interaction of different scattering mechanisms in a one-dimensional random photonic lattice,” in Photonic Band Gap Materials, C. M. Soukoulis, ed., Vol. 315 of NATO ASI Series: Series E, Applied Sciences (Kluwer Academic, Dordrecht, The Netherlands, 1996), pp. 691–702; S. A. Bulgakov, M. Nieto-Vesperinas, “Frequency properties of random photonic lattices,” Waves Random Media 7, 183–192 (1997).
[CrossRef]

S. Datta, C. T. Chan, K. M. Ho, C. M. Soukoulis, E. N. Economou, “Photonic band gaps in periodic dielectric structures: Relation to the single-scatterer MIE resonances,” in Photonic Band Gaps and Localization, C. M. Soukoulis, ed., Vol. 308 of NATO ASI Series: Series B, Physics (Plenum, New York, 1993), pp. 289–297.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Field distribution, 2 log|E|/|Emax|, inside samples of a random lattice for in-gap frequency (W=3.0) versus normalized space coordinate x/d along the lattice. The incident wave comes from the right. (a) and (b) Two different random realizations, (c) regular lattice. The right vertical axis shows the distribution of dielectric permittivity.

Fig. 2
Fig. 2

Same as in Fig. 1 for out-of-gap frequency (W=2.25).

Fig. 3
Fig. 3

Field distribution, 2 log|E|/|Emax|, versus x/d, averaged over 40 realizations of a random lattice; α=0.5. (a) In-gap frequency and (b) out-of-gap frequency. The incident wave comes from the right.

Fig. 4
Fig. 4

Decay length averaged over 200 realizations, as a function of the lattice length; α=0.5. (a) In-gap frequency, (b) out-of-gap frequency. Observe the convergence to the localization length l beyond Lth.

Fig. 5
Fig. 5

Field distribution inside a random low contrast lattice at a BR frequency of the first resonance [Eq. (10), m=1], averaged over 40 realizations of a random lattice. (a) Whole structure, (b) a particular region in enlarged scale. The incident wave comes from the right.

Fig. 6
Fig. 6

Field distribution for a frequency shifted from a BR resonant one (Fig. 5), averaged over 100 realizations of a random lattice. (a) W=0.95WBR, (b) W=1.1WBR.

Equations (16)

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t0=Tˆ1r,
T11=T22*=cos k2α+i2k2k1+k1k2×sin k2αexp[ik1(1-α)],
T12=T21*=i2k2k1-k1k2sin k2α exp[ik1(1+α)]
α=ad.
Em(x)=Cm expik2xd-m+Dm exp-ik2xd-m,
Em(x)=Am expik1xd-m+Bm exp-ik1xd-m,
2Cm=Am(1+k1/k2)exp[-iα(k1-k2)]+Bm(1-k1/k2)exp[iα(k1+k2)],
2Dm=Am(1-k1/k2)exp[-iα(k1+k2)]+Bm(1+k1/k2)exp[iα(k1-k2)].
A1=t,B1=0form=1,
Am+1Bm+1=TmAmBm.
Wgapωgapdckπback(1-α)+slabα,
δϕ=ωdc[back(1-α)+slabα].
l=-Llog T;
WBR=πmback,minteger,
sin W1+sin W2,
λ-=4mscatback-1,λ+=4mscatback+1.

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