Abstract

A one-dimensional random photonic lattice is studied both by the plane-wave method and by the transfer matrix approach for arbitrary contrast in its dielectric permittivity. The roles and competition of different scattering mechanisms such as Bragg diffraction, single-scatterer resonances, and Bragg remnants are investigated. The localization length, band-gap width, and middle-gap frequency are analyzed for both random and regular lattices in the higher-frequency bands. An analytical expression allowing the prediction of the existence of band-gap closing is obtained. It is shown not only that strong localization results from Bragg diffraction and disorder in the scatterers’ distribution but also that Bragg remnants produce localization for a medium with small contrast.

© 1996 Optical Society of America

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  1. E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283–295 (1993); H. O. Everitt, “Application of photonic band gap structures,” Opt. Photon. News, November, 1992, pp. 20–23; S. John, “Localization of light,” Phys. Today 41(5), 32–40 (1991).
    [Crossref]
  2. 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).
    [Crossref]
  3. Z. Daozhong, H. Wei, Z. Youlong, L. 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]
  4. 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).
    [Crossref]
  5. D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structure and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993).
    [Crossref]
  6. M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
    [Crossref]
  7. K. M. Leung, Y. F. Lin, “Photon band structures: the plane-wave method,” Phys. Rev. B 41, 10,188–10,190 (1990).
    [Crossref]
  8. C. M. Soukoulis, Photonic Band Gaps and Localization (Plenum, New York, 1993).
  9. A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13,120–13,125 (1993).
    [Crossref]
  10. P. Sheng, Scattering and Localization of Classical Waves in Random Media (World Scientific, Singapore, 1990).
  11. J. B. Pendry, “Symmetry and transport of waves in 1D disordered systems,” Adv. Phys. 43, 461–542 (1994).
    [Crossref]
  12. M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B 48, 14,121–14,126 (1993).
    [Crossref]
  13. A. A. Bulgakov, V. R. Kovtun, “Surface optic oscillations in a limited stratified-periodic medium,” Opt. Spectrosc. 56, 269–274 (1984) (in Russian); “Study of surface optical oscillations in periodical multilayer media,” Solid State Commun. 56, 781–785 (1985).
  14. F. G. Bass, A. A. Bulgakov, Kinetic and Electrodynamical Phenomena in Classical and Quantum Semiconductor Superlattices (Nova Science, New York) (to be published).
  15. A. Kondilis, P. Tzanetakis, “Light propagation and localization in disordered binary multilayer films: an approximate analytical solution,” J. Opt. Soc. Am. A 11, 1661–1666 (1994).
    [Crossref]
  16. A. Kondilis, P. Tzanetakis, “Numerical calculation on optical localization in multilayer structures with random-thickness layers,” Phys. Rev. B 46, 15,426–15,431 (1992).
    [Crossref]
  17. C. Martijn de Sterke, R. C. McPhedran, “Bragg remnants in stratified random media,” Phys. Rev. B 47, 7780–7787 (1993).
    [Crossref]
  18. C. M. Soukoulis, S. Datta, E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994); E. N. Economou, A. D. Zdetsis, “Classical wave propagation in periodic structures,” Phys. Rev. B 40, 1334–1337 (1989).
    [Crossref]
  19. P. Sheng, B. White, Zhao-Qing Zhang, G. Papanicolaou, “Minimum wave-localization length in a one-dimensional random medium,” Phys. Rev. B 34, 4757–4761 (1986); C. M. Soukoulis, E. N. Economou, G. S. Grest, M. H. Cohen, “Existence of Anderson localization of classical waves in a random two-component medium,” Phys. Rev. Lett. 62, 575–578 (1989).
    [Crossref] [PubMed]
  20. E. N. Economou, C. M. Soukoulis, M. H. Cohen, “Localization for correlated binary-alloy disorder,” Phys. Rev. B 37, 4399–4407 (1988).
    [Crossref]
  21. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, Tokyo, 1965).
  22. Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
    [Crossref] [PubMed]
  23. C. KittelIntroduction to Solid State Physics (Wiley, New York, 1986).
  24. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
    [Crossref] [PubMed]

1994 (4)

Z. Daozhong, H. Wei, Z. Youlong, L. 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 1D disordered systems,” Adv. Phys. 43, 461–542 (1994).
[Crossref]

A. Kondilis, P. Tzanetakis, “Light propagation and localization in disordered binary multilayer films: an approximate analytical solution,” J. Opt. Soc. Am. A 11, 1661–1666 (1994).
[Crossref]

C. M. Soukoulis, S. Datta, E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994); E. N. Economou, A. D. Zdetsis, “Classical wave propagation in periodic structures,” Phys. Rev. B 40, 1334–1337 (1989).
[Crossref]

1993 (5)

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13,120–13,125 (1993).
[Crossref]

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

M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B 48, 14,121–14,126 (1993).
[Crossref]

D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structure and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993).
[Crossref]

E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283–295 (1993); H. O. Everitt, “Application of photonic band gap structures,” Opt. Photon. News, November, 1992, pp. 20–23; S. John, “Localization of light,” Phys. Today 41(5), 32–40 (1991).
[Crossref]

1992 (1)

A. Kondilis, P. Tzanetakis, “Numerical calculation on optical localization in multilayer structures with random-thickness layers,” Phys. Rev. B 46, 15,426–15,431 (1992).
[Crossref]

1991 (3)

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).
[Crossref]

M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[Crossref]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[Crossref] [PubMed]

1990 (2)

K. M. Leung, Y. F. Lin, “Photon band structures: the plane-wave method,” Phys. Rev. B 41, 10,188–10,190 (1990).
[Crossref]

Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[Crossref] [PubMed]

1988 (1)

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

1986 (1)

P. Sheng, B. White, Zhao-Qing Zhang, G. Papanicolaou, “Minimum wave-localization length in a one-dimensional random medium,” Phys. Rev. B 34, 4757–4761 (1986); C. M. Soukoulis, E. N. Economou, G. S. Grest, M. H. Cohen, “Existence of Anderson localization of classical waves in a random two-component medium,” Phys. Rev. Lett. 62, 575–578 (1989).
[Crossref] [PubMed]

1984 (1)

A. A. Bulgakov, V. R. Kovtun, “Surface optic oscillations in a limited stratified-periodic medium,” Opt. Spectrosc. 56, 269–274 (1984) (in Russian); “Study of surface optical oscillations in periodical multilayer media,” Solid State Commun. 56, 781–785 (1985).

1977 (1)

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).
[Crossref]

Bass, F. G.

F. G. Bass, A. A. Bulgakov, Kinetic and Electrodynamical Phenomena in Classical and Quantum Semiconductor Superlattices (Nova Science, New York) (to be published).

Bingying, C.

Z. Daozhong, H. Wei, Z. Youlong, L. 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]

Brommer, K. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[Crossref] [PubMed]

Bulgakov, A. A.

A. A. Bulgakov, V. R. Kovtun, “Surface optic oscillations in a limited stratified-periodic medium,” Opt. Spectrosc. 56, 269–274 (1984) (in Russian); “Study of surface optical oscillations in periodical multilayer media,” Solid State Commun. 56, 781–785 (1985).

F. G. Bass, A. A. Bulgakov, Kinetic and Electrodynamical Phenomena in Classical and Quantum Semiconductor Superlattices (Nova Science, New York) (to be published).

Chan, C. T.

M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B 48, 14,121–14,126 (1993).
[Crossref]

Christensen, K. T.

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13,120–13,125 (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.

D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structure and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993).
[Crossref]

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).
[Crossref]

Daozhong, Z.

Z. Daozhong, H. Wei, Z. Youlong, L. 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.

C. M. Soukoulis, S. Datta, E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994); E. N. Economou, A. D. Zdetsis, “Classical wave propagation in periodic structures,” Phys. Rev. B 40, 1334–1337 (1989).
[Crossref]

Economou, E. N.

C. M. Soukoulis, S. Datta, E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994); E. N. Economou, A. D. Zdetsis, “Classical wave propagation in periodic structures,” Phys. Rev. B 40, 1334–1337 (1989).
[Crossref]

M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B 48, 14,121–14,126 (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]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[Crossref] [PubMed]

Guozhen, Y.

Z. Daozhong, H. Wei, Z. Youlong, L. 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.

M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B 48, 14,121–14,126 (1993).
[Crossref]

Hong, C. S.

Joannopoulos, J. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[Crossref] [PubMed]

Kittel, C.

C. KittelIntroduction to Solid State Physics (Wiley, New York, 1986).

Kondilis, A.

A. Kondilis, P. Tzanetakis, “Light propagation and localization in disordered binary multilayer films: an approximate analytical solution,” J. Opt. Soc. Am. A 11, 1661–1666 (1994).
[Crossref]

A. Kondilis, P. Tzanetakis, “Numerical calculation on optical localization in multilayer structures with random-thickness layers,” Phys. Rev. B 46, 15,426–15,431 (1992).
[Crossref]

Kovtun, V. R.

A. A. Bulgakov, V. R. Kovtun, “Surface optic oscillations in a limited stratified-periodic medium,” Opt. Spectrosc. 56, 269–274 (1984) (in Russian); “Study of surface optical oscillations in periodical multilayer media,” Solid State Commun. 56, 781–785 (1985).

Kroll, N.

Leung, K. M.

K. M. Leung, Y. F. Lin, “Photon band structures: the plane-wave method,” Phys. Rev. B 41, 10,188–10,190 (1990).
[Crossref]

Lin, Y. F.

K. M. Leung, Y. F. Lin, “Photon band structures: the plane-wave method,” Phys. Rev. B 41, 10,188–10,190 (1990).
[Crossref]

Maradudin, A. A.

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13,120–13,125 (1993).
[Crossref]

M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[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.

D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structure and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993).
[Crossref]

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).
[Crossref]

McGurn, A. R.

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13,120–13,125 (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]

Meade, R. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[Crossref] [PubMed]

Mueller, F. M.

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13,120–13,125 (1993).
[Crossref]

Papanicolaou, G.

P. Sheng, B. White, Zhao-Qing Zhang, G. Papanicolaou, “Minimum wave-localization length in a one-dimensional random medium,” Phys. Rev. B 34, 4757–4761 (1986); C. M. Soukoulis, E. N. Economou, G. S. Grest, M. H. Cohen, “Existence of Anderson localization of classical waves in a random two-component medium,” Phys. Rev. Lett. 62, 575–578 (1989).
[Crossref] [PubMed]

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, Tokyo, 1965).

Pendry, J. B.

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

Platzman, P. M.

D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structure and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993).
[Crossref]

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).
[Crossref]

Plihal, M.

M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[Crossref]

Rappe, A. M.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[Crossref] [PubMed]

Satpathy, S.

Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[Crossref] [PubMed]

Schultz, S.

D. R. Smith, R. Dalichaouch, N. Kroll, S. Schultz, S. L. McCall, P. M. Platzman, “Photonic band structure and defects in one and two dimensions,” J. Opt. Soc. Am. B 10, 314–321 (1993).
[Crossref]

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).
[Crossref]

Shambrook, A.

M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[Crossref]

Sheng, P.

M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[Crossref]

P. Sheng, B. White, Zhao-Qing Zhang, G. Papanicolaou, “Minimum wave-localization length in a one-dimensional random medium,” Phys. Rev. B 34, 4757–4761 (1986); C. M. Soukoulis, E. N. Economou, G. S. Grest, M. H. Cohen, “Existence of Anderson localization of classical waves in a random two-component medium,” Phys. Rev. Lett. 62, 575–578 (1989).
[Crossref] [PubMed]

P. Sheng, Scattering and Localization of Classical Waves in Random Media (World Scientific, Singapore, 1990).

Sigalas, M.

M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B 48, 14,121–14,126 (1993).
[Crossref]

Smith, D. R.

Soukoulis, C. M.

C. M. Soukoulis, S. Datta, E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994); E. N. Economou, A. D. Zdetsis, “Classical wave propagation in periodic structures,” Phys. Rev. B 40, 1334–1337 (1989).
[Crossref]

M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B 48, 14,121–14,126 (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]

C. M. Soukoulis, Photonic Band Gaps and Localization (Plenum, New York, 1993).

Tzanetakis, P.

A. Kondilis, P. Tzanetakis, “Light propagation and localization in disordered binary multilayer films: an approximate analytical solution,” J. Opt. Soc. Am. A 11, 1661–1666 (1994).
[Crossref]

A. Kondilis, P. Tzanetakis, “Numerical calculation on optical localization in multilayer structures with random-thickness layers,” Phys. Rev. B 46, 15,426–15,431 (1992).
[Crossref]

Wei, H.

Z. Daozhong, H. Wei, Z. Youlong, L. 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]

White, B.

P. Sheng, B. White, Zhao-Qing Zhang, G. Papanicolaou, “Minimum wave-localization length in a one-dimensional random medium,” Phys. Rev. B 34, 4757–4761 (1986); C. M. Soukoulis, E. N. Economou, G. S. Grest, M. H. Cohen, “Existence of Anderson localization of classical waves in a random two-component medium,” Phys. Rev. Lett. 62, 575–578 (1989).
[Crossref] [PubMed]

Yablonovitch, E.

Yariv, A.

Yeh, D.

Youlong, Z.

Z. Daozhong, H. Wei, Z. Youlong, L. 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]

Zhang, Z.

Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[Crossref] [PubMed]

Zhang, Zhao-Qing

P. Sheng, B. White, Zhao-Qing Zhang, G. Papanicolaou, “Minimum wave-localization length in a one-dimensional random medium,” Phys. Rev. B 34, 4757–4761 (1986); C. M. Soukoulis, E. N. Economou, G. S. Grest, M. H. Cohen, “Existence of Anderson localization of classical waves in a random two-component medium,” Phys. Rev. Lett. 62, 575–578 (1989).
[Crossref] [PubMed]

Zhaolin, L.

Z. Daozhong, H. Wei, Z. Youlong, L. 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. (1)

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

J. Opt. Soc. Am. (1)

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

J. Opt. Soc. Am. B (2)

Nature (London) (1)

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).
[Crossref]

Opt. Commun. (1)

M. Plihal, A. Shambrook, A. A. Maradudin, P. Sheng, “Two-dimensional photonic band structures,” Opt. Commun. 80, 199–204 (1991).
[Crossref]

Opt. Spectrosc. (1)

A. A. Bulgakov, V. R. Kovtun, “Surface optic oscillations in a limited stratified-periodic medium,” Opt. Spectrosc. 56, 269–274 (1984) (in Russian); “Study of surface optical oscillations in periodical multilayer media,” Solid State Commun. 56, 781–785 (1985).

Phys. Rev. B (9)

M. Sigalas, C. M. Soukoulis, E. N. Economou, C. T. Chan, K. M. Ho, “Photonic band gaps and defects in two dimensions: studies of the transmission coefficient,” Phys. Rev. B 48, 14,121–14,126 (1993).
[Crossref]

A. Kondilis, P. Tzanetakis, “Numerical calculation on optical localization in multilayer structures with random-thickness layers,” Phys. Rev. B 46, 15,426–15,431 (1992).
[Crossref]

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

C. M. Soukoulis, S. Datta, E. N. Economou, “Propagation of classical waves in random media,” Phys. Rev. B 49, 3800–3810 (1994); E. N. Economou, A. D. Zdetsis, “Classical wave propagation in periodic structures,” Phys. Rev. B 40, 1334–1337 (1989).
[Crossref]

P. Sheng, B. White, Zhao-Qing Zhang, G. Papanicolaou, “Minimum wave-localization length in a one-dimensional random medium,” Phys. Rev. B 34, 4757–4761 (1986); C. M. Soukoulis, E. N. Economou, G. S. Grest, M. H. Cohen, “Existence of Anderson localization of classical waves in a random two-component medium,” Phys. Rev. Lett. 62, 575–578 (1989).
[Crossref] [PubMed]

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

K. M. Leung, Y. F. Lin, “Photon band structures: the plane-wave method,” Phys. Rev. B 41, 10,188–10,190 (1990).
[Crossref]

Z. Daozhong, H. Wei, Z. Youlong, L. 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]

A. R. McGurn, K. T. Christensen, F. M. Mueller, A. A. Maradudin, “Anderson localization in one-dimensional randomly disordered optical systems that are periodic on average,” Phys. Rev. B 47, 13,120–13,125 (1993).
[Crossref]

Phys. Rev. Lett. (2)

Z. Zhang, S. Satpathy, “Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell’s equations,” Phys. Rev. Lett. 65, 2650–2653 (1990).
[Crossref] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[Crossref] [PubMed]

Other (5)

C. KittelIntroduction to Solid State Physics (Wiley, New York, 1986).

P. Sheng, Scattering and Localization of Classical Waves in Random Media (World Scientific, Singapore, 1990).

C. M. Soukoulis, Photonic Band Gaps and Localization (Plenum, New York, 1993).

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, Tokyo, 1965).

F. G. Bass, A. A. Bulgakov, Kinetic and Electrodynamical Phenomena in Classical and Quantum Semiconductor Superlattices (Nova Science, New York) (to be published).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the scattering structure: (a) regular lattice, (b) superlattice with a random structure inside a superperiod of length L = ld, with l, n, m being integers. In (b) each slab is represented by a vertical segment.

Fig. 2
Fig. 2

BGW (in units of ωd/c) as a function of filling factor for a regular lattice for different frequency bands; back = 1, slab = 9.

Fig. 3
Fig. 3

MGF (in units of ωd/c) as a function of filling factor for a regular lattice for different frequency bands (thin curves); Fm × n ¯ (thick curves). back = 1, slab = 9.

Fig. 4
Fig. 4

Random superlattice. The superperiod contains 50 slabs with randomly chosen permittivity; each curve is obtained after averaging over 30 realizations. (a) BGW and (b) MGF versus filling factor (thin curves); Fm × n ¯ (thick curves). The frequencies are given in units of ωd/c.

Fig. 5
Fig. 5

Normalized LL as a function of dimensionless frequency W = ωd/c for a periodic structure having 100 unit cells of length d with back = 1, slab = 9, α = 0.5.

Fig. 6
Fig. 6

Same as Fig. 5 but for a single random realization.

Fig. 7
Fig. 7

Logarithm of the LL as a function of both frequency W and filling factor α; ∊back = 1, slab = 9.

Fig. 8
Fig. 8

LL as a function of frequency W; ∊slab = 9; (a) α = 0.25, back = 1; (b) α = 0.98, back = 1; (c) α = 0.25, back = 8.

Fig. 9
Fig. 9

LL as a function background permittivity; slab = 9; α = 0.25; W W BR = 2 π / back (thick curve); W = 2.4 (thin curve). The inset shows details of the region back > 5.

Equations (29)

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P R = 1 - k = 1 R R ! k ! ( R - k ) ! ( 1 l ) k ( 1 - 1 l ) R - k .
2 E ( z , t ) z 2 = ( z ) c 2 2 E ( z , t ) t 2
E ( z , t ) = E ( z ) exp ( - i ω t ) .
2 E ( z ) z 2 + ( z ) c 2 ω 2 E ( z ) = 0.
E ( z ) = exp ( i K z ) E K ( z ) ,
E K ( z ) = E K ( z + L ) ,
( z ) = ( z + L ) .
E K ( z ) = G = - E G K exp ( i G z ) , ( z ) = G = - G exp ( i G z ) .
( G + K ) 2 E G K - ω K 2 c 2 G = - G - G E G K = 0 .
n = 1 L 0 L ( z ) exp ( - i 2 π n z L ) d z .
n = a d l exp [ - i π n l ( 2 - a d ) ] S ( π n l a d ) × j = 1 l ¯ j exp [ - i 2 π n ( j - 1 ) l ] + back l ( 1 - a d ) × exp [ - i π n l ( 1 - a d ) ] S [ π n l ( 1 - a d ) ] × j = 1 l exp [ - i 2 π n ( j - 1 ) l ] ;
( 1 r ) = T ^ ( t 0 ) .
T ¯ 11 j = exp [ - i κ 1 j ( 1 - α ) ] [ cos ( κ 2 j α ) - 1 / 2 i ( κ 2 j / κ 1 j + κ 1 j / κ 2 j ) sin κ 2 j α ] , T ¯ 12 j = exp [ i κ 1 j ( 1 - α ) ] × [ - 1 / 2 i ( κ 2 j / κ 1 j - κ 1 j / κ 2 j ) sin κ 2 j α ] , T ¯ 22 j = ( T ¯ 11 j ) * ,             T ¯ 21 j = ( T ¯ 12 j ) * ,             α = a / d , κ 1 j = ω d c back ,             κ 2 j = ω d c { slab or back } ,
K ( ω ) = 1 d cos - 1 [ 1 2 ( T ¯ 11 + T ¯ 22 ) ] .
L = d ,             l = 1 ,             T ¯ 11 = T ¯ 22 * = T ¯ 11 j ,             j = 1 , κ 1 κ 1 1 = ω d c back ,             κ 2 κ 2 1 = ω d c slab .
T ¯ 11 + T ¯ 22 = 2.
F m ( N ) ω d / c = π N / , = back , α = 0 , = slab , α = 1.
n ¯ = slab α + slab ( 1 - α ) .
Q ( W ) = T ¯ 11 + T ¯ 22 - 2 ,
d Q ( W ) d W | W = W c = 0.
{ sin ( W c slab α ) = 0 sin [ W c back ( 1 - α ) ] = 0 .
{ W c = k π slab 1 α back slab 1 - α α = m k ,             k , m integers .
r 2 = 0 ;             t 2 = 1 ,
m + k = N .
= - L ln ( T ) .
W BR = m π back
2 π back = k π α - 1 slab ,
K c = ω ,
m λ BR 2 = d ,             m integer .

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