Abstract

A detailed analytical study of an impurity-induced polariton band arising inside a spectral gap between lower and upper polariton branches is presented. Using the microcanonical method, we calculate the density of states and the localization length of the impurity polaritons. Analytical results are compared with numerical simulations, and excellent agreement is found.

© 2000 Optical Society of America

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  1. S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
    [Crossref]
  2. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
    [Crossref]
  3. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  4. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, Princeton, N.J., 1995).
  5. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [Crossref] [PubMed]
  6. I. M. Lifshitz, “Some problems of the dynamic theory of non-ideal crystal lattices,” Nuovo Cimento 3, 716–734 (1956).
    [Crossref]
  7. I. M. Lifshitz and A. M. Kosevich, “The dynamics of a crystal lattice with defects,” in Lattice Dynamics (Benjamin, New York, 1969), pp. 53–90.
  8. I. M. Lifshitz and V. Ya. Kirpichnikov, “Tunnel transparency of disordered systems,” Sov. Phys. JETP 50, 499–511 (1979).
  9. A. A. Maradudin, “Some effects of point defects on the vibrations of crystal Lattices,” in Lattice Dynamics (Benjamin, New York, 1969), pp. 1–52.
  10. A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatova, Theory of Lattice Dynamics in the Harmonic Approximation, 2nd ed. (Academic, New York, 1971).
  11. B. I. Schklovskii and A. L. Efros, Electron Properties of Doped Semiconductors (Springer, New York, 1984).
  12. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987);S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
    [Crossref] [PubMed]
  13. 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]
  14. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Photonic bound states in periodic dielectric materials,” Phys. Rev. B 44, 13772–13774 (1991).
    [Crossref]
  15. V. I. Rupasov and M. Singh, “Quantum gap solitons and soliton pinning in dispersive medium and photonic-band-gap materials: Bethe-ansatz solution,” Phys. Rev. A 54, 3614–3625 (1996);“Two-atom problem and polariton-impurity band in dispersive media and photonic-band-gap materials,” Phys. Rev. A 56, 898–904 (1997)
    [Crossref] [PubMed]
  16. S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990);“Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991)
    [Crossref] [PubMed]
  17. M. R. Singh and W. Lau, “Polariton effective mass and spectral density in III–IV semiconductors doped with an ordered chain of identical two-level atoms,” Phys. Status Solidi A 203, 401–410 (1997).
    [Crossref]
  18. A. A. Lisyansky and L. I. Deych, “Localization of polaritons by impurities,” Bull. Am. Phys. Soc. 42, 203–204 (1997); L. I. Deych and A. A. Lisyansky, “Local polariton states in polar crystals with impurities,” Phys. Lett. A 240, 329–333 (1998).
    [Crossref]
  19. V. S. Podolsky, L. I. Deych, and A. A. Lisyansky, “Local polariton states in impure ionic crystals,” Phys. Rev. B 57, 5168–5176 (1998).
    [Crossref]
  20. V. M. Shalaev, R. Botet, and A. V. Butenko, “Localization of collective dipole excitations on fractals,” Phys. Rev. B 48, 6662–6664 (1993);S. I. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and V. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
    [Crossref]
  21. M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Optical absorption and localization of eigenmodes in disordered clusters,” Phys. Rev. B 51, 185–195 (1995);M. I. Stockman, L. N. Pandey, and T. F. George, “Inhomogeneous localization of polar eigenmodes in fractals,” Phys. Rev. B 53, 2183–2186 (1996);M. I. Stockman, “Femtosecond optical responses of disordered clusters, composites, and rough surfaces: ‘the ninth wave’ effect,” Phys. Rev. Lett. 84, 1011–1014 (2000).
    [Crossref] [PubMed]
  22. L. I. Deych and A. A. Lisyansky, “Resonance tunneling of polaritons in 1-D chain with a single defect,” Phys. Lett. A 243, 156–162 (1998).
    [Crossref]
  23. L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Defect-induced resonant tunneling of electromagnetic waves through a polariton gap,” Europhys. Lett. 46, 534–539 (1999).
    [Crossref]
  24. L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Effects of resonant tunneling in electromagnetic wave propagation through a polariton gap,” Phys. Rev. B 59, 11339–11348 (1999).
    [Crossref]
  25. D. W. Taylor, “Phonon response theory and the infrared and Raman experiments,” in Optical Properties of Mixed Crystals, R. J. Elliott and I. P. Ipatova, eds. (North-Holland, Amsterdam, 1988), pp. 35–132.
  26. D. S. Citrin, “Exciton radiative decay and polaritons in multiquantum wells: quantum-well-to-superlattice crossover,” Solid State Commun. 89, 139–143 (1994).
    [Crossref]
  27. E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Phys. Solid State 36, 1156–1161 (1994).
  28. L. C. Andreani, “Polaritons in multiple quantum wells,” Phys. Status Solidi B 188, 29–42 (1995).
    [Crossref]
  29. T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
    [Crossref]
  30. Y. Merle, D. Aubigné, A. Waseila, H. Mariette, and T. Dietl, “Polariton effects in multiple-quantum-well structures of CdTe/Cd1-xZnxTe,” Phys. Rev. B 54, 14003–14011 (1996).
    [Crossref]
  31. M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
    [Crossref] [PubMed]
  32. M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
    [Crossref]
  33. D. S. Citrin, “Waveguiding without a waveguide: local-mode exciton polaritons in multiple quantum wells,” Appl. Phys. Lett. 66, 994–996 (1995).
    [Crossref]
  34. A. Dereux, J.-P. Vigneron, P. Lambin, and A. Lucas, “Polaritons in semiconductor multilayered materials,” Phys. Rev. B 38, 5438–5452 (1988).
    [Crossref]
  35. M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, “Resonant and localized electromagnetic modes in finite superlattices,” Phys. Rev. B 61, 2059–2064 (2000).
    [Crossref]
  36. D. Citrin, “Coherent transport of excitons in quantum-dot chains: role of retardation,” Opt. Lett. 20, 901–903 (1995).
    [Crossref] [PubMed]
  37. J. M. Deutsch and G. Paladin, “Product of random matrices in a microcanonical ensemble,” Phys. Rev. Lett. 62, 695–699 (1989).
    [Crossref] [PubMed]
  38. I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).
  39. D. J. Thouless, “A relation between the density of states and range of localization for one dimensional random system,” J. Phys. C 5, 77–81 (1972).
    [Crossref]

2000 (1)

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, “Resonant and localized electromagnetic modes in finite superlattices,” Phys. Rev. B 61, 2059–2064 (2000).
[Crossref]

1999 (3)

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[Crossref]

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Defect-induced resonant tunneling of electromagnetic waves through a polariton gap,” Europhys. Lett. 46, 534–539 (1999).
[Crossref]

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Effects of resonant tunneling in electromagnetic wave propagation through a polariton gap,” Phys. Rev. B 59, 11339–11348 (1999).
[Crossref]

1998 (2)

L. I. Deych and A. A. Lisyansky, “Resonance tunneling of polaritons in 1-D chain with a single defect,” Phys. Lett. A 243, 156–162 (1998).
[Crossref]

V. S. Podolsky, L. I. Deych, and A. A. Lisyansky, “Local polariton states in impure ionic crystals,” Phys. Rev. B 57, 5168–5176 (1998).
[Crossref]

1997 (3)

M. R. Singh and W. Lau, “Polariton effective mass and spectral density in III–IV semiconductors doped with an ordered chain of identical two-level atoms,” Phys. Status Solidi A 203, 401–410 (1997).
[Crossref]

A. A. Lisyansky and L. I. Deych, “Localization of polaritons by impurities,” Bull. Am. Phys. Soc. 42, 203–204 (1997); L. I. Deych and A. A. Lisyansky, “Local polariton states in polar crystals with impurities,” Phys. Lett. A 240, 329–333 (1998).
[Crossref]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[Crossref]

1996 (4)

V. I. Rupasov and M. Singh, “Quantum gap solitons and soliton pinning in dispersive medium and photonic-band-gap materials: Bethe-ansatz solution,” Phys. Rev. A 54, 3614–3625 (1996);“Two-atom problem and polariton-impurity band in dispersive media and photonic-band-gap materials,” Phys. Rev. A 56, 898–904 (1997)
[Crossref] [PubMed]

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

Y. Merle, D. Aubigné, A. Waseila, H. Mariette, and T. Dietl, “Polariton effects in multiple-quantum-well structures of CdTe/Cd1-xZnxTe,” Phys. Rev. B 54, 14003–14011 (1996).
[Crossref]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref] [PubMed]

1995 (4)

L. C. Andreani, “Polaritons in multiple quantum wells,” Phys. Status Solidi B 188, 29–42 (1995).
[Crossref]

D. S. Citrin, “Waveguiding without a waveguide: local-mode exciton polaritons in multiple quantum wells,” Appl. Phys. Lett. 66, 994–996 (1995).
[Crossref]

D. Citrin, “Coherent transport of excitons in quantum-dot chains: role of retardation,” Opt. Lett. 20, 901–903 (1995).
[Crossref] [PubMed]

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Optical absorption and localization of eigenmodes in disordered clusters,” Phys. Rev. B 51, 185–195 (1995);M. I. Stockman, L. N. Pandey, and T. F. George, “Inhomogeneous localization of polar eigenmodes in fractals,” Phys. Rev. B 53, 2183–2186 (1996);M. I. Stockman, “Femtosecond optical responses of disordered clusters, composites, and rough surfaces: ‘the ninth wave’ effect,” Phys. Rev. Lett. 84, 1011–1014 (2000).
[Crossref] [PubMed]

1994 (2)

D. S. Citrin, “Exciton radiative decay and polaritons in multiquantum wells: quantum-well-to-superlattice crossover,” Solid State Commun. 89, 139–143 (1994).
[Crossref]

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Phys. Solid State 36, 1156–1161 (1994).

1993 (1)

V. M. Shalaev, R. Botet, and A. V. Butenko, “Localization of collective dipole excitations on fractals,” Phys. Rev. B 48, 6662–6664 (1993);S. I. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and V. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[Crossref]

1991 (2)

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]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Photonic bound states in periodic dielectric materials,” Phys. Rev. B 44, 13772–13774 (1991).
[Crossref]

1990 (1)

S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990);“Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991)
[Crossref] [PubMed]

1989 (1)

J. M. Deutsch and G. Paladin, “Product of random matrices in a microcanonical ensemble,” Phys. Rev. Lett. 62, 695–699 (1989).
[Crossref] [PubMed]

1988 (1)

A. Dereux, J.-P. Vigneron, P. Lambin, and A. Lucas, “Polaritons in semiconductor multilayered materials,” Phys. Rev. B 38, 5438–5452 (1988).
[Crossref]

1987 (3)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987);S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[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]

1984 (1)

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
[Crossref]

1979 (1)

I. M. Lifshitz and V. Ya. Kirpichnikov, “Tunnel transparency of disordered systems,” Sov. Phys. JETP 50, 499–511 (1979).

1972 (1)

D. J. Thouless, “A relation between the density of states and range of localization for one dimensional random system,” J. Phys. C 5, 77–81 (1972).
[Crossref]

1956 (1)

I. M. Lifshitz, “Some problems of the dynamic theory of non-ideal crystal lattices,” Nuovo Cimento 3, 716–734 (1956).
[Crossref]

Akjouj, A.

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, “Resonant and localized electromagnetic modes in finite superlattices,” Phys. Rev. B 61, 2059–2064 (2000).
[Crossref]

Andreani, L. C.

L. C. Andreani, “Polaritons in multiple quantum wells,” Phys. Status Solidi B 188, 29–42 (1995).
[Crossref]

Aubigné, D.

Y. Merle, D. Aubigné, A. Waseila, H. Mariette, and T. Dietl, “Polariton effects in multiple-quantum-well structures of CdTe/Cd1-xZnxTe,” Phys. Rev. B 54, 14003–14011 (1996).
[Crossref]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[Crossref]

Botet, R.

V. M. Shalaev, R. Botet, and A. V. Butenko, “Localization of collective dipole excitations on fractals,” Phys. Rev. B 48, 6662–6664 (1993);S. I. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and V. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[Crossref]

Brick, P.

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[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]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Photonic bound states in periodic dielectric materials,” Phys. Rev. B 44, 13772–13774 (1991).
[Crossref]

Butenko, A. V.

V. M. Shalaev, R. Botet, and A. V. Butenko, “Localization of collective dipole excitations on fractals,” Phys. Rev. B 48, 6662–6664 (1993);S. I. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and V. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[Crossref]

Citrin, D.

Citrin, D. S.

D. S. Citrin, “Waveguiding without a waveguide: local-mode exciton polaritons in multiple quantum wells,” Appl. Phys. Lett. 66, 994–996 (1995).
[Crossref]

D. S. Citrin, “Exciton radiative decay and polaritons in multiquantum wells: quantum-well-to-superlattice crossover,” Solid State Commun. 89, 139–143 (1994).
[Crossref]

Dereux, A.

A. Dereux, J.-P. Vigneron, P. Lambin, and A. Lucas, “Polaritons in semiconductor multilayered materials,” Phys. Rev. B 38, 5438–5452 (1988).
[Crossref]

Deutsch, J. M.

J. M. Deutsch and G. Paladin, “Product of random matrices in a microcanonical ensemble,” Phys. Rev. Lett. 62, 695–699 (1989).
[Crossref] [PubMed]

Deych, L. I.

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Effects of resonant tunneling in electromagnetic wave propagation through a polariton gap,” Phys. Rev. B 59, 11339–11348 (1999).
[Crossref]

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Defect-induced resonant tunneling of electromagnetic waves through a polariton gap,” Europhys. Lett. 46, 534–539 (1999).
[Crossref]

L. I. Deych and A. A. Lisyansky, “Resonance tunneling of polaritons in 1-D chain with a single defect,” Phys. Lett. A 243, 156–162 (1998).
[Crossref]

V. S. Podolsky, L. I. Deych, and A. A. Lisyansky, “Local polariton states in impure ionic crystals,” Phys. Rev. B 57, 5168–5176 (1998).
[Crossref]

A. A. Lisyansky and L. I. Deych, “Localization of polaritons by impurities,” Bull. Am. Phys. Soc. 42, 203–204 (1997); L. I. Deych and A. A. Lisyansky, “Local polariton states in polar crystals with impurities,” Phys. Lett. A 240, 329–333 (1998).
[Crossref]

Dietl, T.

Y. Merle, D. Aubigné, A. Waseila, H. Mariette, and T. Dietl, “Polariton effects in multiple-quantum-well structures of CdTe/Cd1-xZnxTe,” Phys. Rev. B 54, 14003–14011 (1996).
[Crossref]

Djafari-Rouhani, B.

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, “Resonant and localized electromagnetic modes in finite superlattices,” Phys. Rev. B 61, 2059–2064 (2000).
[Crossref]

Dobrzynski, L.

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, “Resonant and localized electromagnetic modes in finite superlattices,” Phys. Rev. B 61, 2059–2064 (2000).
[Crossref]

Efros, A. L.

B. I. Schklovskii and A. L. Efros, Electron Properties of Doped Semiconductors (Springer, New York, 1984).

Ell, C.

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[Crossref]

George, T. F.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Optical absorption and localization of eigenmodes in disordered clusters,” Phys. Rev. B 51, 185–195 (1995);M. I. Stockman, L. N. Pandey, and T. F. George, “Inhomogeneous localization of polar eigenmodes in fractals,” Phys. Rev. B 53, 2183–2186 (1996);M. I. Stockman, “Femtosecond optical responses of disordered clusters, composites, and rough surfaces: ‘the ninth wave’ effect,” Phys. Rev. Lett. 84, 1011–1014 (2000).
[Crossref] [PubMed]

Gibbs, H. M.

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[Crossref]

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]

Gredeskul, S. A.

I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Hey, R.

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref] [PubMed]

Hübner, M.

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[Crossref]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref] [PubMed]

Ipatova, I. P.

A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatova, Theory of Lattice Dynamics in the Harmonic Approximation, 2nd ed. (Academic, New York, 1971).

Ivchenko, E. L.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Phys. Solid State 36, 1156–1161 (1994).

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]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Photonic bound states in periodic dielectric materials,” Phys. Rev. B 44, 13772–13774 (1991).
[Crossref]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, Princeton, N.J., 1995).

John, S.

S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990);“Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991)
[Crossref] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
[Crossref]

Jorda, S.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Phys. Solid State 36, 1156–1161 (1994).

Khitrova, G.

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[Crossref]

Kirpichnikov, V. Ya.

I. M. Lifshitz and V. Ya. Kirpichnikov, “Tunnel transparency of disordered systems,” Sov. Phys. JETP 50, 499–511 (1979).

Knorr, A.

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref] [PubMed]

Koch, S. W.

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[Crossref]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref] [PubMed]

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

Kosevich, A. M.

I. M. Lifshitz and A. M. Kosevich, “The dynamics of a crystal lattice with defects,” in Lattice Dynamics (Benjamin, New York, 1969), pp. 53–90.

Kuhl, J.

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref] [PubMed]

Lagendijk, A.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[Crossref]

Lahlaouti, M. L. H.

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, “Resonant and localized electromagnetic modes in finite superlattices,” Phys. Rev. B 61, 2059–2064 (2000).
[Crossref]

Lambin, P.

A. Dereux, J.-P. Vigneron, P. Lambin, and A. Lucas, “Polaritons in semiconductor multilayered materials,” Phys. Rev. B 38, 5438–5452 (1988).
[Crossref]

Lau, W.

M. R. Singh and W. Lau, “Polariton effective mass and spectral density in III–IV semiconductors doped with an ordered chain of identical two-level atoms,” Phys. Status Solidi A 203, 401–410 (1997).
[Crossref]

Lee, E. S.

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[Crossref]

Lifshitz, I. M.

I. M. Lifshitz and V. Ya. Kirpichnikov, “Tunnel transparency of disordered systems,” Sov. Phys. JETP 50, 499–511 (1979).

I. M. Lifshitz, “Some problems of the dynamic theory of non-ideal crystal lattices,” Nuovo Cimento 3, 716–734 (1956).
[Crossref]

I. M. Lifshitz and A. M. Kosevich, “The dynamics of a crystal lattice with defects,” in Lattice Dynamics (Benjamin, New York, 1969), pp. 53–90.

I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Lisyansky, A. A.

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Defect-induced resonant tunneling of electromagnetic waves through a polariton gap,” Europhys. Lett. 46, 534–539 (1999).
[Crossref]

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Effects of resonant tunneling in electromagnetic wave propagation through a polariton gap,” Phys. Rev. B 59, 11339–11348 (1999).
[Crossref]

L. I. Deych and A. A. Lisyansky, “Resonance tunneling of polaritons in 1-D chain with a single defect,” Phys. Lett. A 243, 156–162 (1998).
[Crossref]

V. S. Podolsky, L. I. Deych, and A. A. Lisyansky, “Local polariton states in impure ionic crystals,” Phys. Rev. B 57, 5168–5176 (1998).
[Crossref]

A. A. Lisyansky and L. I. Deych, “Localization of polaritons by impurities,” Bull. Am. Phys. Soc. 42, 203–204 (1997); L. I. Deych and A. A. Lisyansky, “Local polariton states in polar crystals with impurities,” Phys. Lett. A 240, 329–333 (1998).
[Crossref]

Lucas, A.

A. Dereux, J.-P. Vigneron, P. Lambin, and A. Lucas, “Polaritons in semiconductor multilayered materials,” Phys. Rev. B 38, 5438–5452 (1988).
[Crossref]

Maradudin, A. A.

A. A. Maradudin, “Some effects of point defects on the vibrations of crystal Lattices,” in Lattice Dynamics (Benjamin, New York, 1969), pp. 1–52.

A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatova, Theory of Lattice Dynamics in the Harmonic Approximation, 2nd ed. (Academic, New York, 1971).

Mariette, H.

Y. Merle, D. Aubigné, A. Waseila, H. Mariette, and T. Dietl, “Polariton effects in multiple-quantum-well structures of CdTe/Cd1-xZnxTe,” Phys. Rev. B 54, 14003–14011 (1996).
[Crossref]

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Photonic bound states in periodic dielectric materials,” Phys. Rev. B 44, 13772–13774 (1991).
[Crossref]

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]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, Princeton, N.J., 1995).

Merle, Y.

Y. Merle, D. Aubigné, A. Waseila, H. Mariette, and T. Dietl, “Polariton effects in multiple-quantum-well structures of CdTe/Cd1-xZnxTe,” Phys. Rev. B 54, 14003–14011 (1996).
[Crossref]

Montroll, E. W.

A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatova, Theory of Lattice Dynamics in the Harmonic Approximation, 2nd ed. (Academic, New York, 1971).

Muratov, L. S.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Optical absorption and localization of eigenmodes in disordered clusters,” Phys. Rev. B 51, 185–195 (1995);M. I. Stockman, L. N. Pandey, and T. F. George, “Inhomogeneous localization of polar eigenmodes in fractals,” Phys. Rev. B 53, 2183–2186 (1996);M. I. Stockman, “Femtosecond optical responses of disordered clusters, composites, and rough surfaces: ‘the ninth wave’ effect,” Phys. Rev. Lett. 84, 1011–1014 (2000).
[Crossref] [PubMed]

Nesvizhskii, A. I.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Phys. Solid State 36, 1156–1161 (1994).

Paladin, G.

J. M. Deutsch and G. Paladin, “Product of random matrices in a microcanonical ensemble,” Phys. Rev. Lett. 62, 695–699 (1989).
[Crossref] [PubMed]

Pandey, L. N.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Optical absorption and localization of eigenmodes in disordered clusters,” Phys. Rev. B 51, 185–195 (1995);M. I. Stockman, L. N. Pandey, and T. F. George, “Inhomogeneous localization of polar eigenmodes in fractals,” Phys. Rev. B 53, 2183–2186 (1996);M. I. Stockman, “Femtosecond optical responses of disordered clusters, composites, and rough surfaces: ‘the ninth wave’ effect,” Phys. Rev. Lett. 84, 1011–1014 (2000).
[Crossref] [PubMed]

Pastur, L. A.

I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

Ploog, K.

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref] [PubMed]

Podolsky, V. S.

V. S. Podolsky, L. I. Deych, and A. A. Lisyansky, “Local polariton states in impure ionic crystals,” Phys. Rev. B 57, 5168–5176 (1998).
[Crossref]

Prineas, J. P.

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[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]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Photonic bound states in periodic dielectric materials,” Phys. Rev. B 44, 13772–13774 (1991).
[Crossref]

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[Crossref]

Rupasov, V. I.

V. I. Rupasov and M. Singh, “Quantum gap solitons and soliton pinning in dispersive medium and photonic-band-gap materials: Bethe-ansatz solution,” Phys. Rev. A 54, 3614–3625 (1996);“Two-atom problem and polariton-impurity band in dispersive media and photonic-band-gap materials,” Phys. Rev. A 56, 898–904 (1997)
[Crossref] [PubMed]

Schklovskii, B. I.

B. I. Schklovskii and A. L. Efros, Electron Properties of Doped Semiconductors (Springer, New York, 1984).

Shalaev, V. M.

V. M. Shalaev, R. Botet, and A. V. Butenko, “Localization of collective dipole excitations on fractals,” Phys. Rev. B 48, 6662–6664 (1993);S. I. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and V. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[Crossref]

Singh, M.

V. I. Rupasov and M. Singh, “Quantum gap solitons and soliton pinning in dispersive medium and photonic-band-gap materials: Bethe-ansatz solution,” Phys. Rev. A 54, 3614–3625 (1996);“Two-atom problem and polariton-impurity band in dispersive media and photonic-band-gap materials,” Phys. Rev. A 56, 898–904 (1997)
[Crossref] [PubMed]

Singh, M. R.

M. R. Singh and W. Lau, “Polariton effective mass and spectral density in III–IV semiconductors doped with an ordered chain of identical two-level atoms,” Phys. Status Solidi A 203, 401–410 (1997).
[Crossref]

Stockman, M. I.

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Optical absorption and localization of eigenmodes in disordered clusters,” Phys. Rev. B 51, 185–195 (1995);M. I. Stockman, L. N. Pandey, and T. F. George, “Inhomogeneous localization of polar eigenmodes in fractals,” Phys. Rev. B 53, 2183–2186 (1996);M. I. Stockman, “Femtosecond optical responses of disordered clusters, composites, and rough surfaces: ‘the ninth wave’ effect,” Phys. Rev. Lett. 84, 1011–1014 (2000).
[Crossref] [PubMed]

Stroucken, T.

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref] [PubMed]

Taylor, D. W.

D. W. Taylor, “Phonon response theory and the infrared and Raman experiments,” in Optical Properties of Mixed Crystals, R. J. Elliott and I. P. Ipatova, eds. (North-Holland, Amsterdam, 1988), pp. 35–132.

Thomas, P.

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

Thouless, D. J.

D. J. Thouless, “A relation between the density of states and range of localization for one dimensional random system,” J. Phys. C 5, 77–81 (1972).
[Crossref]

Vigneron, J.-P.

A. Dereux, J.-P. Vigneron, P. Lambin, and A. Lucas, “Polaritons in semiconductor multilayered materials,” Phys. Rev. B 38, 5438–5452 (1988).
[Crossref]

Wang, J.

S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990);“Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991)
[Crossref] [PubMed]

Waseila, A.

Y. Merle, D. Aubigné, A. Waseila, H. Mariette, and T. Dietl, “Polariton effects in multiple-quantum-well structures of CdTe/Cd1-xZnxTe,” Phys. Rev. B 54, 14003–14011 (1996).
[Crossref]

Weiss, G. H.

A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatova, Theory of Lattice Dynamics in the Harmonic Approximation, 2nd ed. (Academic, New York, 1971).

Wiersma, D. S.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, Princeton, N.J., 1995).

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);S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[Crossref] [PubMed]

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

Yamilov, A.

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Effects of resonant tunneling in electromagnetic wave propagation through a polariton gap,” Phys. Rev. B 59, 11339–11348 (1999).
[Crossref]

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Defect-induced resonant tunneling of electromagnetic waves through a polariton gap,” Europhys. Lett. 46, 534–539 (1999).
[Crossref]

Appl. Phys. Lett. (1)

D. S. Citrin, “Waveguiding without a waveguide: local-mode exciton polaritons in multiple quantum wells,” Appl. Phys. Lett. 66, 994–996 (1995).
[Crossref]

Bull. Am. Phys. Soc. (1)

A. A. Lisyansky and L. I. Deych, “Localization of polaritons by impurities,” Bull. Am. Phys. Soc. 42, 203–204 (1997); L. I. Deych and A. A. Lisyansky, “Local polariton states in polar crystals with impurities,” Phys. Lett. A 240, 329–333 (1998).
[Crossref]

Europhys. Lett. (1)

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Defect-induced resonant tunneling of electromagnetic waves through a polariton gap,” Europhys. Lett. 46, 534–539 (1999).
[Crossref]

J. Phys. C (1)

D. J. Thouless, “A relation between the density of states and range of localization for one dimensional random system,” J. Phys. C 5, 77–81 (1972).
[Crossref]

Nature (1)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).
[Crossref]

Nuovo Cimento (1)

I. M. Lifshitz, “Some problems of the dynamic theory of non-ideal crystal lattices,” Nuovo Cimento 3, 716–734 (1956).
[Crossref]

Opt. Lett. (1)

Phys. Lett. A (1)

L. I. Deych and A. A. Lisyansky, “Resonance tunneling of polaritons in 1-D chain with a single defect,” Phys. Lett. A 243, 156–162 (1998).
[Crossref]

Phys. Rev. A (1)

V. I. Rupasov and M. Singh, “Quantum gap solitons and soliton pinning in dispersive medium and photonic-band-gap materials: Bethe-ansatz solution,” Phys. Rev. A 54, 3614–3625 (1996);“Two-atom problem and polariton-impurity band in dispersive media and photonic-band-gap materials,” Phys. Rev. A 56, 898–904 (1997)
[Crossref] [PubMed]

Phys. Rev. B (9)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Photonic bound states in periodic dielectric materials,” Phys. Rev. B 44, 13772–13774 (1991).
[Crossref]

L. I. Deych, A. Yamilov, and A. A. Lisyansky, “Effects of resonant tunneling in electromagnetic wave propagation through a polariton gap,” Phys. Rev. B 59, 11339–11348 (1999).
[Crossref]

A. Dereux, J.-P. Vigneron, P. Lambin, and A. Lucas, “Polaritons in semiconductor multilayered materials,” Phys. Rev. B 38, 5438–5452 (1988).
[Crossref]

M. L. H. Lahlaouti, A. Akjouj, B. Djafari-Rouhani, and L. Dobrzynski, “Resonant and localized electromagnetic modes in finite superlattices,” Phys. Rev. B 61, 2059–2064 (2000).
[Crossref]

T. Stroucken, A. Knorr, P. Thomas, and S. W. Koch, “Coherent dynamics of radiatively coupled quantum-well excitons,” Phys. Rev. B 53, 2026–2033 (1996).
[Crossref]

Y. Merle, D. Aubigné, A. Waseila, H. Mariette, and T. Dietl, “Polariton effects in multiple-quantum-well structures of CdTe/Cd1-xZnxTe,” Phys. Rev. B 54, 14003–14011 (1996).
[Crossref]

V. S. Podolsky, L. I. Deych, and A. A. Lisyansky, “Local polariton states in impure ionic crystals,” Phys. Rev. B 57, 5168–5176 (1998).
[Crossref]

V. M. Shalaev, R. Botet, and A. V. Butenko, “Localization of collective dipole excitations on fractals,” Phys. Rev. B 48, 6662–6664 (1993);S. I. Bozhevolnyi, V. A. Markel, V. Coello, W. Kim, and V. Shalaev, “Direct observation of localized dipolar excitations on rough nanostructured surfaces,” Phys. Rev. B 58, 11441–11448 (1998).
[Crossref]

M. I. Stockman, L. N. Pandey, L. S. Muratov, and T. F. George, “Optical absorption and localization of eigenmodes in disordered clusters,” Phys. Rev. B 51, 185–195 (1995);M. I. Stockman, L. N. Pandey, and T. F. George, “Inhomogeneous localization of polar eigenmodes in fractals,” Phys. Rev. B 53, 2183–2186 (1996);M. I. Stockman, “Femtosecond optical responses of disordered clusters, composites, and rough surfaces: ‘the ninth wave’ effect,” Phys. Rev. Lett. 84, 1011–1014 (2000).
[Crossref] [PubMed]

Phys. Rev. Lett. (9)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987);S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[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]

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

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
[Crossref]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[Crossref] [PubMed]

M. Hübner, J. Kuhl, T. Stroucken, A. Knorr, S. W. Koch, R. Hey, and K. Ploog, “Collective effects of excitons in multiple-quantum-well Bragg and anti-Bragg structures,” Phys. Rev. Lett. 76, 4199–4202 (1996).
[Crossref] [PubMed]

M. Hübner, J. P. Prineas, C. Ell, P. Brick, E. S. Lee, G. Khitrova, H. M. Gibbs, and S. W. Koch, “Optical lattices achieved by excitons in periodic quantum well structures,” Phys. Rev. Lett. 83, 2841–2844 (1999).
[Crossref]

J. M. Deutsch and G. Paladin, “Product of random matrices in a microcanonical ensemble,” Phys. Rev. Lett. 62, 695–699 (1989).
[Crossref] [PubMed]

S. John and J. Wang, “Quantum electrodynamics near a photonic band gap: photon bound states and dressed atoms,” Phys. Rev. Lett. 64, 2418–2421 (1990);“Quantum optics of localized light in a photonic band gap,” Phys. Rev. B 43, 12772–12789 (1991)
[Crossref] [PubMed]

Phys. Solid State (1)

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Phys. Solid State 36, 1156–1161 (1994).

Phys. Status Solidi A (1)

M. R. Singh and W. Lau, “Polariton effective mass and spectral density in III–IV semiconductors doped with an ordered chain of identical two-level atoms,” Phys. Status Solidi A 203, 401–410 (1997).
[Crossref]

Phys. Status Solidi B (1)

L. C. Andreani, “Polaritons in multiple quantum wells,” Phys. Status Solidi B 188, 29–42 (1995).
[Crossref]

Solid State Commun. (1)

D. S. Citrin, “Exciton radiative decay and polaritons in multiquantum wells: quantum-well-to-superlattice crossover,” Solid State Commun. 89, 139–143 (1994).
[Crossref]

Sov. Phys. JETP (1)

I. M. Lifshitz and V. Ya. Kirpichnikov, “Tunnel transparency of disordered systems,” Sov. Phys. JETP 50, 499–511 (1979).

Other (7)

A. A. Maradudin, “Some effects of point defects on the vibrations of crystal Lattices,” in Lattice Dynamics (Benjamin, New York, 1969), pp. 1–52.

A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatova, Theory of Lattice Dynamics in the Harmonic Approximation, 2nd ed. (Academic, New York, 1971).

B. I. Schklovskii and A. L. Efros, Electron Properties of Doped Semiconductors (Springer, New York, 1984).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, Princeton, N.J., 1995).

I. M. Lifshitz and A. M. Kosevich, “The dynamics of a crystal lattice with defects,” in Lattice Dynamics (Benjamin, New York, 1969), pp. 53–90.

D. W. Taylor, “Phonon response theory and the infrared and Raman experiments,” in Optical Properties of Mixed Crystals, R. J. Elliott and I. P. Ipatova, eds. (North-Holland, Amsterdam, 1988), pp. 35–132.

I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988).

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Figures (3)

Fig. 1
Fig. 1

LE for a chain with a defect concentration of 10% (solid curve) in comparison with a pure system (dashed curve).

Fig. 2
Fig. 2

Dependences of LE (solid curve) and DOS (dashed curve) on concentration for a frequency in the interval Ω0<ω<Ω1.

Fig. 3
Fig. 3

Comparison of LE calculated both with (dashed curve) and without (solid curve) spatial dispersion in the vicinity of Ω1. The concentration of defects for both curves is 1%.

Equations (66)

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

(Ωn2-ω2)Pn=αE(xn),
Ωn2=Ω02+ΔΩ2cn,
ω2c2 E(x)+d2Edx2=-4π ω2c2nPnδ(na-x),
vn+1=τ^nvn,
τ^n=cos kasin ka-sin ka+βn(ka)cos kacos ka+βn(ka)sin ka.
 
βn=d2ω2-Ωn2,
ωloc2=Ω12-d2ωloca2cΔΩ2(ωloc2-Ω02)(Ω02+d2-ωloc2),
λ=limL1LlnΠ1Nτ^nv0v0,
1Nτ^n=NpN-11(pN)!pNxpN (τ^0+xτ^1)Nx=0,
1Nτ^n=NpN-112πiCdx νN(x)xpN+1 Dˆ(x),
Dˆ(x)=ν-N(x)(τ^0+xτ^1)N,
λ˜=limN 1Llnlargesteigenvalue1Nτ^n=1a [lnν(x0)-(1-p)ln x0+p ln p+(1-p)ln(1-p)],
 lnν(x) ln xx=x0=p.
λ=Re[λ˜],
N(ω)=-1πIm[λ˜].
ν1+x+1+xν=κ(x)=2 cos(ka)+β0+xβ11+x,
κ(y)=(1-y)ν(y)+1(1-y)ν(y)=κ0(ω)+yF(ω),
κ0(ω)=2 cos(ka)+d2ka sin(ka) 1ω2-Ω02,
F(ω)=d2ka sin(ka) Ω12-Ω02(ω2-Ω02)(ω2-Ω12).
F(ω)2f(ω),
κ0(ω)2+2γ(ω),
f(ω)d2(Ω12-Ω02)(ω2-Ω02)(ω2-Ω12)
γ(ω)=1+d2Ω02-ω2,
λ˜(p)=ln{[1-y0(p)]ν[y0(p)]}-p lny0(p)p+(1-p) ln1-y0(p)1-p,
±y(1-y)F(κ0+yF)2-4+yy=y0=p.
λ˜(ω)=1aln12κ0+y0F±y0(1-y0)Fp-y0-p lny0p+(1-p)ln1-y01-p,
y03F[F(1-p)+κ0]+y02[κ0F(1-3p)+k02-4]
+y0κ0(F-2κ02+4)+p(κ02-4)=0.
y=p-p(1-p) f2pf-γ +p(1-p)× 2(pf-γ)f(1-2p)-fp(1-p)8(pf-γ)2 f22,
λ˜(ω)=ωcpf(ω)-γ(ω)-p(1-p)f2(ω)8[pf(ω)-γ(ω)] .
pf(ω)-γ(ω)0.
ωil2=(Ω02+Ω12+d2)-(Ω02+d2-Ω12)2+4d2(Ω12-Ω02)p2,
ωpu2=(Ω02+Ω12+d2)+(Ω02+d2-Ω12)2+4d2(Ω12-Ω02)p2,
 
ωpl2=Ω02,
Ωiu2=Ω12,
Δim2
=(Ω02+d2-Ω12)2+4d2(Ω12-Ω02)p-(Ω02+d2-Ω12)2.
Δim2d2(Ω12-Ω02)pΩ02+d2-Ω12.
Δim2d2(Ω12-Ω02)p.
1p(Ω02+d2-Ω12)24d2(Ω12-Ω02).
λ(ω)=-p(1-p)f28(pf-γ)ωc +O(2),
N(ω)=1πωc|pf-γ|+O(2);
λ(ω)=ωcpf-γ-p(1-p)f28(pf-γ),
N(ω)=0.
N(ω)=(1-p)N02(ω)+pN12(ω),
N(ω)=1πl01+4|γ|ωcpd2 (ω-ωc)+Oω-ωcd2,
ωc2=Ω12-12 Δim2,
ρ(ωc)=4|γ|ωcπl0pd2=2πl0δ,
v=d24πc2|γ|3/2 pcc,
l(ω)=λ(ω)-1=2l0(pl0)1-20γ2p2ω2-ωc2d22.
y=p+Bα,
pf-γ=ζα.
p(1-p)f2ζ+Bf+B=0.
pf-γ=3p2/3(1-p)2/3-f24/32/3,
ω˜il2=Ω12-d2(Ω12-Ω02)d2-(Ω12-Ω02) p1+3a4pl02/3,
ω˜pu2=ΩL2+d2(Ω12-Ω02)d2-(Ω12-Ω02) p1-3a16pl01/3,
λ˜=-p(1-p)f2B 4/3=(pf-γ)+Bf2/3.
ρ(ω)=3πdγl01/21(l0p)1/2ω(ω2-ω˜il2)1/2,
m=9γ2pd2l02=9γ22pc2ωild2.
c˜=cp/9γ2.
λ=12l014pl01/31+12d(γl0)1/2(4l0p)1/6 (ω˜il2-ω2)1/2,
λ=12l014pl01/31-12dγl0(4l0p)1/3 (ω2-ω˜il2),
ρ(ω)=dωp1/2πc(Ω12-ω2)3/2,
ρ(ω)=1πdcω[ω2-ω˜up2(p)]1/2×1+p2d2(Ω12-Ω02)d2-(Ω12-Ω02)2.

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