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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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).

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).

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).

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).

1998 (2)

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

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).

1997 (2)

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).

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

1996 (3)

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).

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).

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).

1995 (3)

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

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

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

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).

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

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).

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).

1989 (1)

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

1988 (1)

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

1987 (2)

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

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

1984 (1)

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

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).

1956 (1)

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

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).

Andreani, L. C.

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

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).

Bartolini, P.

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

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).

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).

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).

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).

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

Dereux, A.

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

Deutsch, J. M.

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

Deych, L. I.

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).

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).

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

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

John, S.

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

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

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).

Kirpichnikov, V. Ya.

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

Knorr, A.

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).

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).

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).

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).

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).

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).

Lagendijk, A.

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

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).

Lambin, P.

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

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).

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).

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).

Lisyansky, A. 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).

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).

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

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).

Lucas, A.

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

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).

Meade, R. D.

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

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).

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).

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).

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).

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).

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).

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).

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).

Righini, R.

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

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).

Stroucken, T.

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