Abstract

We have studied theoretically the optical properties of microcavities with multiple quantum wells in the central layer. The calculations have been performed both numerically, on the basis of the transfer-matrix method, and analytically, in the classical electrodynamic approach. Special attention has been paid to resonant Bragg multiple quantum wells sandwiched between nonresonant distributed Bragg reflectors. In this case the Rabi splitting of the exciton–polariton branches has been shown to increase in proportion to the square root of the well number. We have generalized the theory to calculate oblique-incidence reflection and absorption spectra in microcavities and to describe angle-dependent anticrossing between the photon and the exciton resonances. The fine structure of exciton–polaritons has been analyzed in particular cases for both s- and p-polarized modes.

© 1996 Optical Society of America

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  1. C. Weisbuch, M. Nishioka, A. Ishikava, and Y. Akarawa, “Observation of the coupled exciton –photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992); C. Weisbuch, “Electron vs photon quantinization: physics, applications,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995) pp. 1839–1846.
    [Crossref] [PubMed]
  2. R. Houdré, R. P. Stanley, U. Oesterle, M. Ilegems, and C. Weisbuch, “Room-temperature cavity polaritons in a semiconductor microcavity,” Phys. Rev. B 49, 16761–16763 (1994); R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polariton dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043–2046 (1994); J. Tignon, P. Voisin, C. Delalande, M. Voos, R. Houdré, U. Oesterle, and R. P. Stanley, “From Fermi’s golden rule to the vacuum Rabi splitting: magnetopolaritons in a semiconductor optical microcavity,” Phys. Rev. Lett. 74, 3967–3970 (1995).
    [Crossref] [PubMed]
  3. L. C. Andreani, V. Savona, P. Schwendimann, and A. Quattropani, “Polaritons in high reflectivity microcavities: semi-classical and full quantum treatment of optical properties,” Superlattice Microstruct. 15, 453–458 (1994); V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, “Quantum well excitons in semi-conductor microcavities: unified treatment of weak and strong coupling regimes,” Solid State Commun. 93, 733–739 (1995).
    [Crossref]
  4. L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–649 (1991).
    [Crossref]
  5. E. L. Ivchenko and A. V. Kavokin, “Reflection of light from structures with quantum wells, quantum wires, and quantum dots,” Fiz. Tverd. Tela 34, 1815–1822 (1992) [Sov. Phys. Solid State 34, 968–971 (1992)].
  6. M. A. Kaliteevski and A. V. Kavokin, “Interband and exciton absorption effect on the optical properties of Bragg reflectors,” Fiz. Tverd. Tela 37, 2721–2727 (1995) [Sov. Phys. Solid State 37, 1497–1500 (1995)]; A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microcavities,” Solid State Commun. 95, 859–862 (1995).
    [Crossref]
  7. S. Jorda, “Theory of Rabi splitting in cavity-embedded quantum wells,” Phys. Rev. B 50, 18690–18693 (1990); “Spontaneous emission of quantum well excitons in planar dielectric multilayer cavities,” Solid State Commun. 93, 45–48 (1995).
    [Crossref]
  8. E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Fiz. Tverd. Tela 36, 2118–2129 (1994) [Sov. Phys. Solid State 36, 1156–1161 (1994)]; “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
    [Crossref]
  9. V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
    [Crossref]
  10. A. Wasiela, H. Mariette, Y. M. d’Aubigné, and A. Shen, “Coherence effects in large period multiple quantum wells: giant exciton oscillator strength at Bragg reflection,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995), p. 1201.
  11. H. A. McLeod, Thin-Film Optical Fibers, 2nd ed. (Hilger, Bristol, UK, 1986).
    [Crossref]

1995 (1)

M. A. Kaliteevski and A. V. Kavokin, “Interband and exciton absorption effect on the optical properties of Bragg reflectors,” Fiz. Tverd. Tela 37, 2721–2727 (1995) [Sov. Phys. Solid State 37, 1497–1500 (1995)]; A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microcavities,” Solid State Commun. 95, 859–862 (1995).
[Crossref]

1994 (4)

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Fiz. Tverd. Tela 36, 2118–2129 (1994) [Sov. Phys. Solid State 36, 1156–1161 (1994)]; “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

R. Houdré, R. P. Stanley, U. Oesterle, M. Ilegems, and C. Weisbuch, “Room-temperature cavity polaritons in a semiconductor microcavity,” Phys. Rev. B 49, 16761–16763 (1994); R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polariton dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043–2046 (1994); J. Tignon, P. Voisin, C. Delalande, M. Voos, R. Houdré, U. Oesterle, and R. P. Stanley, “From Fermi’s golden rule to the vacuum Rabi splitting: magnetopolaritons in a semiconductor optical microcavity,” Phys. Rev. Lett. 74, 3967–3970 (1995).
[Crossref] [PubMed]

L. C. Andreani, V. Savona, P. Schwendimann, and A. Quattropani, “Polaritons in high reflectivity microcavities: semi-classical and full quantum treatment of optical properties,” Superlattice Microstruct. 15, 453–458 (1994); V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, “Quantum well excitons in semi-conductor microcavities: unified treatment of weak and strong coupling regimes,” Solid State Commun. 93, 733–739 (1995).
[Crossref]

1992 (2)

C. Weisbuch, M. Nishioka, A. Ishikava, and Y. Akarawa, “Observation of the coupled exciton –photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992); C. Weisbuch, “Electron vs photon quantinization: physics, applications,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995) pp. 1839–1846.
[Crossref] [PubMed]

E. L. Ivchenko and A. V. Kavokin, “Reflection of light from structures with quantum wells, quantum wires, and quantum dots,” Fiz. Tverd. Tela 34, 1815–1822 (1992) [Sov. Phys. Solid State 34, 968–971 (1992)].

1991 (1)

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–649 (1991).
[Crossref]

1990 (1)

S. Jorda, “Theory of Rabi splitting in cavity-embedded quantum wells,” Phys. Rev. B 50, 18690–18693 (1990); “Spontaneous emission of quantum well excitons in planar dielectric multilayer cavities,” Solid State Commun. 93, 45–48 (1995).
[Crossref]

Akarawa, Y.

C. Weisbuch, M. Nishioka, A. Ishikava, and Y. Akarawa, “Observation of the coupled exciton –photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992); C. Weisbuch, “Electron vs photon quantinization: physics, applications,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995) pp. 1839–1846.
[Crossref] [PubMed]

Andreani, L. C.

L. C. Andreani, V. Savona, P. Schwendimann, and A. Quattropani, “Polaritons in high reflectivity microcavities: semi-classical and full quantum treatment of optical properties,” Superlattice Microstruct. 15, 453–458 (1994); V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, “Quantum well excitons in semi-conductor microcavities: unified treatment of weak and strong coupling regimes,” Solid State Commun. 93, 733–739 (1995).
[Crossref]

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–649 (1991).
[Crossref]

Bassani, F.

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–649 (1991).
[Crossref]

d’Aubigné, Y. M.

A. Wasiela, H. Mariette, Y. M. d’Aubigné, and A. Shen, “Coherence effects in large period multiple quantum wells: giant exciton oscillator strength at Bragg reflection,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995), p. 1201.

Göbel, E. O.

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

Hellmann, R.

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

Houdré, R.

R. Houdré, R. P. Stanley, U. Oesterle, M. Ilegems, and C. Weisbuch, “Room-temperature cavity polaritons in a semiconductor microcavity,” Phys. Rev. B 49, 16761–16763 (1994); R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polariton dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043–2046 (1994); J. Tignon, P. Voisin, C. Delalande, M. Voos, R. Houdré, U. Oesterle, and R. P. Stanley, “From Fermi’s golden rule to the vacuum Rabi splitting: magnetopolaritons in a semiconductor optical microcavity,” Phys. Rev. Lett. 74, 3967–3970 (1995).
[Crossref] [PubMed]

Ilegems, M.

R. Houdré, R. P. Stanley, U. Oesterle, M. Ilegems, and C. Weisbuch, “Room-temperature cavity polaritons in a semiconductor microcavity,” Phys. Rev. B 49, 16761–16763 (1994); R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polariton dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043–2046 (1994); J. Tignon, P. Voisin, C. Delalande, M. Voos, R. Houdré, U. Oesterle, and R. P. Stanley, “From Fermi’s golden rule to the vacuum Rabi splitting: magnetopolaritons in a semiconductor optical microcavity,” Phys. Rev. Lett. 74, 3967–3970 (1995).
[Crossref] [PubMed]

Ishikava, A.

C. Weisbuch, M. Nishioka, A. Ishikava, and Y. Akarawa, “Observation of the coupled exciton –photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992); C. Weisbuch, “Electron vs photon quantinization: physics, applications,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995) pp. 1839–1846.
[Crossref] [PubMed]

Ivchenko, E. L.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Fiz. Tverd. Tela 36, 2118–2129 (1994) [Sov. Phys. Solid State 36, 1156–1161 (1994)]; “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

E. L. Ivchenko and A. V. Kavokin, “Reflection of light from structures with quantum wells, quantum wires, and quantum dots,” Fiz. Tverd. Tela 34, 1815–1822 (1992) [Sov. Phys. Solid State 34, 968–971 (1992)].

Jorda, S.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Fiz. Tverd. Tela 36, 2118–2129 (1994) [Sov. Phys. Solid State 36, 1156–1161 (1994)]; “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

S. Jorda, “Theory of Rabi splitting in cavity-embedded quantum wells,” Phys. Rev. B 50, 18690–18693 (1990); “Spontaneous emission of quantum well excitons in planar dielectric multilayer cavities,” Solid State Commun. 93, 45–48 (1995).
[Crossref]

Kaliteevski, M. A.

M. A. Kaliteevski and A. V. Kavokin, “Interband and exciton absorption effect on the optical properties of Bragg reflectors,” Fiz. Tverd. Tela 37, 2721–2727 (1995) [Sov. Phys. Solid State 37, 1497–1500 (1995)]; A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microcavities,” Solid State Commun. 95, 859–862 (1995).
[Crossref]

Kavokin, A. V.

M. A. Kaliteevski and A. V. Kavokin, “Interband and exciton absorption effect on the optical properties of Bragg reflectors,” Fiz. Tverd. Tela 37, 2721–2727 (1995) [Sov. Phys. Solid State 37, 1497–1500 (1995)]; A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microcavities,” Solid State Commun. 95, 859–862 (1995).
[Crossref]

E. L. Ivchenko and A. V. Kavokin, “Reflection of light from structures with quantum wells, quantum wires, and quantum dots,” Fiz. Tverd. Tela 34, 1815–1822 (1992) [Sov. Phys. Solid State 34, 968–971 (1992)].

Kochereshko, V. P.

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

Landwehr, G.

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

Mariette, H.

A. Wasiela, H. Mariette, Y. M. d’Aubigné, and A. Shen, “Coherence effects in large period multiple quantum wells: giant exciton oscillator strength at Bragg reflection,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995), p. 1201.

McLeod, H. A.

H. A. McLeod, Thin-Film Optical Fibers, 2nd ed. (Hilger, Bristol, UK, 1986).
[Crossref]

Nesvizhskii, A. I.

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Fiz. Tverd. Tela 36, 2118–2129 (1994) [Sov. Phys. Solid State 36, 1156–1161 (1994)]; “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

Nishioka, M.

C. Weisbuch, M. Nishioka, A. Ishikava, and Y. Akarawa, “Observation of the coupled exciton –photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992); C. Weisbuch, “Electron vs photon quantinization: physics, applications,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995) pp. 1839–1846.
[Crossref] [PubMed]

Oesterle, U.

R. Houdré, R. P. Stanley, U. Oesterle, M. Ilegems, and C. Weisbuch, “Room-temperature cavity polaritons in a semiconductor microcavity,” Phys. Rev. B 49, 16761–16763 (1994); R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polariton dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043–2046 (1994); J. Tignon, P. Voisin, C. Delalande, M. Voos, R. Houdré, U. Oesterle, and R. P. Stanley, “From Fermi’s golden rule to the vacuum Rabi splitting: magnetopolaritons in a semiconductor optical microcavity,” Phys. Rev. Lett. 74, 3967–3970 (1995).
[Crossref] [PubMed]

Ossau, W.

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

Pozina, G. R.

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

Quattropani, A.

L. C. Andreani, V. Savona, P. Schwendimann, and A. Quattropani, “Polaritons in high reflectivity microcavities: semi-classical and full quantum treatment of optical properties,” Superlattice Microstruct. 15, 453–458 (1994); V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, “Quantum well excitons in semi-conductor microcavities: unified treatment of weak and strong coupling regimes,” Solid State Commun. 93, 733–739 (1995).
[Crossref]

Savona, V.

L. C. Andreani, V. Savona, P. Schwendimann, and A. Quattropani, “Polaritons in high reflectivity microcavities: semi-classical and full quantum treatment of optical properties,” Superlattice Microstruct. 15, 453–458 (1994); V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, “Quantum well excitons in semi-conductor microcavities: unified treatment of weak and strong coupling regimes,” Solid State Commun. 93, 733–739 (1995).
[Crossref]

Schwendimann, P.

L. C. Andreani, V. Savona, P. Schwendimann, and A. Quattropani, “Polaritons in high reflectivity microcavities: semi-classical and full quantum treatment of optical properties,” Superlattice Microstruct. 15, 453–458 (1994); V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, “Quantum well excitons in semi-conductor microcavities: unified treatment of weak and strong coupling regimes,” Solid State Commun. 93, 733–739 (1995).
[Crossref]

Shen, A.

A. Wasiela, H. Mariette, Y. M. d’Aubigné, and A. Shen, “Coherence effects in large period multiple quantum wells: giant exciton oscillator strength at Bragg reflection,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995), p. 1201.

Stanley, R. P.

R. Houdré, R. P. Stanley, U. Oesterle, M. Ilegems, and C. Weisbuch, “Room-temperature cavity polaritons in a semiconductor microcavity,” Phys. Rev. B 49, 16761–16763 (1994); R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polariton dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043–2046 (1994); J. Tignon, P. Voisin, C. Delalande, M. Voos, R. Houdré, U. Oesterle, and R. P. Stanley, “From Fermi’s golden rule to the vacuum Rabi splitting: magnetopolaritons in a semiconductor optical microcavity,” Phys. Rev. Lett. 74, 3967–3970 (1995).
[Crossref] [PubMed]

Tassone, F.

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–649 (1991).
[Crossref]

Waag, A.

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

Wasiela, A.

A. Wasiela, H. Mariette, Y. M. d’Aubigné, and A. Shen, “Coherence effects in large period multiple quantum wells: giant exciton oscillator strength at Bragg reflection,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995), p. 1201.

Weisbuch, C.

R. Houdré, R. P. Stanley, U. Oesterle, M. Ilegems, and C. Weisbuch, “Room-temperature cavity polaritons in a semiconductor microcavity,” Phys. Rev. B 49, 16761–16763 (1994); R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polariton dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043–2046 (1994); J. Tignon, P. Voisin, C. Delalande, M. Voos, R. Houdré, U. Oesterle, and R. P. Stanley, “From Fermi’s golden rule to the vacuum Rabi splitting: magnetopolaritons in a semiconductor optical microcavity,” Phys. Rev. Lett. 74, 3967–3970 (1995).
[Crossref] [PubMed]

C. Weisbuch, M. Nishioka, A. Ishikava, and Y. Akarawa, “Observation of the coupled exciton –photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992); C. Weisbuch, “Electron vs photon quantinization: physics, applications,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995) pp. 1839–1846.
[Crossref] [PubMed]

Yakovlev, D. R.

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

Fiz. Tverd. Tela (3)

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, “Bragg reflection of light from quantum-well structures,” Fiz. Tverd. Tela 36, 2118–2129 (1994) [Sov. Phys. Solid State 36, 1156–1161 (1994)]; “Resonant Bragg reflection from quantum-well structures,” Superlattices Microstruct. 16, 17–20 (1994).
[Crossref]

E. L. Ivchenko and A. V. Kavokin, “Reflection of light from structures with quantum wells, quantum wires, and quantum dots,” Fiz. Tverd. Tela 34, 1815–1822 (1992) [Sov. Phys. Solid State 34, 968–971 (1992)].

M. A. Kaliteevski and A. V. Kavokin, “Interband and exciton absorption effect on the optical properties of Bragg reflectors,” Fiz. Tverd. Tela 37, 2721–2727 (1995) [Sov. Phys. Solid State 37, 1497–1500 (1995)]; A. V. Kavokin and M. A. Kaliteevski, “Excitonic light reflection and absorption in semiconductor microcavities,” Solid State Commun. 95, 859–862 (1995).
[Crossref]

Phys. Rev. B (2)

S. Jorda, “Theory of Rabi splitting in cavity-embedded quantum wells,” Phys. Rev. B 50, 18690–18693 (1990); “Spontaneous emission of quantum well excitons in planar dielectric multilayer cavities,” Solid State Commun. 93, 45–48 (1995).
[Crossref]

R. Houdré, R. P. Stanley, U. Oesterle, M. Ilegems, and C. Weisbuch, “Room-temperature cavity polaritons in a semiconductor microcavity,” Phys. Rev. B 49, 16761–16763 (1994); R. Houdré, C. Weisbuch, R. P. Stanley, U. Oesterle, P. Pellandini, and M. Ilegems, “Measurement of cavity-polariton dispersion curve from angle resolved photoluminescence experiments,” Phys. Rev. Lett. 73, 2043–2046 (1994); J. Tignon, P. Voisin, C. Delalande, M. Voos, R. Houdré, U. Oesterle, and R. P. Stanley, “From Fermi’s golden rule to the vacuum Rabi splitting: magnetopolaritons in a semiconductor optical microcavity,” Phys. Rev. Lett. 74, 3967–3970 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

C. Weisbuch, M. Nishioka, A. Ishikava, and Y. Akarawa, “Observation of the coupled exciton –photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69, 3314–3317 (1992); C. Weisbuch, “Electron vs photon quantinization: physics, applications,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995) pp. 1839–1846.
[Crossref] [PubMed]

Solid State Commun. (1)

L. C. Andreani, F. Tassone, and F. Bassani, “Radiative lifetime of free excitons in quantum wells,” Solid State Commun. 77, 641–649 (1991).
[Crossref]

Superlattice Microstruct. (1)

L. C. Andreani, V. Savona, P. Schwendimann, and A. Quattropani, “Polaritons in high reflectivity microcavities: semi-classical and full quantum treatment of optical properties,” Superlattice Microstruct. 15, 453–458 (1994); V. Savona, L. C. Andreani, P. Schwendimann, and A. Quattropani, “Quantum well excitons in semi-conductor microcavities: unified treatment of weak and strong coupling regimes,” Solid State Commun. 93, 733–739 (1995).
[Crossref]

Superlattices Microstruct. (1)

V. P. Kochereshko, G. R. Pozina, E. L. Ivchenko, D. R. Yakovlev, A. Waag, W. Ossau, G. Landwehr, R. Hellmann, and E. O. Göbel, “Giant exciton resonance reflectance in Bragg MQW structures,” Superlattices Microstruct. 15, 471–473 (1994); D. R. Yakovlev, G. R. Pozina, V. P. Kochereshko, A. Waag, W. Ossau, and G. Landwehr, “Exciton polaritons in quantum-well structures under Bragg light reflection,” Pis’ma Zh. Eksp. Teor. Fiz. 61, 613–616 (1995).
[Crossref]

Other (2)

A. Wasiela, H. Mariette, Y. M. d’Aubigné, and A. Shen, “Coherence effects in large period multiple quantum wells: giant exciton oscillator strength at Bragg reflection,” in Proceedings of the XXII International Conference on Physics of Semiconductors, D. J. Lockwood, ed. (World Scientific, Singapore, 1995), p. 1201.

H. A. McLeod, Thin-Film Optical Fibers, 2nd ed. (Hilger, Bristol, UK, 1986).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Schematic of the structure under study: a, Active region C containing multiple QW’s is sandwiched between two Bragg mirrors made up of two kinds of material, B and C. The structure is grown upon substrate A. b, The symmetrical reference structure, which is more suitable for analytical description.

Fig. 2
Fig. 2

a, Calculated normal-incidence spectra from an empty microcavity (curve 1) and microcavities with one QW (curve 2) and seven resonant Bragg QW’s (curve 3). b, Energy spacing between resonant features in the computed reflection (circles), transmission (triangles), and absorption (squares) spectra versus the number N of resonant Bragg QW’s. The solid curve shows the Rabi splitting calculated from the analytical theory.

Fig. 3
Fig. 3

a, Calculated reflection spectra from a microcavity with seven embedded resonant Bragg QW’s under normal incidence (curve 1) and at oblique incidence angles φ0 = 45° (curve 2) and φ0 = 60° (curve 3) in the s-polarized geometry. b, The resonance energies in the theoretical s-polarized reflection (circles) and absorption (pluses) spectra as a function of the incidence angle. The calculated energies of the exciton –polariton branches are shown by the solid curves.

Fig. 4
Fig. 4

Calculated p-polarized absorption (solid curves) and reflection (dashed curves) spectra near the light-hole exciton resonance frequency in a single QW embedded in the central layer of the reference structure shown in Fig. 1b. The angles of incidence from the semi-finite B layer (AlAs) are a, 31.5° and b, 32°.

Fig. 5
Fig. 5

Energies of exciton –polaritons versus the incidence angle for a symmetrical microcavity with embedded double QW’s. The solid curve shows a real part of the solutions of the dispersion equation, and the circles indicate positions of the resonant features in the computed reflection spectra.

Fig. 6
Fig. 6

Normal-incidence absorption (solid curve) and reflection (dashed curve) spectra from a microcavity that contains two sets of resonant Bragg QW’s, with each set consisting of three wells. The spacing between the leftmost QW of the right-hand set and the rightmost QW of the left-hand set satisfies the quarter-wavelength condition.

Equations (42)

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r m 1 r m 2 ( t 2 r 2 ) exp ( 2 i ψ c ) + ( r m 1 + r m 2 ) r exp ( i ψ c ) 1 = 0 .
ψ c = n c ω c L c cos φ c .
r m 2 ( t 2 r 2 ) exp ( 2 i ψ c ) + 2 r m r exp ( i ψ c ) 1 = 0 .
[ R m r s exp ( i ψ ) 1 ] [ R m r a exp ( i ψ ) 1 ] = 0 ,
n c ω ¯ c L c = N c π , n 1 ω ¯ c a 1 = n 2 ω ¯ c a 2 = π 2 ,
R m 1 4 n ext n c ( n 1 n 2 ) 2 N m , ψ m n c L ¯ c ( ω ω ¯ ) ,
L ¯ = λ ¯ 2 n c n 1 n 2 n 2 n 1 , λ ¯ = 2 π c ω ¯ n c ,
ψ m n c L ¯ c α ( ω β ω ¯ ) ,
α = cos 2 φ 1 cos 2 φ 2 cos φ c , β = n 1 cos φ 1 + n 2 cos φ 2 cos φ 1 cos φ 2 ( n 1 + n 2 ) .
R m exp ( i ψ ) ( 1 ) N c [ 1 + i n c ( L ¯ + L c ) c f R m × ( ω g ω ¯ + i γ c ) ] ,
f = α L ¯ + L c cos φ c L ¯ + L c , g = α β L ¯ + L c α L ¯ + L c cos φ c , γ c = 1 R m R m c n c ( L ¯ + L c ) f .
( ω 0 / c ) n c d = π ,
r ˜ N γ = T 11 r ˜ N 2 γ T 21 T 22 T 12 r ˜ N 2 γ .
T ˆ = 1 t ˜ 1 [ t ˜ 1 2 r ˜ 1 2 r ˜ 1 r ˜ 1 1 ] ,
t ˜ 1 = exp ( i k z d ) t 1 , r ˜ 1 = exp ( i k z d ) r 1 .
R = | r m 1 + r ˜ ( t m 1 t m 1 r m 1 r m 1 ) exp ( i ψ c ) 1 r ˜ r m 1 exp ( i ψ c ) | 2 , T = n A | t m 1 t ˜ exp ( i ψ c / 2 ) 1 r ˜ r m 1 exp ( i ψ c ) | 2 ,
r ˜ = r + ( t 2 r 2 ) r m 2 exp ( i ψ c ) 1 r r m 2 exp ( i ψ c ) , t ˜ = t t m 2 exp ( i ψ c / 2 ) 1 r r m 2 exp ( i ψ c ) ,
r N = exp ( i δ ) i N Γ 0 ω 0 ω i ( Γ + N Γ 0 ) , t N = 1 + exp ( i δ ) r N ,
δ = n c ω c ( l 1 l 2 ) ,
( ω ω ¯ + i γ c ) ( ω ω 0 + i Γ ) = V 2 N eff ,
V 2 = 1 + R m R m c Γ 0 n c ( L ¯ + L c ) , N eff = N 2 [ 1 ( 1 ) N + N c ] .
V N V N eff = V N .
u max ( N Γ 0 | ω 0 ω ± | ) 1 .
r N = exp ( i δ ) sin N k d sin k d i Γ 0 ω 0 ω i Γ , t N = ( 1 + i N Γ 0 ω 0 ω i Γ ) ,
N eff = 1 2 [ N + ( 1 ) N c sin N k d sin k d cos δ ] .
N Γ 0 [ 1 + 1 N eff ( ω 0 ω ¯ 2 V ) 2 ] 1 / 2 V N eff .
E ( z ) = E 0 cos [ k ( z z ¯ ) ] ,
Ψ ˜ μ = i = 1 N C i ( μ ) Ψ i ,
C i ( 1 ) = C 0 cos [ k ( z i z ˜ ) ] , C 0 = [ i cos 2 k ( z i z ¯ ) ] 1 / 2 ,
i C i ( μ ) * C 0 cos [ k ( z i z ¯ ) ] = δ μ , 1 .
E 0 i C i ( μ ) * cos [ k ( z i z ¯ ) ] = E 0 C 0 δ μ , 1 .
C 0 2 = 1 2 [ N + sin N k d sin k d cos ( 2 k z ¯ δ ) ] .
r 1 = i Γ ˜ 0 ω 0 ω i ( Γ + Γ ˜ 0 ) , t 1 = 1 + r 1 ,
g ( φ 0 ) 1 + s sin 2 φ 0 , s = 1 2 n 2 2 [ 1 + ( n 2 n 1 ) n 2 n 1 2 L ¯ L ¯ + L c ] .
ω ± ω 0 = 1 + s 2 ( sin 2 φ 0 sin 2 φ ¯ 0 ) ± [ s 2 4 ( sin 2 φ 0 sin 2 φ ¯ 0 ) 2 + ( V ω 0 ) 2 N eff ] 1 / 2 .
r 1 p = p 0 p 1 , t 1 p = 1 + p 0 + p 1 ,
p 0 = i Γ ¯ x cos φ c ω 0 ω i ( Γ ¯ x cos φ c + Γ ) , p 1 = i Γ ¯ x ( cos 1 φ c cos φ c ) ω 0 + Δ ω 0 ω i ( Γ ¯ z ( cos 1 φ c cos φ c ) + Γ ] ,
r 2 s = 1 2 i 1 + cos ϕ y + i ( 1 + η ) , r 2 a = 1 + 2 i 1 cos ϕ y + i ( 1 η ) ,
( ω ω m + i γ c ) ( ω ω 0 Γ ˜ 0 sin ϕ + i Γ ) = V 2 1 2 ( 2 + sin 2 ϕ sin ϕ ) .
ω = ω 0 Γ ˜ 0 sin ϕ i Γ 1 R m exp ( i ψ ) 1 + R m exp ( i ψ ) × i Γ ˜ 0 ( 1 cos ϕ ) ,
( ω ω m + i γ c ) ( ω ω 0 + Γ ˜ 0 sin ϕ + i Γ ) = V 2 1 2 ( 2 sin 2 ϕ sin ϕ ) ,
ω = ω 0 + Γ ˜ 0 sin ϕ i Γ 1 + R m exp ( i ψ ) 1 R m exp ( i ψ ) × i Γ ˜ 0 ( 1 + cos ϕ ) .

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