Abstract

A theoretical study of the electromagnetic field inside a multiple-quantum-well (MQW) structure possessing a quadratic optical nonlinearity is undertaken. The nonlocal response of each quantum well of the structure is analyzed on the basis of the integral equation for the local field inside the well. The light propagation inside the structure at the fundamental and sum frequencies is described within the generalized transfer-matrix technique. An application of the developed technique to calculation of the optical response of a model MQW structure is demonstrated.

© 2006 Optical Society of America

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  1. O. A. Aktsipetrov, V. N. Golovkina, A. V. Zayats, T. V. Murzina, A. A. Nikulin, and A. A. Fedyanin, "Generation of anisotropic optical second-harmonic in Si:SiO2 superlattices," Phys. Dokl. 40, 12-14 (1995).
  2. O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (1996).
  3. V. V. Savkin, A. A. Fedyanin, F. A. Pudonin, A. N. Rubtsov, and O. A. Aktsipetrov, "Oscillatoric bias dependence of dc-electric field induced second harmonic generation from Si-SiO2 multiple quantum wells," Thin Solid Films 336, 350-353 (1998).
    [CrossRef]
  4. O. A. Aktsipetrov and A. A. Fedyanin, "DC-electric-field-induced second-harmonic generation in Si-SiO2 multiple quantum wells," Thin Solid Films 294, 235-237 (1997).
    [CrossRef]
  5. L. L. Chang, L. Esaki, W. E. Howard, and R. Ludeke, "The growth of GaAs-GaAlAs superlattice," J. Vac. Sci. Technol. 10, 11-16 (1973).
    [CrossRef]
  6. Z.-C. Feng, Semiconductor Interfaces and Microstructures (World Scientific Publishing, l992).
  7. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).
  8. D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
    [CrossRef] [PubMed]
  9. O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).
  10. T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
    [CrossRef]
  11. P. J. Feibelman, "Surface electromagnetic fields," Prog. Surf. Sci. 12, 287-407 (1982).
    [CrossRef]
  12. O. Keller, A. Liu, and A. Zayats, "Characterization of the linear optical properties of multiple quantum well structure in the sheet-model approximation," Opt. Commun. 110, 604-610 (1994).
    [CrossRef]
  13. O. Keller, "Sheet-model description of the linear optical response of quantum wells," J. Opt. Soc. Am. B 12, 987-996 (1995).
    [CrossRef]
  14. O. Keller, "Optical response of a quantum-well sheet: internal electrodynamics," J. Opt. Soc. Am. B 12, 997-1005 (1995).
    [CrossRef]
  15. P. J. Feibelman, "Microscopic calculation of electromagnetic fields in refraction at a jellium-vacuum interface," Phys. Rev. B 12, 1319-1336 (1975).
    [CrossRef]
  16. A. Bagchi, "Transverse dielectric response of a semi-infinite metal: surface effect," Phys. Rev. B 15, 3060-3077 (1977).
    [CrossRef]
  17. A. Liu and O. Keller, "Local-field calculation of the optical diamagnetic response of a metallic quantum well," Phys. Rev. B 49, 2072-2085 (1994).
    [CrossRef]
  18. A. Liu, "Local-field effect on the linear optical intersubband absorption in multiple quantum wells," Phys. Rev. B 50, 8569-8576 (1994).
    [CrossRef]
  19. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, 1970).
  20. D. S. Bethune, "Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques," J. Opt. Soc. Am. B 6, 910-916 (1989).
    [CrossRef]
  21. D. S. Bethune, "Optical harmonic generation and mixing in multilayer media: extension of optical transfer matrix approach to include anisotropic materials," J. Opt. Soc. Am. B 8, 367-373 (1991).
    [CrossRef]
  22. 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]
  23. A. Liu and O. Keller, "Local field study of the optical second-harmonic generation in a symmetric quantum-well structure," Phys. Rev. B 49, 13616-13623 (1994).
    [CrossRef]

2002 (1)

T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
[CrossRef]

1998 (1)

V. V. Savkin, A. A. Fedyanin, F. A. Pudonin, A. N. Rubtsov, and O. A. Aktsipetrov, "Oscillatoric bias dependence of dc-electric field induced second harmonic generation from Si-SiO2 multiple quantum wells," Thin Solid Films 336, 350-353 (1998).
[CrossRef]

1997 (2)

O. A. Aktsipetrov and A. A. Fedyanin, "DC-electric-field-induced second-harmonic generation in Si-SiO2 multiple quantum wells," Thin Solid Films 294, 235-237 (1997).
[CrossRef]

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

1996 (3)

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (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).
[CrossRef]

1995 (3)

O. A. Aktsipetrov, V. N. Golovkina, A. V. Zayats, T. V. Murzina, A. A. Nikulin, and A. A. Fedyanin, "Generation of anisotropic optical second-harmonic in Si:SiO2 superlattices," Phys. Dokl. 40, 12-14 (1995).

O. Keller, "Sheet-model description of the linear optical response of quantum wells," J. Opt. Soc. Am. B 12, 987-996 (1995).
[CrossRef]

O. Keller, "Optical response of a quantum-well sheet: internal electrodynamics," J. Opt. Soc. Am. B 12, 997-1005 (1995).
[CrossRef]

1994 (4)

A. Liu and O. Keller, "Local field study of the optical second-harmonic generation in a symmetric quantum-well structure," Phys. Rev. B 49, 13616-13623 (1994).
[CrossRef]

O. Keller, A. Liu, and A. Zayats, "Characterization of the linear optical properties of multiple quantum well structure in the sheet-model approximation," Opt. Commun. 110, 604-610 (1994).
[CrossRef]

A. Liu and O. Keller, "Local-field calculation of the optical diamagnetic response of a metallic quantum well," Phys. Rev. B 49, 2072-2085 (1994).
[CrossRef]

A. Liu, "Local-field effect on the linear optical intersubband absorption in multiple quantum wells," Phys. Rev. B 50, 8569-8576 (1994).
[CrossRef]

1991 (1)

1989 (1)

1982 (1)

P. J. Feibelman, "Surface electromagnetic fields," Prog. Surf. Sci. 12, 287-407 (1982).
[CrossRef]

1977 (1)

A. Bagchi, "Transverse dielectric response of a semi-infinite metal: surface effect," Phys. Rev. B 15, 3060-3077 (1977).
[CrossRef]

1975 (1)

P. J. Feibelman, "Microscopic calculation of electromagnetic fields in refraction at a jellium-vacuum interface," Phys. Rev. B 12, 1319-1336 (1975).
[CrossRef]

1973 (1)

L. L. Chang, L. Esaki, W. E. Howard, and R. Ludeke, "The growth of GaAs-GaAlAs superlattice," J. Vac. Sci. Technol. 10, 11-16 (1973).
[CrossRef]

Aktsipetrov, O. A.

T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
[CrossRef]

V. V. Savkin, A. A. Fedyanin, F. A. Pudonin, A. N. Rubtsov, and O. A. Aktsipetrov, "Oscillatoric bias dependence of dc-electric field induced second harmonic generation from Si-SiO2 multiple quantum wells," Thin Solid Films 336, 350-353 (1998).
[CrossRef]

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

O. A. Aktsipetrov and A. A. Fedyanin, "DC-electric-field-induced second-harmonic generation in Si-SiO2 multiple quantum wells," Thin Solid Films 294, 235-237 (1997).
[CrossRef]

O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (1996).

O. A. Aktsipetrov, V. N. Golovkina, A. V. Zayats, T. V. Murzina, A. A. Nikulin, and A. A. Fedyanin, "Generation of anisotropic optical second-harmonic in Si:SiO2 superlattices," Phys. Dokl. 40, 12-14 (1995).

Avramenko, V. G.

T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
[CrossRef]

Bagchi, A.

A. Bagchi, "Transverse dielectric response of a semi-infinite metal: surface effect," Phys. Rev. B 15, 3060-3077 (1977).
[CrossRef]

Baribeau, J. M.

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

Bethune, D. S.

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, 1970).

Chang, L. L.

L. L. Chang, L. Esaki, W. E. Howard, and R. Ludeke, "The growth of GaAs-GaAlAs superlattice," J. Vac. Sci. Technol. 10, 11-16 (1973).
[CrossRef]

de Jong, W.

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (1996).

Devillers, M. A. C.

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

Dolgova, T. V.

T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
[CrossRef]

Elyutin, P. V.

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

Esaki, L.

L. L. Chang, L. Esaki, W. E. Howard, and R. Ludeke, "The growth of GaAs-GaAlAs superlattice," J. Vac. Sci. Technol. 10, 11-16 (1973).
[CrossRef]

Fedyanin, A. A.

T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
[CrossRef]

V. V. Savkin, A. A. Fedyanin, F. A. Pudonin, A. N. Rubtsov, and O. A. Aktsipetrov, "Oscillatoric bias dependence of dc-electric field induced second harmonic generation from Si-SiO2 multiple quantum wells," Thin Solid Films 336, 350-353 (1998).
[CrossRef]

O. A. Aktsipetrov and A. A. Fedyanin, "DC-electric-field-induced second-harmonic generation in Si-SiO2 multiple quantum wells," Thin Solid Films 294, 235-237 (1997).
[CrossRef]

O. A. Aktsipetrov, V. N. Golovkina, A. V. Zayats, T. V. Murzina, A. A. Nikulin, and A. A. Fedyanin, "Generation of anisotropic optical second-harmonic in Si:SiO2 superlattices," Phys. Dokl. 40, 12-14 (1995).

Feibelman, P. J.

P. J. Feibelman, "Surface electromagnetic fields," Prog. Surf. Sci. 12, 287-407 (1982).
[CrossRef]

P. J. Feibelman, "Microscopic calculation of electromagnetic fields in refraction at a jellium-vacuum interface," Phys. Rev. B 12, 1319-1336 (1975).
[CrossRef]

Feng, Z.-C.

Z.-C. Feng, Semiconductor Interfaces and Microstructures (World Scientific Publishing, l992).

Golovkina, V. N.

O. A. Aktsipetrov, V. N. Golovkina, A. V. Zayats, T. V. Murzina, A. A. Nikulin, and A. A. Fedyanin, "Generation of anisotropic optical second-harmonic in Si:SiO2 superlattices," Phys. Dokl. 40, 12-14 (1995).

Howard, W. E.

L. L. Chang, L. Esaki, W. E. Howard, and R. Ludeke, "The growth of GaAs-GaAlAs superlattice," J. Vac. Sci. Technol. 10, 11-16 (1973).
[CrossRef]

Joannopoulos, J. D.

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

Keller, O.

O. Keller, "Sheet-model description of the linear optical response of quantum wells," J. Opt. Soc. Am. B 12, 987-996 (1995).
[CrossRef]

O. Keller, "Optical response of a quantum-well sheet: internal electrodynamics," J. Opt. Soc. Am. B 12, 997-1005 (1995).
[CrossRef]

A. Liu and O. Keller, "Local field study of the optical second-harmonic generation in a symmetric quantum-well structure," Phys. Rev. B 49, 13616-13623 (1994).
[CrossRef]

O. Keller, A. Liu, and A. Zayats, "Characterization of the linear optical properties of multiple quantum well structure in the sheet-model approximation," Opt. Commun. 110, 604-610 (1994).
[CrossRef]

A. Liu and O. Keller, "Local-field calculation of the optical diamagnetic response of a metallic quantum well," Phys. Rev. B 49, 2072-2085 (1994).
[CrossRef]

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]

Koch, S. W.

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]

Liu, A.

A. Liu, "Local-field effect on the linear optical intersubband absorption in multiple quantum wells," Phys. Rev. B 50, 8569-8576 (1994).
[CrossRef]

O. Keller, A. Liu, and A. Zayats, "Characterization of the linear optical properties of multiple quantum well structure in the sheet-model approximation," Opt. Commun. 110, 604-610 (1994).
[CrossRef]

A. Liu and O. Keller, "Local field study of the optical second-harmonic generation in a symmetric quantum-well structure," Phys. Rev. B 49, 13616-13623 (1994).
[CrossRef]

A. Liu and O. Keller, "Local-field calculation of the optical diamagnetic response of a metallic quantum well," Phys. Rev. B 49, 2072-2085 (1994).
[CrossRef]

Lockwood, D. J.

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

Lu, Z. H.

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

Ludeke, R.

L. L. Chang, L. Esaki, W. E. Howard, and R. Ludeke, "The growth of GaAs-GaAlAs superlattice," J. Vac. Sci. Technol. 10, 11-16 (1973).
[CrossRef]

Malinnikova, E. V.

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

Marowsky, G.

T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
[CrossRef]

Meade, R. D.

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

Mishina, E. D.

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (1996).

Murzina, T. V.

O. A. Aktsipetrov, V. N. Golovkina, A. V. Zayats, T. V. Murzina, A. A. Nikulin, and A. A. Fedyanin, "Generation of anisotropic optical second-harmonic in Si:SiO2 superlattices," Phys. Dokl. 40, 12-14 (1995).

Nikulin, A. A.

T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
[CrossRef]

O. A. Aktsipetrov, V. N. Golovkina, A. V. Zayats, T. V. Murzina, A. A. Nikulin, and A. A. Fedyanin, "Generation of anisotropic optical second-harmonic in Si:SiO2 superlattices," Phys. Dokl. 40, 12-14 (1995).

Pudonin, F. A.

T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
[CrossRef]

V. V. Savkin, A. A. Fedyanin, F. A. Pudonin, A. N. Rubtsov, and O. A. Aktsipetrov, "Oscillatoric bias dependence of dc-electric field induced second harmonic generation from Si-SiO2 multiple quantum wells," Thin Solid Films 336, 350-353 (1998).
[CrossRef]

Rasing, T.

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (1996).

Rubtsov, A. N.

V. V. Savkin, A. A. Fedyanin, F. A. Pudonin, A. N. Rubtsov, and O. A. Aktsipetrov, "Oscillatoric bias dependence of dc-electric field induced second harmonic generation from Si-SiO2 multiple quantum wells," Thin Solid Films 336, 350-353 (1998).
[CrossRef]

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (1996).

Savkin, V. V.

V. V. Savkin, A. A. Fedyanin, F. A. Pudonin, A. N. Rubtsov, and O. A. Aktsipetrov, "Oscillatoric bias dependence of dc-electric field induced second harmonic generation from Si-SiO2 multiple quantum wells," Thin Solid Films 336, 350-353 (1998).
[CrossRef]

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]

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]

van Hasselt, C. W.

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (1996).

Winn, J. N.

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, 1970).

Zayats, A.

O. Keller, A. Liu, and A. Zayats, "Characterization of the linear optical properties of multiple quantum well structure in the sheet-model approximation," Opt. Commun. 110, 604-610 (1994).
[CrossRef]

Zayats, A. V.

O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (1996).

O. A. Aktsipetrov, V. N. Golovkina, A. V. Zayats, T. V. Murzina, A. A. Nikulin, and A. A. Fedyanin, "Generation of anisotropic optical second-harmonic in Si:SiO2 superlattices," Phys. Dokl. 40, 12-14 (1995).

Appl. Phys. B (1)

T. V. Dolgova, V. G. Avramenko, A. A. Nikulin, G. Marowsky, F. A. Pudonin, A. A. Fedyanin, and O. A. Aktsipetrov, "Second-harmonic spectroscopy of electronic structure of Si/SiO2 multiple quantum well," Appl. Phys. B 74, 671-675 (2002).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Vac. Sci. Technol. (1)

L. L. Chang, L. Esaki, W. E. Howard, and R. Ludeke, "The growth of GaAs-GaAlAs superlattice," J. Vac. Sci. Technol. 10, 11-16 (1973).
[CrossRef]

Opt. Commun. (1)

O. Keller, A. Liu, and A. Zayats, "Characterization of the linear optical properties of multiple quantum well structure in the sheet-model approximation," Opt. Commun. 110, 604-610 (1994).
[CrossRef]

Phys. Dokl. (2)

O. A. Aktsipetrov, P. V. Elyutin, E. V. Malinnikova, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and T. Rasing, "Quantum-size effects for electron states in Si-SiO2 quantum wells and resonant second-harmonic generation spectroscopy," Phys. Dokl. 42, 340-343 (1997).

O. A. Aktsipetrov, V. N. Golovkina, A. V. Zayats, T. V. Murzina, A. A. Nikulin, and A. A. Fedyanin, "Generation of anisotropic optical second-harmonic in Si:SiO2 superlattices," Phys. Dokl. 40, 12-14 (1995).

Phys. Rev. B (6)

P. J. Feibelman, "Microscopic calculation of electromagnetic fields in refraction at a jellium-vacuum interface," Phys. Rev. B 12, 1319-1336 (1975).
[CrossRef]

A. Bagchi, "Transverse dielectric response of a semi-infinite metal: surface effect," Phys. Rev. B 15, 3060-3077 (1977).
[CrossRef]

A. Liu and O. Keller, "Local-field calculation of the optical diamagnetic response of a metallic quantum well," Phys. Rev. B 49, 2072-2085 (1994).
[CrossRef]

A. Liu, "Local-field effect on the linear optical intersubband absorption in multiple quantum wells," Phys. Rev. B 50, 8569-8576 (1994).
[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]

A. Liu and O. Keller, "Local field study of the optical second-harmonic generation in a symmetric quantum-well structure," Phys. Rev. B 49, 13616-13623 (1994).
[CrossRef]

Phys. Rev. Lett. (1)

D. J. Lockwood, Z. H. Lu, and J. M. Baribeau, "Quantum confined luminescence in Si/SiO2 superlattices," Phys. Rev. Lett. 76, 539-541 (1996).
[CrossRef] [PubMed]

Prog. Surf. Sci. (1)

P. J. Feibelman, "Surface electromagnetic fields," Prog. Surf. Sci. 12, 287-407 (1982).
[CrossRef]

Thin Solid Films (2)

V. V. Savkin, A. A. Fedyanin, F. A. Pudonin, A. N. Rubtsov, and O. A. Aktsipetrov, "Oscillatoric bias dependence of dc-electric field induced second harmonic generation from Si-SiO2 multiple quantum wells," Thin Solid Films 336, 350-353 (1998).
[CrossRef]

O. A. Aktsipetrov and A. A. Fedyanin, "DC-electric-field-induced second-harmonic generation in Si-SiO2 multiple quantum wells," Thin Solid Films 294, 235-237 (1997).
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

O. A. Aktsipetrov, A. V. Zayats, E. D. Mishina, A. N. Rubtsov, W. de Jong, C. W. van Hasselt, and T. Rasing, "Resonant second-harmonic generation in periodic Si:SiO2 quantum wells," Zh. Eksp. Teor. Fiz. 109, 1240-1248 (1996).

Other (3)

Z.-C. Feng, Semiconductor Interfaces and Microstructures (World Scientific Publishing, l992).

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

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon Press, 1970).

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Figures (2)

Fig. 1
Fig. 1

Schematics of (a) a typical MQW structure consisting of N QWs and (b) an individual QW. Due to “spill-out” of the electronic density p ( z ) , the nonlocal component of the optical response is nonzero in the crosshatched region that includes the QW layer and the regions of thickness Δ in the host layers.

Fig. 2
Fig. 2

Intensity reflectance spectra of the p-polarized field R p calculated within the frameworks of a few techniques: developed technique (exact solution, solid curve), CSF (dotted curve) and STMT (dashed curve). Dependencies of the peak position of the reflectance spectra ω 0 on the number of QW in the structure are plotted in the inset: the solid curve corresponds to the exact solution, and the dashed curve is calculated with a STMT.

Equations (95)

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E m ( r , t ) = E m ω ( z ) exp [ i m ω ( x sin θ c t ) ] , m = 1 , 2 .
E ω ( z n ) = E ω b ( z n ) i γ m = 1 N G ̂ ω ( n ) σ ̂ ω E ω ( z m ) ,
G ̂ ω ( n ) f ( z m ) = D qw ( m ) G ω ( z n , z m ) f ( z m ) d z m ,
σ ̂ ω E ω ( z m ) = D qw ( m ) σ ω ( z m , z m ) E ω ( z m ) d z m ,
L ̂ z G ω ( z , z ) = U δ ( z z ) ,
L ̂ z = U [ ε ( z ) ω 2 c 2 q x 2 + 2 z 2 ] ( i e x q x + e z z ) ( i e x q x + e z z ) .
E 2 ω b ( z ) = i 2 γ m = 1 N G ̂ 2 ω ( n ) J nl ( z m ) ,
J nl ( z n ) = D qw ( n ) D qw ( n ) Σ 2 ω ( z n , z , z ) : E ω ( n ) ( z ) E ω ( n ) ( z ) d z d z .
E ( ω , z ) = α = s , p [ e + ( α ) E ω ( α ) ( z ) exp ( i q z z ) + e ( α ) E ¯ ω ( α ) ( z ) exp ( i q z z ) ] ,
E ω , α ( m , β ) = E ω ( α ) ( z m , β ) exp ( i q z z m , β ) ,
E ¯ ω , α ( m , β ) = E ¯ ω ( α ) ( z m , β ) exp ( i q z z m , β )
G ω ( z , z ) = G ω ( z , z ) + g ω ( z , z ) ,
ε qw ( z ) = { ε h , z > d 2 ε q , z d 2
L ̂ z G ω ( z , z ) = U δ ( z z ) ,
L ̂ z g ω ( z , z ) = 0 ,
E ω ( z ) = E ω ext ( z ) i γ G ̂ ω σ ̂ E ω ( z ) ,
G ̂ ω f ( z ) = z l z r G ω ( z , z ) f ( z ) d z .
E ext ( z ) = i γ m n G ̂ ω ( n m ) σ ̂ ω E ω ( z m ) i γ g ̂ ω σ ̂ E ω ( z )
L ̂ z E ω ext ( z ) = 0
E ω ext ( z ) = T ̃ ω ext ( z ) E ̃ ω ( n ) ,
E ̃ ω ( n ) = ( E ω , s ( n , l ) E ¯ ω , s ( n , r ) E ω , p ( n , l ) E ¯ ω , p ( n , r ) ) .
Q ω ( z , z ) + i γ T ω ( z , z ) = U δ ( z z ) ,
T ω ( z , z ) = z l z r z l z r G ω ( z , z ) σ ω ( z , z ) Q ω ( z , z ) d z d z .
E ω ( z ) = P ̃ ω ( z ) E ̃ ω ( n ) ,
P ̃ ω ( z ) = z l z r Q ω ( z , z ) T ̃ ω ext ( z ) d z .
E ω ( n , r ) = M ω qw E ω ( n , l ) ,
E ω ( n , β ) = ( E ω , s ( n , β ) E ¯ ω , s ( n , β ) E ω , p ( n , β ) E ¯ ω , p ( n , β ) )
M ω qw = [ M ω qw 0 0 M ω , p qw ] ,
M ω , α qw = 1 κ 4 [ κ 1 κ 4 + κ 2 κ 3 κ 2 κ 3 1 ] ,
E ω ( z ) = P ω ( z ) E ω ( n , l ) ,
[ P ω ( z ) ] i j = [ P ̃ ω ( z ) ] i j + [ P ̃ ω ( z ) ] i 2 [ M ω qw ] 2 j + [ P ̃ ω ( z ) ] i 4 [ M ω qw ] 4 j
[ P ω ( z ) ] i j = [ P ̃ ω ( z ) ] i 2 [ M ω qw ] 2 j + [ P ̃ ω ( z ) ] i 4 [ M ω qw ] 4 j
T ω , s mqw = M ω , s ( s , h ) T ω ( e ) ( M ω , s qw T ω , ( b ) ) N 1 M ω , s qw T ω ( e ) M ω , s ( h , v ) ,
T ω ( e ) = T ω ( h ) ( D Δ ) ,
T ω ( b ) = T ω ( h ) ( D 2 Δ ) ,
r ω , s = [ T ω , s mqw ] 21 [ T ω , s mqw ] 22 .
( E ω , s ( j , l ) E ¯ ω , s ( j , l ) ) = L ω , s ( j ) ( 1 r ω , s ) E ω , s ( v ) ,
L ω , s ( j ) = ( T ω ( b ) M ω , s ( qw ) ) j 1 T ω ( e ) M ω , s ( h , v ) .
E 2 ω ( z ) = T 2 ω nl ( z ) : E ω ( n , l ) E ω ( n , l ) + T ̃ 2 ω ext ( z ) E ̃ 2 ω ( n ) 2 i γ G ̂ 2 ω σ ̂ 2 ω E 2 ω ( z ) ,
T 2 ω nl ( z ) = 2 i γ G ̂ 2 ω Σ ̂ 2 ω ( z ) : P ω P ω ,
Σ ̂ 2 ω ( z ) : P ω P ω = z l z r z l z r Σ 2 ω ( z , z , z ) : P ω ( z ) P ω ( z ) d z d z .
E 2 ω ( z ) = P 2 ω ( nl ) ( z ) : E ω ( n , l ) E ω ( n , l ) + P ̃ 2 ω ( z ) E ̃ 2 ω ( n ) ,
P 2 ω nl ( z ) = z l z r Q 2 ω ( z , z ) T 2 ω nl ( z ) d z .
E 2 ω ( n , r ) = M 2 ω qw E 2 ω ( n , l ) + S 2 ω qw : E ω ( n , l ) E ω ( n , l ) ,
[ S 2 ω qw ] 1 j k = [ P 2 ω nl ( z r ) ] 2 j k μ 1 1 μ 2 [ P 2 ω nl ( z l ) ] 2 j k ,
[ S 2 ω qw ] 2 j k = [ P 2 ω nl ( z r ) ] 2 j k μ 2 ,
[ S 2 ω qw ] 3 j k = [ P 2 ω nl ( z r ) ] 1 j k cos θ h μ 3 1 μ 4 [ P 2 ω nl ( z l ) ] 1 j k ,
[ S 2 ω qw ] 4 j k = [ P 2 ω nl ( z r ) ] 1 j k μ 4 ,
S ̃ ( n ) = S 2 ω qw : E ω ( n ) E ω ( n ) ,
S ( j ) = ( [ S ̃ ( n ) ] 1 [ S ̃ ( n ) ] 2 )
L 2 ω , s ( j ) = M 2 ω , s qw ( T 2 ω ( b ) M 2 ω , s qw ) j 1 T 2 ω ( e ) M 2 ω , s ( h , v ) ,
R 2 ω , s ( j ) = [ M 2 ω , s s , h T 2 ω ( e ) ( M 2 ω , s qw T 2 ω ( b ) ) N j ] 1 .
( E 2 ω , s ( s , j ) E ¯ 2 ω , s ( v , j ) ) = K 2 ω , s ( [ L 2 ω , s ( j ) ] 22 [ L 2 ω , s ( j ) ] 12 [ R 2 ω , s ( j ) ] 21 [ R 2 ω , s ( j ) ] 11 ) S ( j ) ,
K 2 ω , s = 1 [ R 2 ω , s ( j ) ] 11 [ L 2 ω , s ( j ) ] 22 [ R 2 ω , s ( j ) ] 21 [ L 2 ω , s ( j ) ] 12 .
E ¯ 2 ω , s ( v ) = j = 1 N E ¯ 2 ω , s ( v , j ) .
[ σ ω ( z , z ) ] x x = [ σ ω ( z , z ) ] y y = Ω ω ( ) ϕ ( z ) ϕ ( z ) ,
[ σ ω ( z , z ) ] z z = Ω ω ( ) Φ ( z ) Φ ( z ) ,
Ω ω ( ) = i e 2 π 2 ω ( ϵ 2 ϵ 1 ) ( ϵ F ϵ 1 ) 2 [ ( ω + i τ ) ] 2 ( ϵ 2 ϵ 1 ) 2 ,
Ω ω ( ) = i e 2 2 π m * ω ( ϵ 2 ϵ 1 ) ( ϵ F ϵ 1 ) [ ( ω + i τ ) ] 2 ( ϵ 2 ϵ 1 ) 2 ,
ϕ ( z ) = φ 1 ( z ) φ 2 ( z ) ,
Φ ( z ) = φ 1 ( z ) φ 2 ( z ) z φ 2 ( z ) φ 1 ( z ) z ,
J sh ( ω ) = d ¯ 2 d ¯ 2 σ ω ( z , z ) E ω ( z ) d z d z = S sh ( ω ) E ω ( d ¯ 2 ) ,
G ω ( z , z ) = c 2 ω 2 ε q δ ( z z ) e z e z ,
E ω ext ( z ) = E ω ( d ̃ 2 ) .
S x x sh ( ω ) = S y y sh ( ω ) = Ω ω ( ) [ d ̃ 2 d ̃ 2 ϕ ( z ) d z ] 2 ,
S z z sh ( ω ) = Ω ω ( ) [ d ̃ 2 d ̃ 2 Φ ( z ) d z ] 2 1 + i ( 4 π ε q ω ) Ω ω ( ) d ̃ 2 d ̃ 2 Φ 2 ( z ) d z ,
M ω , s qw = U + i q ω d ̃ U ¯ + 2 π ω S y y sh q ω c 2 [ 1 1 1 1 ] ,
M ω , p qw = U + i q ω d ̃ U ¯ + 2 π q ω S x x sh ω [ 1 1 1 1 ] + 2 π q x 2 S z z sh ω q ω [ 1 1 1 1 ] ,
U ¯ = [ 1 0 0 1 ]
ε ̃ x x ( ω ) = ε ̃ y y ( ω ) = ε q + i 4 π ω d ̃ Ω ω ( ) [ d ¯ 2 d ̃ 2 ϕ ( z ) d z ] 2 ,
ε ̃ z z ( ω ) = ε q + i 4 π ω d ̃ Ω ω ( ) [ d ¯ 2 d ̃ 2 Φ ( z ) d z ] 2
1 + i 4 π ω 0 Ω ω 0 ( ) d ¯ 2 d ̃ 2 Φ 2 ( z ) d z = 0 ,
1 + i 4 π ω ̃ 0 d ̃ Ω ω ̃ 0 ( ) [ d ̃ 2 d ¯ 2 Φ ( z ) d z ] 2 = 0 .
d 2 d 2 J nl ( z ) d z = d 2 d 2 d 2 d 2 d 2 d 2 Σ 2 ω ( z , z , z ) : E ω ( z ) E ω ( z ) d z d z d z = 0 ,
E ω 3 ( n , r ) = M ω 3 qw E ω 3 ( n , l ) + S ω 3 , ω 1 , ω 2 qw : E ω 1 ( n , l ) E ω 2 ( n , l ) ,
E m ω ( n , r ) = M m ω qw E m ω ( n , l ) + S m ω qw : [ E ω ( n , l ) ] m ,
( E ω , α ( i ) E ¯ ω , α ( i ) ) = M ω , α ( i , j ) ( E ω , α ( i ) E ¯ ω , α ( j ) ) ,
M ω , α ( i , j ) = 1 t ω , α ( i , j ) [ 1 r ω , α ( i , j ) r ω , α ( i , j ) 1 ] ,
( E ω , α ( j ) ( z + δ z ) E ¯ ω , α ( j ) ( z + δ z ) ) = T ω ( j ) ( δ z ) ( E ω , α ( j ) ( z ) E ¯ ω , α ( j ) ( z ) ) ,
T ω ( j ) ( δ z ) = [ exp ( i q ω ( j ) δ z ) 0 0 exp ( i q ω ( j ) δ z ) ] ,
L ω ( α ) ( z ) = [ [ T ω ( h ) ( z + 0.5 d + Δ ) ] 1 , z < 0.5 d [ T ω ( q ) ( z + 0.5 d ) M ω , α ( 1 , 1 ) ] 1 , z 0.5 d [ T ω ( h ) ( z 0.5 d ) M ω , α ( 1 , 2 ) ] 1 , z > 0.5 d ] ,
M ω , α ( 1 , 1 ) = M ω , α ( q , h ) T ω , α ( h ) ( Δ ) ,
M ω , α ( 1 , 2 ) = M ω , α ( h , q ) T ω ( q ) ( d ) M ω , α ( q , h ) T ω ( h ) Δ ,
R ω ( α ) ( z ) = [ M ω , α ( 2 , 1 ) T ω ( h ) ( 0.5 d z ) , z < 0.5 d M ω , α ( 2 , 2 ) T ω ( h ) ( 0.5 d z ) , z 0.5 d T ω ( h ) ( 0.5 d + Δ z ) , z > 0.5 d ] ,
M ω , α ( 2 , 1 ) = T ω ( h ) ( Δ ) M ω , α ( h , q ) T ω ( h ) ( d ) M ω , α ( q , h ) ,
M ω , α ( 2 , 2 ) = T ω ( h ) ( Δ ) M ω , α ( h , q )
E ω ( α ) ( z ) = [ E ω , α ( n , l ) R 22 ( ω , α ) ( z ) E ¯ ω , α ( n , r ) L 12 ( ω , α ) ( z ) ] D ω ( α ) ( z ) ,
E ¯ ω ( α ) ( z ) = [ E ¯ ω , α ( n , r ) L 11 ( ω , α ) ( z ) E ω , α ( n , l ) R 21 ( ω , α ) ( z ) ] D ω ( α ) ( z ) ,
D ω ( α ) ( z ) = 1 L 11 ( ω , α ) ( z ) R 22 ( ω , α ) ( z ) L 12 ( ω , α ) ( z ) R 21 ( ω , α ) ( z ) ,
[ T ̃ ω ext ( z ) ] 13 = cos θ h [ R 22 ( ω , p ) ( z ) R 21 ( ω , p ) ( z ) ] D ω ( p ) ( z ) ,
[ T ̃ ω ext ( z ) ] 14 = cos θ h [ L 11 ( ω , p ) ( z ) L 12 ( ω , p ) ( z ) ] D ω ( p ) ( z ) ,
[ T ̃ ω ext ( z ) ] 33 = sin θ h [ R 21 ( ω , p ) ( z ) R 22 ( ω , p ) ( z ) ] D ω ( p ) ( z ) ,
[ T ̃ ω ext ( z ) ] 34 = sin θ h [ L 11 ( ω , p ) ( z ) + L 12 ( ω , p ) ( z ) ] D ω ( p ) ( z ) ,
[ T ̃ ω ext ( z ) ] 21 = [ R 22 ( ω , s ) ( z ) R 21 ( ω , s ) ( z ) ] D ω ( s ) ( z ) ,
[ T ̃ ω ext ( z ) ] 22 = [ L 11 ( ω , s ) ( z ) L 12 ( ω , s ) ( z ) ] D ω ( s ) ( z ) ,

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