Abstract

We present a nonlocal local-field calculation of optical sum-frequency generation (SFG) in a quantum well (QW) associated with intersubband processes. The QW is positioned inside a microcavity and pumped by a strong light beam as one of the fundamental waves for the SFG. The third-order optical nonlinearity of the QW in connection with the strong field is included in the calculation of the sum-frequency (SF) conversion efficiency. From the microscopic Maxwell–Lorentz equation combined with light-induced linear and third-order nonlinear current densities, we solve the fundamental and SF local fields exactly. In turn we define the conversion efficiency of the SFG. For a GaAs/Al0.4Ga0.6As QW placed between vacuum and a GaAs/AlAs distributed Bragg reflector (DBR) followed by a GaAs prism, we calculate the SF energy reflection spectra for different values of the incident light intensity and the DBR period. The numerical results show that a significant enhancement of the SF conversion efficiency occurs when the DBR period and the input light intensity are optimally chosen. This is attributed to the cavity- and light-induced local-field enhancement in the QW system.

© 1998 Optical Society of America

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  1. M. K. Gurnick and T. A. DeTemple, IEEE J. Quantum Electron. QE-19, 791 (1983).
    [CrossRef]
  2. J. Khurgin, J. Opt. Soc. Am. B 6, 1673 (1989).
    [CrossRef]
  3. C. Lien, Y. Huang, and T.-F. Lei, J. Appl. Phys. 75, 2177 (1994).
    [CrossRef]
  4. A. Liu and O. Keller, Proc. SPIE 2139, 342 (1994).
    [CrossRef]
  5. A. Liu and O. Keller, Phys. Rev. B 49, 13616 (1994).
    [CrossRef]
  6. A. Liu, Opt. Commun. 119, 191 (1995).
    [CrossRef]
  7. M. Zaluzny, Phys. Rev. B 51, 9757 (1995).
    [CrossRef]
  8. M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, and J. S. Harris, Jr., Phys. Rev. Lett. 62, 1041 (1989).
    [CrossRef] [PubMed]
  9. P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
    [CrossRef]
  10. S. J. B. Yoo, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 58, 1724 (1991).
    [CrossRef]
  11. P. Boucaud, F. H. Julien, D. D. Yang, J.-M. Lourtioz, E. Rosencher, and P. Bois, Opt. Lett. 16, 199 (1991).
    [CrossRef] [PubMed]
  12. E. Rosencher and P. Bois, Phys. Rev. B 44, 11315 (1991).
    [CrossRef]
  13. C. Sirtori, F. Capasso, D. L. Sivco, S. N. G. Chu, and A. Y. Cho, Appl. Phys. Lett. 59, 2302 (1991).
    [CrossRef]
  14. Z. Chen, D. Cui, M. Li, C. Jiang, J. Zhou, and G. Yang, Appl. Phys. Lett. 61, 2401 (1992).
    [CrossRef]
  15. C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, Appl. Phys. Lett. 60, 151 (1992).
    [CrossRef]
  16. Z. Chen, M. Li, D. Cui, H. Lu, and G. Yang, Appl. Phys. Lett. 62, 1502 (1993).
    [CrossRef]
  17. F. Capasso, C. Sirtori, and Y. Cho, IEEE J. Quantum Electron. QE-30, 1313 (1994).
    [CrossRef]
  18. W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, Phys. Rev. B 48, 2376 (1993).
    [CrossRef]
  19. J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
    [CrossRef] [PubMed]
  20. C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. 65, 445 (1994).
    [CrossRef]
  21. H. C. Liu, E. Costard, E. Rosencher, and J. Nagle, IEEE J. Quantum Electron. QE-31, 1659 (1995).
    [CrossRef]
  22. A. Neogi, Opt. Commun. 129, 387 (1996).
    [CrossRef]
  23. U. Ekenberg, Phys. Rev. B 40, 7714 (1989).
    [CrossRef]
  24. A. Liu and O. Keller, Phys. Scr. 52, 116 (1995).
    [CrossRef]
  25. M. E. Lazzouni and L. J. Sham, Phys. Rev. B 48, 8948 (1993), and references therein.
    [CrossRef]
  26. O. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976).
    [CrossRef]
  27. A. Liu, Phys. Rev. B 55, 7101 (1997).
    [CrossRef]
  28. P. Yeh, A. Yariv, and C.-S. Hong, J. Opt. Soc. Am. 67, 423 (1977).
    [CrossRef]

1997 (1)

A. Liu, Phys. Rev. B 55, 7101 (1997).
[CrossRef]

1996 (1)

A. Neogi, Opt. Commun. 129, 387 (1996).
[CrossRef]

1995 (4)

A. Liu and O. Keller, Phys. Scr. 52, 116 (1995).
[CrossRef]

H. C. Liu, E. Costard, E. Rosencher, and J. Nagle, IEEE J. Quantum Electron. QE-31, 1659 (1995).
[CrossRef]

A. Liu, Opt. Commun. 119, 191 (1995).
[CrossRef]

M. Zaluzny, Phys. Rev. B 51, 9757 (1995).
[CrossRef]

1994 (6)

F. Capasso, C. Sirtori, and Y. Cho, IEEE J. Quantum Electron. QE-30, 1313 (1994).
[CrossRef]

C. Lien, Y. Huang, and T.-F. Lei, J. Appl. Phys. 75, 2177 (1994).
[CrossRef]

A. Liu and O. Keller, Proc. SPIE 2139, 342 (1994).
[CrossRef]

A. Liu and O. Keller, Phys. Rev. B 49, 13616 (1994).
[CrossRef]

J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
[CrossRef] [PubMed]

C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. 65, 445 (1994).
[CrossRef]

1993 (3)

M. E. Lazzouni and L. J. Sham, Phys. Rev. B 48, 8948 (1993), and references therein.
[CrossRef]

W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, Phys. Rev. B 48, 2376 (1993).
[CrossRef]

Z. Chen, M. Li, D. Cui, H. Lu, and G. Yang, Appl. Phys. Lett. 62, 1502 (1993).
[CrossRef]

1992 (2)

Z. Chen, D. Cui, M. Li, C. Jiang, J. Zhou, and G. Yang, Appl. Phys. Lett. 61, 2401 (1992).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, Appl. Phys. Lett. 60, 151 (1992).
[CrossRef]

1991 (4)

S. J. B. Yoo, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 58, 1724 (1991).
[CrossRef]

P. Boucaud, F. H. Julien, D. D. Yang, J.-M. Lourtioz, E. Rosencher, and P. Bois, Opt. Lett. 16, 199 (1991).
[CrossRef] [PubMed]

E. Rosencher and P. Bois, Phys. Rev. B 44, 11315 (1991).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, S. N. G. Chu, and A. Y. Cho, Appl. Phys. Lett. 59, 2302 (1991).
[CrossRef]

1990 (1)

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
[CrossRef]

1989 (3)

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, and J. S. Harris, Jr., Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

J. Khurgin, J. Opt. Soc. Am. B 6, 1673 (1989).
[CrossRef]

U. Ekenberg, Phys. Rev. B 40, 7714 (1989).
[CrossRef]

1983 (1)

M. K. Gurnick and T. A. DeTemple, IEEE J. Quantum Electron. QE-19, 791 (1983).
[CrossRef]

1977 (1)

1976 (1)

O. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976).
[CrossRef]

Bewley, W. W.

W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, Phys. Rev. B 48, 2376 (1993).
[CrossRef]

Bois, P.

P. Boucaud, F. H. Julien, D. D. Yang, J.-M. Lourtioz, E. Rosencher, and P. Bois, Opt. Lett. 16, 199 (1991).
[CrossRef] [PubMed]

E. Rosencher and P. Bois, Phys. Rev. B 44, 11315 (1991).
[CrossRef]

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
[CrossRef]

Boucaud, P.

P. Boucaud, F. H. Julien, D. D. Yang, J.-M. Lourtioz, E. Rosencher, and P. Bois, Opt. Lett. 16, 199 (1991).
[CrossRef] [PubMed]

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
[CrossRef]

Byer, R. L.

S. J. B. Yoo, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 58, 1724 (1991).
[CrossRef]

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, and J. S. Harris, Jr., Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Campman, K.

J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
[CrossRef] [PubMed]

Capasso, F.

F. Capasso, C. Sirtori, and Y. Cho, IEEE J. Quantum Electron. QE-30, 1313 (1994).
[CrossRef]

C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. 65, 445 (1994).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, Appl. Phys. Lett. 60, 151 (1992).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, S. N. G. Chu, and A. Y. Cho, Appl. Phys. Lett. 59, 2302 (1991).
[CrossRef]

Chen, Z.

Z. Chen, M. Li, D. Cui, H. Lu, and G. Yang, Appl. Phys. Lett. 62, 1502 (1993).
[CrossRef]

Z. Chen, D. Cui, M. Li, C. Jiang, J. Zhou, and G. Yang, Appl. Phys. Lett. 61, 2401 (1992).
[CrossRef]

Cho, A. Y.

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, Appl. Phys. Lett. 60, 151 (1992).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, S. N. G. Chu, and A. Y. Cho, Appl. Phys. Lett. 59, 2302 (1991).
[CrossRef]

Cho, Y.

F. Capasso, C. Sirtori, and Y. Cho, IEEE J. Quantum Electron. QE-30, 1313 (1994).
[CrossRef]

Chu, S. N. G.

C. Sirtori, F. Capasso, D. L. Sivco, S. N. G. Chu, and A. Y. Cho, Appl. Phys. Lett. 59, 2302 (1991).
[CrossRef]

Costard, E.

H. C. Liu, E. Costard, E. Rosencher, and J. Nagle, IEEE J. Quantum Electron. QE-31, 1659 (1995).
[CrossRef]

Craig, K.

J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
[CrossRef] [PubMed]

Cui, D.

Z. Chen, M. Li, D. Cui, H. Lu, and G. Yang, Appl. Phys. Lett. 62, 1502 (1993).
[CrossRef]

Z. Chen, D. Cui, M. Li, C. Jiang, J. Zhou, and G. Yang, Appl. Phys. Lett. 61, 2401 (1992).
[CrossRef]

DeTemple, T. A.

M. K. Gurnick and T. A. DeTemple, IEEE J. Quantum Electron. QE-19, 791 (1983).
[CrossRef]

Ekenberg, U.

U. Ekenberg, Phys. Rev. B 40, 7714 (1989).
[CrossRef]

Fafard, S.

J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
[CrossRef] [PubMed]

Faist, J.

C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. 65, 445 (1994).
[CrossRef]

Fejer, M. M.

S. J. B. Yoo, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 58, 1724 (1991).
[CrossRef]

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, and J. S. Harris, Jr., Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Felix, C. L.

W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, Phys. Rev. B 48, 2376 (1993).
[CrossRef]

Galdrikian, B.

J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
[CrossRef] [PubMed]

Gossard, A. C.

J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
[CrossRef] [PubMed]

W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, Phys. Rev. B 48, 2376 (1993).
[CrossRef]

Gunnarsson, O.

O. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976).
[CrossRef]

Gurnick, M. K.

M. K. Gurnick and T. A. DeTemple, IEEE J. Quantum Electron. QE-19, 791 (1983).
[CrossRef]

Harris, Jr., J. S.

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, and J. S. Harris, Jr., Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Harwit, A.

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, and J. S. Harris, Jr., Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Heyman, J. N.

J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
[CrossRef] [PubMed]

Hong, C.-S.

Hopkins, P. F.

J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
[CrossRef] [PubMed]

W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, Phys. Rev. B 48, 2376 (1993).
[CrossRef]

Huang, Y.

C. Lien, Y. Huang, and T.-F. Lei, J. Appl. Phys. 75, 2177 (1994).
[CrossRef]

Hutchinson, A. L.

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, Appl. Phys. Lett. 60, 151 (1992).
[CrossRef]

Jiang, C.

Z. Chen, D. Cui, M. Li, C. Jiang, J. Zhou, and G. Yang, Appl. Phys. Lett. 61, 2401 (1992).
[CrossRef]

Julien, F. H.

P. Boucaud, F. H. Julien, D. D. Yang, J.-M. Lourtioz, E. Rosencher, and P. Bois, Opt. Lett. 16, 199 (1991).
[CrossRef] [PubMed]

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
[CrossRef]

Keller, O.

A. Liu and O. Keller, Phys. Scr. 52, 116 (1995).
[CrossRef]

A. Liu and O. Keller, Proc. SPIE 2139, 342 (1994).
[CrossRef]

A. Liu and O. Keller, Phys. Rev. B 49, 13616 (1994).
[CrossRef]

Khurgin, J.

Lazzouni, M. E.

M. E. Lazzouni and L. J. Sham, Phys. Rev. B 48, 8948 (1993), and references therein.
[CrossRef]

Lei, T.-F.

C. Lien, Y. Huang, and T.-F. Lei, J. Appl. Phys. 75, 2177 (1994).
[CrossRef]

Li, M.

Z. Chen, M. Li, D. Cui, H. Lu, and G. Yang, Appl. Phys. Lett. 62, 1502 (1993).
[CrossRef]

Z. Chen, D. Cui, M. Li, C. Jiang, J. Zhou, and G. Yang, Appl. Phys. Lett. 61, 2401 (1992).
[CrossRef]

Lien, C.

C. Lien, Y. Huang, and T.-F. Lei, J. Appl. Phys. 75, 2177 (1994).
[CrossRef]

Liu, A.

A. Liu, Phys. Rev. B 55, 7101 (1997).
[CrossRef]

A. Liu and O. Keller, Phys. Scr. 52, 116 (1995).
[CrossRef]

A. Liu, Opt. Commun. 119, 191 (1995).
[CrossRef]

A. Liu and O. Keller, Phys. Rev. B 49, 13616 (1994).
[CrossRef]

A. Liu and O. Keller, Proc. SPIE 2139, 342 (1994).
[CrossRef]

Liu, H. C.

H. C. Liu, E. Costard, E. Rosencher, and J. Nagle, IEEE J. Quantum Electron. QE-31, 1659 (1995).
[CrossRef]

Lourtioz, J. M.

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
[CrossRef]

Lourtioz, J.-M.

Lu, H.

Z. Chen, M. Li, D. Cui, H. Lu, and G. Yang, Appl. Phys. Lett. 62, 1502 (1993).
[CrossRef]

Lundqvist, B. I.

O. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976).
[CrossRef]

Nagle, J.

H. C. Liu, E. Costard, E. Rosencher, and J. Nagle, IEEE J. Quantum Electron. QE-31, 1659 (1995).
[CrossRef]

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
[CrossRef]

Neogi, A.

A. Neogi, Opt. Commun. 129, 387 (1996).
[CrossRef]

Pfeiffer, L. N.

C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. 65, 445 (1994).
[CrossRef]

Plombon, J. J.

W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, Phys. Rev. B 48, 2376 (1993).
[CrossRef]

Rosencher, E.

H. C. Liu, E. Costard, E. Rosencher, and J. Nagle, IEEE J. Quantum Electron. QE-31, 1659 (1995).
[CrossRef]

P. Boucaud, F. H. Julien, D. D. Yang, J.-M. Lourtioz, E. Rosencher, and P. Bois, Opt. Lett. 16, 199 (1991).
[CrossRef] [PubMed]

E. Rosencher and P. Bois, Phys. Rev. B 44, 11315 (1991).
[CrossRef]

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
[CrossRef]

Sham, L. J.

M. E. Lazzouni and L. J. Sham, Phys. Rev. B 48, 8948 (1993), and references therein.
[CrossRef]

Sherwin, M. S.

J. N. Heyman, K. Craig, B. Galdrikian, M. S. Sherwin, K. Campman, P. F. Hopkins, S. Fafard, and A. C. Gossard, Phys. Rev. Lett. 72, 2183 (1994).
[CrossRef] [PubMed]

W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, Phys. Rev. B 48, 2376 (1993).
[CrossRef]

Sirtori, C.

F. Capasso, C. Sirtori, and Y. Cho, IEEE J. Quantum Electron. QE-30, 1313 (1994).
[CrossRef]

C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. 65, 445 (1994).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, Appl. Phys. Lett. 60, 151 (1992).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, S. N. G. Chu, and A. Y. Cho, Appl. Phys. Lett. 59, 2302 (1991).
[CrossRef]

Sivco, D. L.

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, Appl. Phys. Lett. 60, 151 (1992).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, S. N. G. Chu, and A. Y. Cho, Appl. Phys. Lett. 59, 2302 (1991).
[CrossRef]

Sundaram, M.

W. W. Bewley, C. L. Felix, J. J. Plombon, M. S. Sherwin, M. Sundaram, P. F. Hopkins, and A. C. Gossard, Phys. Rev. B 48, 2376 (1993).
[CrossRef]

West, K. W.

C. Sirtori, F. Capasso, J. Faist, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. 65, 445 (1994).
[CrossRef]

Yang, D. D.

P. Boucaud, F. H. Julien, D. D. Yang, J.-M. Lourtioz, E. Rosencher, and P. Bois, Opt. Lett. 16, 199 (1991).
[CrossRef] [PubMed]

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
[CrossRef]

Yang, G.

Z. Chen, M. Li, D. Cui, H. Lu, and G. Yang, Appl. Phys. Lett. 62, 1502 (1993).
[CrossRef]

Z. Chen, D. Cui, M. Li, C. Jiang, J. Zhou, and G. Yang, Appl. Phys. Lett. 61, 2401 (1992).
[CrossRef]

Yariv, A.

Yeh, P.

Yoo, S. J. B.

S. J. B. Yoo, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 58, 1724 (1991).
[CrossRef]

M. M. Fejer, S. J. B. Yoo, R. L. Byer, A. Harwit, and J. S. Harris, Jr., Phys. Rev. Lett. 62, 1041 (1989).
[CrossRef] [PubMed]

Zaluzny, M.

M. Zaluzny, Phys. Rev. B 51, 9757 (1995).
[CrossRef]

Zhou, J.

Z. Chen, D. Cui, M. Li, C. Jiang, J. Zhou, and G. Yang, Appl. Phys. Lett. 61, 2401 (1992).
[CrossRef]

Appl. Phys. Lett. (7)

P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, P. Bois, and J. Nagle, Appl. Phys. Lett. 57, 3 (1990).
[CrossRef]

S. J. B. Yoo, M. M. Fejer, and R. L. Byer, Appl. Phys. Lett. 58, 1724 (1991).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, S. N. G. Chu, and A. Y. Cho, Appl. Phys. Lett. 59, 2302 (1991).
[CrossRef]

Z. Chen, D. Cui, M. Li, C. Jiang, J. Zhou, and G. Yang, Appl. Phys. Lett. 61, 2401 (1992).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and A. Y. Cho, Appl. Phys. Lett. 60, 151 (1992).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram showing the reflected (generated) SF light (ω3) in a QW-embedded microcavity driven by a strong electromagnetic wave (ω1) and a weak light beam (ω2). The Cartesian xyz coordinate system used in describing the QW structure is also indicated.  

Fig. 2
Fig. 2

SF conversion efficiency of a QW inside a cavity as a function of the frequency ω2 for different values of the DBR period number. The cavity length is Λ=3.2608 μm, and the incident intensity of the ω1 wave is I0=0.

Fig. 3
Fig. 3

SF conversion efficiency of a QW inside a cavity as a function of the frequency ω2 for different values of the input intensity I0. The cavity length is Λ=3.2608 μm, and the period number of the DBR is Nm=4.

Fig. 4
Fig. 4

SF conversion efficiency of a QW inside a cavity as a function of the incident intensity I0 at three different values of the frequency ω2, i.e., ω2=142, 145, 150 meV. The cavity length is Λ=3.2608 μm, and the period number of the DBR is Nm=4.

Equations (48)

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JzNL(ω3, z)=ie3m12*16πω1ω2(m*)3 Φ13(z)×N12ω1N23ω20Δ12dx[(ω3+i/τ)-E31-(m12*/m13*)x][(ω1+i/τ)-E21-x]+N12ω2N23ω10Δ12 dx[(ω3+i/τ)-E31-(m12*/m13*)x][(ω2+i/τ)-E21-x],
Jz(ω3, z)=JzNL(ω3, z)+ie2m13*4πω3(m*)2 N13ω3Φ13(z)ln [(ω3+i/τ)]2-[E31]2[(ω3+i/τ)]2-[E31+Δ13]2+e428πiω3ω12 m12*(m*)4 |N12ω1|2N13ω3Φ13(z)×0Δ12 dx[(ω3+i/τ)-E31-(m12*/m13*)x][(ω1-E21-x)2+(/τ)2],
EijEi-Ej,i=2, 3;j=1, 2,
Δ1i=m1*mi*-1[EF-E1],i=2, 3,
mij*=mi*mj*mi*-mj*,i=1,2;j=2, 3,
Nijωm=QWΦij(z)Ezωm(z)dz,i=1, 2;j=2, 3;
m=1, 2, 3,
Φij(z)=ψi(z) dψj(z)dz-ψj(z) dψi(z)dz,i=1, 2;
j=2, 3.
Jz(ω2, z)=ie2m12*4πω2(m*)2 N12ω2Φ12(z)ln [(ω2+i/τ)]2-[E21]2[(ω2+i/τ)]2-[E21+Δ12]2+e424πiω2ω12 m12*(m*)4 |N12ω1|2N12ω2Φ12(z)×0Δ12 dx[(ω2+i/τ)-E21-x][(ω1-E21-x)2+(/τ)2]+ie428πω2ω12 m12*(m*)4 |N12ω1|2N23ω2Φ23(z)×0Δ12 dx[(ω2+i/τ)-E32-(m12*/m23*)x][(ω1-E21-x)2+(/τ)2].
L(ωi)Eωi(z)=-iμ0ωiezJz(ωi, z),i=1, 2, 3.
L(ωi)=Uε(ωi, z) ωi2c02-q2+2z2-iqex+ez z×iqex+ez z,
η=I0ω3I0I0ω2=2 cos2 θε0c0ε1 |B0ω3|2|A0ω1|2|A0ω2|2,
B0ω3=T12T21-T11T22T12-T11 1-γ(ω3)S13+F(0)1-γ(ω3)D13,13A2+1+γ(ω3)S13-F(0)1-γ(ω3)D13,13B2+q2q R(0)+γ(ω3)SzzF(0)1-γ(ω3)D13,13,
γ(ω3)=μ0e2m13*4π(m*)2 ln [(ω3+i/τ)]2-[E31]2[(ω3+i/τ)]2-[E31+Δ13]2-μ0e428πω12 m12*(m*)4 |N12ω1|2×0Δ12 dx[(ω3+i/τ)-E31-(m12*/m13*)x][(ω1-E21-x)2+(/τ)2],
D13,13=c0ω32 1ε2 aa+d[Φ13(z)]2dz+q22iq2 aa+dΦ13(z)exp(iq2|z-z|)Φ13(z)dzdz,
B2=Y1Y2,
Y1=T12r12-T11T12-T11+T12-T11r12T12-T11 γ(ω3)S13+F(0)1-γ(ω3)D13,13V-q2q T12-T11r12T12-T11 R(0)+γ(ω3)SzzF(0)1-γ(ω3)D13,13,
Y2=T12-T11r12T12-T11 1+γ(ω3)S13-F(0)1-γ(ω3)D13,13-T12r12-T11T12-T11+T12-T11r12T12-T11 γ(ω3)S13+F(0)1-γ(ω3)D13,13U,
U=r23γ(ω3)S13-F(Λ)-exp(-iq2Λ)[1-γ(ω3)D13,13]r23{exp(iq2Λ)[1-γ(ω3)D13,13]+γ(ω3)S13+F(Λ)},
V=q2q R(Λ)[1-γ(ω3)D13,13]+γ(ω3)SzzF(Λ)exp(iq2Λ)[1-γ(ω3)D13,13]+γ(ω3)S13+F(Λ),
A2=UB2+V,
Szz=1iε0ε2ω3 aa+dΦ13(z)JzNL(ω3, z)dz-q22ε0ε2ω3q2 aa+dΦ13(z)×exp(iq2|z-z|)JzNL(ω3, z)dzdz,
R(0)=-q22ε0ε2ω3q2 aa+d exp(iq2z)JzNL(ω3, z)dz,
R(Λ)=-q22ε0ε2ω3q2 exp(iq2Λ)×aa+dexp(-iq2z)JzNL(ω3, z)dz,
F(0)=c0ω32 q2S13+2iε2q2,
F(Λ)=c0ω32 q2S13-2iε2q2 exp(iq2Λ),
T=MNm,
M11=exp(-iq1L1)cos(q4L4)-i2 ε4q1ε1q4+ε1q4ε4q1×sin(q4L4),
M12=exp(iq1L1)-i2 ε4q1ε1q4-ε1q4ε4q1sin(q4L4),
M21=exp(-iq1L1)i2 ε4q1ε1q4-ε1q4ε4q1sin(q4L4),
M22=exp(iq1L1)cos(q4L4)+i2 ε4q1ε1q4+ε1q4ε4q1×sin(q4L4),
N12ω2=N˜12T11-T12rp A0ω2,
N23ω2=N˜23T11-T12rp A0ω2,
rp=r12+r23 exp(2iq2Λ)1+r12r23 exp(2iq2Λ)+α(ω2)N˜12X12+β(ω2)N˜23X23,
rij=qiεj-qjεiqiεj+qjεi,i=1, 2;j=2, 3,
qi=ω2c02εi-q21/2,i=1, 2, 3, 4,
α(ω2)=μ0e2m12*4π(m*)2 ln [(ω2+i/τ)]2-[E21]2[(ω2+i/τ)]2-[E21+Δ12]2-μ0e424πω12 m12*(m*)4 |N12ω1|2×0Δ12 dx[(ω2+i/τ)-E21-x][(ω1-E21-x)2+(/τ)2],
β(ω2)=μ0e428πω12 m12*(m*)4 |N12ω1|2×0Δ12 dx[(ω2+i/τ)-E32-(m12*/m23*)x][(ω1-E21-x)2+(/τ)2],
Xij=-c0ω22 q2iε2 1+r121+r12r23 exp(2iq2Λ)×[Sij++r23 exp(2iq2Λ)Sij-],
Sij±=aa+dΦij(z)exp(±iq2z)dz,
 N˜12=[1-β(ω2)K23,23]W12+β(ω2)K12,23W23[1-α(ω2)K12,12][1-β(ω2)K23,23]-α(ω2)β(ω2)K12,23K23,12,
N˜23=[1-α(ω2)K12,12]W23+α(ω2)K23,12W12[1-α(ω2)K12,12][1-β(ω2)K23,23]-α(ω2)β(ω2)K12,23K23,12,
Wij=-qq2 1-r121+r12r23 exp(2iq2Λ)×[Sij++r23 exp(2iq2Λ)Sij-],
Kij,lm=aa+dΦij(z)Gzz(z, z)Φlm(z)dzdz,
Gzz(z, z)=c0ω22 q22iε2q2 exp(iq2|z-z|)+c0ω22 1ε2 δ(z-z)+c0ω22× q22iε2q2 11+r12r23 exp(2iq2Λ)× {r23 exp(2iq2Λ)×exp[-iq2(z+z)]-r12 exp[iq2(z+z)]-2r12r23× exp(2iq2Λ)cos[q2(z-z)]},
N12ω1=N˜12ω1T11ω1-T12ω1rpω1 A0ω1,
N23ω1=N˜23ω1T11ω1-T12ω1rpω1 A0ω1,

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