Abstract

A theoretical study of the local field inside a mesoscopic quantum-well film subjected to an externally impressed optical wave is undertaken. In the wake of a discussion of the basic integral equation for the field–field response tensor, the so-called slave and self-field models are investigated, emphasizing the relation to the sheet-conductivity tensor, which, from an experimental point of view, is the basic quantity. The complexity of the local-field electrodynamics is put into perspective in a study of the microscopic paramagnetic response of a two-level quantum-well system. It is demonstrated that, for the two-level sheet, induced currents can flow only perpendicular to the quantum well. I stress that the complexity necessitates the use of few-level quantum wells for a proper comparison of theory and experiment.

© 1995 Optical Society of America

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References

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  1. J. D. E. McIntyre, in Optical Properties of Solids. New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), p. 555.
  2. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  3. P. J. Feibelman, Phys. Rev. B 12, 1319 (1975).
    [CrossRef]
  4. A. Bagchi, Phys. Rev. B 15, 3060 (1977).
    [CrossRef]
  5. P. J. Feibelman, Prog. Surf. Sci. 12, 287 (1982), and references therein.
    [CrossRef]
  6. F. Forstman and R. R. Gerhardts, Metal Optics Near the Plasma Frequency, Vol. 109 of Springer Tracts in Modern Physics (Springer-Verlag, 1986), and references therein.
    [CrossRef]
  7. O. Keller, Phys. Rev. B 38, 8041 (1988).
    [CrossRef]
  8. L. C. West and S. J. Eglash, Appl. Phys. Lett. 46, 1156 (1985).
    [CrossRef]
  9. A. Harwit and J. S. Harris, Jr., Appl. Phys. Lett. 50, 685 (1987).
    [CrossRef]
  10. B. C. Covington, C. C. Lee, B. H. Hu, H. F. Taylor, and D. C. Streit, Appl. Phys. Lett. 54, 2145 (1989).
    [CrossRef]
  11. M. O. Manasreh, F. Szmulowicz, T. Vaughan, K. R. Evans, C. E. Stutz, and D. W. Fischer, Phys. Rev. B 43, 9996 (1991).
    [CrossRef]
  12. A. Liebsch, G. Hincelin, and T. López-Rios, Phys. Rev. B 41, 10463 (1990).
    [CrossRef]
  13. E. V. Alieva, E. I. Firsov, L. A. Kuzik, V. A. Yakovlev, and F. A. Pudonin, Phys. Lett. A 152, 89 (1991).
    [CrossRef]
  14. M. Yamamoto and T. Namioka, Appl. Opt. 31, 1612 (1992).
    [CrossRef] [PubMed]
  15. O. Keller and A. Liu, Phys. Lett. A 167, 301 (1992); 172, 299 (1993).
    [CrossRef]
  16. O. Keller and A. Liu, Phys. Rev. B 49, 2072 (1994).
    [CrossRef]
  17. A. Liu and O. Keller, Phys. Lett. A 177, 441 (1993).
    [CrossRef]
  18. O. Keller and A. Liu, Local-Field Calculation of the Optical Paramagnetic Response inside a Two-Level Quantum Well, Phys. Scr. (to be published).
  19. 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]
  20. L. Tsang, S. L. Chuang, and S. M. Lee, Phys. Rev. B 41, 5942 (1990).
    [CrossRef]
  21. 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]
  22. P. Boucaud, F. H. Julien, D. D. Yang, J. M. Lourtioz, E. Rosencher, and P. Bois, Opt. Lett. 16, 199 (1991).
    [CrossRef] [PubMed]
  23. D. Ahn and S. L. Chuang, IEEE J. Quantum Electron. QE-23, 2196 (1987).
  24. Z. Ikonić, V. Milanović, and D. Tjapkin, IEEE J. Quantum Electron. 25, 54 (1989).
    [CrossRef]
  25. J. T. Lue, K. Y. Lo, and C. C. Tzeng, IEEE J. Quantum Electron. 28, 302 (1992).
    [CrossRef]
  26. A. Liu and O. Keller, in Quantum Well and Superlattice Physics V, G. H. Doehler and E. S. Koteles, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2139, 342 (1994).
    [CrossRef]
  27. A. Liu and O. Keller, Phys. Rev. B 49, 13616 (1994).
    [CrossRef]
  28. O. Keller, Phys. Rev. B 48, 4786 (1993).
    [CrossRef]
  29. A. Bagchi, R. G. Barrera, and A. K. Rajagopal, Phys. Rev. B 20, 4824 (1979).
    [CrossRef]
  30. O. Keller, in Studies in Classical and Quantum Nonlinear Optics, O. Keller, ed. (Nova Science, New York, 1995).
  31. N. Raj and D. R. Tilley, in The Dielectric Function of Condensed Systems, L. V. Keldysh, D. A. Kirzhnitz, and A. A. Maradudin, eds., Vol. 24 of Modern Problems in Condensed Matter Sciences (North-Holland, Amsterdam, 1989), p. 459.
    [CrossRef]
  32. O. Keller, J. Opt. Soc. Am. B 12, 987 (1995).
    [CrossRef]
  33. O. Keller, J. Opt. Soc. Am. B 11, 1480 (1994).
    [CrossRef]
  34. O. Keller, A. Liu, and A. Zayats, Opt. Commun. 110, 604 (1994).
    [CrossRef]

Ahn, D.

D. Ahn and S. L. Chuang, IEEE J. Quantum Electron. QE-23, 2196 (1987).

Alieva, E. V.

E. V. Alieva, E. I. Firsov, L. A. Kuzik, V. A. Yakovlev, and F. A. Pudonin, Phys. Lett. A 152, 89 (1991).
[CrossRef]

Bagchi, A.

A. Bagchi, Phys. Rev. B 15, 3060 (1977).
[CrossRef]

A. Bagchi, R. G. Barrera, and A. K. Rajagopal, Phys. Rev. B 20, 4824 (1979).
[CrossRef]

Barrera, R. G.

A. Bagchi, R. G. Barrera, and A. K. Rajagopal, Phys. Rev. B 20, 4824 (1979).
[CrossRef]

Bois, P.

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]

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

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.

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]

Chuang, S. L.

L. Tsang, S. L. Chuang, and S. M. Lee, Phys. Rev. B 41, 5942 (1990).
[CrossRef]

D. Ahn and S. L. Chuang, IEEE J. Quantum Electron. QE-23, 2196 (1987).

Covington, B. C.

B. C. Covington, C. C. Lee, B. H. Hu, H. F. Taylor, and D. C. Streit, Appl. Phys. Lett. 54, 2145 (1989).
[CrossRef]

Eglash, S. J.

L. C. West and S. J. Eglash, Appl. Phys. Lett. 46, 1156 (1985).
[CrossRef]

Evans, K. R.

M. O. Manasreh, F. Szmulowicz, T. Vaughan, K. R. Evans, C. E. Stutz, and D. W. Fischer, Phys. Rev. B 43, 9996 (1991).
[CrossRef]

Feibelman, P. J.

P. J. Feibelman, Prog. Surf. Sci. 12, 287 (1982), and references therein.
[CrossRef]

P. J. Feibelman, Phys. Rev. B 12, 1319 (1975).
[CrossRef]

Fejer, M. M.

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]

Firsov, E. I.

E. V. Alieva, E. I. Firsov, L. A. Kuzik, V. A. Yakovlev, and F. A. Pudonin, Phys. Lett. A 152, 89 (1991).
[CrossRef]

Fischer, D. W.

M. O. Manasreh, F. Szmulowicz, T. Vaughan, K. R. Evans, C. E. Stutz, and D. W. Fischer, Phys. Rev. B 43, 9996 (1991).
[CrossRef]

Forstman, F.

F. Forstman and R. R. Gerhardts, Metal Optics Near the Plasma Frequency, Vol. 109 of Springer Tracts in Modern Physics (Springer-Verlag, 1986), and references therein.
[CrossRef]

Gerhardts, R. R.

F. Forstman and R. R. Gerhardts, Metal Optics Near the Plasma Frequency, Vol. 109 of Springer Tracts in Modern Physics (Springer-Verlag, 1986), and references therein.
[CrossRef]

Harris, J. S.

A. Harwit and J. S. Harris, Jr., Appl. Phys. Lett. 50, 685 (1987).
[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]

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]

A. Harwit and J. S. Harris, Jr., Appl. Phys. Lett. 50, 685 (1987).
[CrossRef]

Hincelin, G.

A. Liebsch, G. Hincelin, and T. López-Rios, Phys. Rev. B 41, 10463 (1990).
[CrossRef]

Hu, B. H.

B. C. Covington, C. C. Lee, B. H. Hu, H. F. Taylor, and D. C. Streit, Appl. Phys. Lett. 54, 2145 (1989).
[CrossRef]

Ikonic, Z.

Z. Ikonić, V. Milanović, and D. Tjapkin, IEEE J. Quantum Electron. 25, 54 (1989).
[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.

O. Keller and A. Liu, Phys. Rev. B 49, 2072 (1994).
[CrossRef]

A. Liu and O. Keller, Phys. Lett. A 177, 441 (1993).
[CrossRef]

O. Keller and A. Liu, Local-Field Calculation of the Optical Paramagnetic Response inside a Two-Level Quantum Well, Phys. Scr. (to be published).

A. Liu and O. Keller, in Quantum Well and Superlattice Physics V, G. H. Doehler and E. S. Koteles, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2139, 342 (1994).
[CrossRef]

O. Keller, Phys. Rev. B 38, 8041 (1988).
[CrossRef]

O. Keller and A. Liu, Phys. Lett. A 167, 301 (1992); 172, 299 (1993).
[CrossRef]

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

O. Keller, Phys. Rev. B 48, 4786 (1993).
[CrossRef]

O. Keller, J. Opt. Soc. Am. B 12, 987 (1995).
[CrossRef]

O. Keller, J. Opt. Soc. Am. B 11, 1480 (1994).
[CrossRef]

O. Keller, A. Liu, and A. Zayats, Opt. Commun. 110, 604 (1994).
[CrossRef]

O. Keller, in Studies in Classical and Quantum Nonlinear Optics, O. Keller, ed. (Nova Science, New York, 1995).

Kuzik, L. A.

E. V. Alieva, E. I. Firsov, L. A. Kuzik, V. A. Yakovlev, and F. A. Pudonin, Phys. Lett. A 152, 89 (1991).
[CrossRef]

Lee, C. C.

B. C. Covington, C. C. Lee, B. H. Hu, H. F. Taylor, and D. C. Streit, Appl. Phys. Lett. 54, 2145 (1989).
[CrossRef]

Lee, S. M.

L. Tsang, S. L. Chuang, and S. M. Lee, Phys. Rev. B 41, 5942 (1990).
[CrossRef]

Liebsch, A.

A. Liebsch, G. Hincelin, and T. López-Rios, Phys. Rev. B 41, 10463 (1990).
[CrossRef]

Liu, A.

O. Keller and A. Liu, Phys. Lett. A 167, 301 (1992); 172, 299 (1993).
[CrossRef]

O. Keller and A. Liu, Local-Field Calculation of the Optical Paramagnetic Response inside a Two-Level Quantum Well, Phys. Scr. (to be published).

O. Keller and A. Liu, Phys. Rev. B 49, 2072 (1994).
[CrossRef]

A. Liu and O. Keller, Phys. Lett. A 177, 441 (1993).
[CrossRef]

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

A. Liu and O. Keller, in Quantum Well and Superlattice Physics V, G. H. Doehler and E. S. Koteles, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2139, 342 (1994).
[CrossRef]

O. Keller, A. Liu, and A. Zayats, Opt. Commun. 110, 604 (1994).
[CrossRef]

Lo, K. Y.

J. T. Lue, K. Y. Lo, and C. C. Tzeng, IEEE J. Quantum Electron. 28, 302 (1992).
[CrossRef]

López-Rios, T.

A. Liebsch, G. Hincelin, and T. López-Rios, Phys. Rev. B 41, 10463 (1990).
[CrossRef]

Lourtioz, J. M.

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]

Lue, J. T.

J. T. Lue, K. Y. Lo, and C. C. Tzeng, IEEE J. Quantum Electron. 28, 302 (1992).
[CrossRef]

Manasreh, M. O.

M. O. Manasreh, F. Szmulowicz, T. Vaughan, K. R. Evans, C. E. Stutz, and D. W. Fischer, Phys. Rev. B 43, 9996 (1991).
[CrossRef]

McIntyre, J. D. E.

J. D. E. McIntyre, in Optical Properties of Solids. New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), p. 555.

Milanovic, V.

Z. Ikonić, V. Milanović, and D. Tjapkin, IEEE J. Quantum Electron. 25, 54 (1989).
[CrossRef]

Nagle, J.

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]

Namioka, T.

M. Yamamoto and T. Namioka, Appl. Opt. 31, 1612 (1992).
[CrossRef] [PubMed]

Pudonin, F. A.

E. V. Alieva, E. I. Firsov, L. A. Kuzik, V. A. Yakovlev, and F. A. Pudonin, Phys. Lett. A 152, 89 (1991).
[CrossRef]

Raj, N.

N. Raj and D. R. Tilley, in The Dielectric Function of Condensed Systems, L. V. Keldysh, D. A. Kirzhnitz, and A. A. Maradudin, eds., Vol. 24 of Modern Problems in Condensed Matter Sciences (North-Holland, Amsterdam, 1989), p. 459.
[CrossRef]

Rajagopal, A. K.

A. Bagchi, R. G. Barrera, and A. K. Rajagopal, Phys. Rev. B 20, 4824 (1979).
[CrossRef]

Rosencher, E.

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]

Streit, D. C.

B. C. Covington, C. C. Lee, B. H. Hu, H. F. Taylor, and D. C. Streit, Appl. Phys. Lett. 54, 2145 (1989).
[CrossRef]

Stutz, C. E.

M. O. Manasreh, F. Szmulowicz, T. Vaughan, K. R. Evans, C. E. Stutz, and D. W. Fischer, Phys. Rev. B 43, 9996 (1991).
[CrossRef]

Szmulowicz, F.

M. O. Manasreh, F. Szmulowicz, T. Vaughan, K. R. Evans, C. E. Stutz, and D. W. Fischer, Phys. Rev. B 43, 9996 (1991).
[CrossRef]

Taylor, H. F.

B. C. Covington, C. C. Lee, B. H. Hu, H. F. Taylor, and D. C. Streit, Appl. Phys. Lett. 54, 2145 (1989).
[CrossRef]

Tilley, D. R.

N. Raj and D. R. Tilley, in The Dielectric Function of Condensed Systems, L. V. Keldysh, D. A. Kirzhnitz, and A. A. Maradudin, eds., Vol. 24 of Modern Problems in Condensed Matter Sciences (North-Holland, Amsterdam, 1989), p. 459.
[CrossRef]

Tjapkin, D.

Z. Ikonić, V. Milanović, and D. Tjapkin, IEEE J. Quantum Electron. 25, 54 (1989).
[CrossRef]

Tsang, L.

L. Tsang, S. L. Chuang, and S. M. Lee, Phys. Rev. B 41, 5942 (1990).
[CrossRef]

Tzeng, C. C.

J. T. Lue, K. Y. Lo, and C. C. Tzeng, IEEE J. Quantum Electron. 28, 302 (1992).
[CrossRef]

Vaughan, T.

M. O. Manasreh, F. Szmulowicz, T. Vaughan, K. R. Evans, C. E. Stutz, and D. W. Fischer, Phys. Rev. B 43, 9996 (1991).
[CrossRef]

West, L. C.

L. C. West and S. J. Eglash, Appl. Phys. Lett. 46, 1156 (1985).
[CrossRef]

Yakovlev, V. A.

E. V. Alieva, E. I. Firsov, L. A. Kuzik, V. A. Yakovlev, and F. A. Pudonin, Phys. Lett. A 152, 89 (1991).
[CrossRef]

Yamamoto, M.

M. Yamamoto and T. Namioka, Appl. Opt. 31, 1612 (1992).
[CrossRef] [PubMed]

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]

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

Yoo, S. J. B.

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]

Zayats, A.

O. Keller, A. Liu, and A. Zayats, Opt. Commun. 110, 604 (1994).
[CrossRef]

Other (34)

J. D. E. McIntyre, in Optical Properties of Solids. New Developments, B. O. Seraphin, ed. (North-Holland, Amsterdam, 1976), p. 555.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

P. J. Feibelman, Phys. Rev. B 12, 1319 (1975).
[CrossRef]

A. Bagchi, Phys. Rev. B 15, 3060 (1977).
[CrossRef]

P. J. Feibelman, Prog. Surf. Sci. 12, 287 (1982), and references therein.
[CrossRef]

F. Forstman and R. R. Gerhardts, Metal Optics Near the Plasma Frequency, Vol. 109 of Springer Tracts in Modern Physics (Springer-Verlag, 1986), and references therein.
[CrossRef]

O. Keller, Phys. Rev. B 38, 8041 (1988).
[CrossRef]

L. C. West and S. J. Eglash, Appl. Phys. Lett. 46, 1156 (1985).
[CrossRef]

A. Harwit and J. S. Harris, Jr., Appl. Phys. Lett. 50, 685 (1987).
[CrossRef]

B. C. Covington, C. C. Lee, B. H. Hu, H. F. Taylor, and D. C. Streit, Appl. Phys. Lett. 54, 2145 (1989).
[CrossRef]

M. O. Manasreh, F. Szmulowicz, T. Vaughan, K. R. Evans, C. E. Stutz, and D. W. Fischer, Phys. Rev. B 43, 9996 (1991).
[CrossRef]

A. Liebsch, G. Hincelin, and T. López-Rios, Phys. Rev. B 41, 10463 (1990).
[CrossRef]

E. V. Alieva, E. I. Firsov, L. A. Kuzik, V. A. Yakovlev, and F. A. Pudonin, Phys. Lett. A 152, 89 (1991).
[CrossRef]

M. Yamamoto and T. Namioka, Appl. Opt. 31, 1612 (1992).
[CrossRef] [PubMed]

O. Keller and A. Liu, Phys. Lett. A 167, 301 (1992); 172, 299 (1993).
[CrossRef]

O. Keller and A. Liu, Phys. Rev. B 49, 2072 (1994).
[CrossRef]

A. Liu and O. Keller, Phys. Lett. A 177, 441 (1993).
[CrossRef]

O. Keller and A. Liu, Local-Field Calculation of the Optical Paramagnetic Response inside a Two-Level Quantum Well, Phys. Scr. (to be published).

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]

L. Tsang, S. L. Chuang, and S. M. Lee, Phys. Rev. B 41, 5942 (1990).
[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]

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

D. Ahn and S. L. Chuang, IEEE J. Quantum Electron. QE-23, 2196 (1987).

Z. Ikonić, V. Milanović, and D. Tjapkin, IEEE J. Quantum Electron. 25, 54 (1989).
[CrossRef]

J. T. Lue, K. Y. Lo, and C. C. Tzeng, IEEE J. Quantum Electron. 28, 302 (1992).
[CrossRef]

A. Liu and O. Keller, in Quantum Well and Superlattice Physics V, G. H. Doehler and E. S. Koteles, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2139, 342 (1994).
[CrossRef]

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

O. Keller, Phys. Rev. B 48, 4786 (1993).
[CrossRef]

A. Bagchi, R. G. Barrera, and A. K. Rajagopal, Phys. Rev. B 20, 4824 (1979).
[CrossRef]

O. Keller, in Studies in Classical and Quantum Nonlinear Optics, O. Keller, ed. (Nova Science, New York, 1995).

N. Raj and D. R. Tilley, in The Dielectric Function of Condensed Systems, L. V. Keldysh, D. A. Kirzhnitz, and A. A. Maradudin, eds., Vol. 24 of Modern Problems in Condensed Matter Sciences (North-Holland, Amsterdam, 1989), p. 459.
[CrossRef]

O. Keller, J. Opt. Soc. Am. B 12, 987 (1995).
[CrossRef]

O. Keller, J. Opt. Soc. Am. B 11, 1480 (1994).
[CrossRef]

O. Keller, A. Liu, and A. Zayats, Opt. Commun. 110, 604 (1994).
[CrossRef]

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Equations (97)

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

E ( z ) = E B ( z ) + QW K ( z , z ) E ( z ) d z ,
K ( z , z ) = i μ 0 ω QW G B ( z , z ) σ ( z , z ) d z .
E ( z ) = QW Γ ( z , z ) E B ( z ) d z ,
Γ ( z , z ) = U δ ( z z ) + QW K ( z , z ) Γ ( z , z ) d z .
J ( z ) = QW σ B ( z , z ) E B ( z ) d z ,
σ B ( z , z ) = QW σ ( z , z ) Γ ( z , z ) d z
J ( z ) = QW σ ( z , z ) E ( z ) d z
E ( z ) = E B ( z ) i μ 0 ω P B ( z , 0 ) J S ( 0 ) ,
J S ( 0 ) = S ( 0 ) E B ( 0 )
S ( 0 ) = QW N ( z , 0 ) σ B ( z , z ) N ( z , 0 ) d z d z ,
E B ( z ) = N ( z , 0 ) E B ( 0 ) .
E r ( d ) = exp ( 2 i q 0 d ) [ r p ( 0 ) ( e z e z e x e x ) + r s ( 0 ) e y e y ] E i ( d ) ,
r p ( 0 ) = r p ( 0 ) + μ 0 ω 2 q 0 { ( q 0 ) 2 [ 1 r p ( 0 ) ] 2 S x x ( 0 ) q 2 [ 1 + r p ( 0 ) ] 2 S z z ( 0 ) + q q 0 [ 1 r p 2 ( 0 ) ] × [ S z x ( 0 ) S x z ( 0 ) ] } ,
r s ( 0 ) = r s ( 0 ) μ 0 ω 2 q 0 [ 1 + r s ( 0 ) ] 2 S y y ( 0 ) ,
K ( z , z ) = [ K x x ( z , z ) 0 K x z ( z , z ) 0 K y y ( z , z ) 0 K z x ( z , z ) 0 K z z ( z , z ) ] ,
K x x ( z , z ) = i μ 0 ω QW [ G x x B ( z , z ) σ x x ( z , z ) + G x z B ( z , z ) σ z x ( z , z ) ] d z ,
K x z ( z , z ) = i μ 0 ω QW [ G x x B ( z , z ) σ x z ( z , z ) + G x z B ( z , z ) σ z z ( z , z ) ] d z ,
K z x ( z , z ) = i μ 0 ω QW [ G z x B ( z , z ) σ x x ( z , z ) + G z z B ( z , z ) σ z x ( z , z ) ] d z ,
K z z ( z , z ) = i μ 0 ω QW [ G z x B ( z , z ) σ x z ( z , z ) + G z z B ( z , z ) σ z z ( z , z ) ] d z ,
K y y ( z , z ) = i μ 0 ω QW [ G y y B ( z , z ) σ y y ( z , z ) d z ,
Γ x x ( z , z ) = δ ( z z ) + QW [ K x x ( z , z ) Γ x x ( z , z ) + K x z ( z , z ) Γ z x ( z , z ) ] d z ,
Γ z x ( z , z ) = QW [ K z x ( z , z ) Γ x x ( z , z ) + K z z ( z , z ) Γ z x ( z , z ) ] d z ,
Γ x z ( z , z ) = QW [ K x x ( z , z ) Γ x z ( z , z ) + K x z ( z , z ) Γ z z ( z , z ) ] d z ,
Γ z z ( z , z ) = δ ( z z ) + QW [ K z x ( z , z ) Γ x z ( z , z ) + K z z ( z , z ) Γ z z ( z , z ) ] d z ,
Γ y y ( z , z ) = δ ( z z ) + QW K y y ( z , z ) Γ y y ( z , z ) d z .
G B ( z , z ) ( c 0 ω ) 2 δ ( z z ) e z e z .
K ( z , z ) = 1 i ɛ 0 ω [ σ z x ( z , z ) e z e x + σ z z ( z , z ) e z e z ] .
Γ x z ( z , z ) = 0 ,
Γ x x ( z , z ) = Γ y y ( z , z ) = δ ( z z ) .
Γ z x ( z , z ) = 1 i ɛ 0 ω [ σ z x ( z , z ) + QW σ z z ( z , z ) Γ z x ( z , z ) d z ] ,
Γ z x ( z , z ) = δ ( z z ) + 1 i ɛ 0 ω QW σ z z ( z , z ) Γ z z ( z , z ) d z .
σ x x B ( z , z ) = σ x x ( z , z ) + QW σ x z ( z , z ) Γ z x ( z , z ) d z ,
σ x z B ( z , z ) = QW σ x z ( z , z ) Γ z z ( z , z ) d z ,
σ y y B ( z , z ) = σ y y ( z , z ) ,
σ z x B ( z , z ) = σ z x ( z , z ) + QW σ z z ( z , z ) Γ z x ( z , z ) d z ,
σ z z B ( z , z ) = QW σ z z ( z , z ) Γ z z ( z , z ) d z .
S = S ED ED QW σ B ( z , z ) d z d z ,
ɛ z z ( z , z ) = δ ( z z ) + i ɛ 0 ω σ z z ( z , z ) ,
QW ɛ z z ( z , z ) Γ z x ( z , z ) d z = 1 i ɛ 0 ω σ z z ( z , z ) ,
QW ɛ z z ( z , z ) Γ z z ( z , z ) d z = δ ( z z ) .
Γ z z ( z , z ) ɛ z z 1 ( z , z ) .
E x ( z ) = E x B ( z ) ,
E y ( z ) = E y B ( z ) ,
E z ( z ) = QW Γ z z ( z , z ) E z B ( z ) d z .
E z B ( z ) = QW ɛ z z ( z , z ) E z ( z ) d z .
σ x x B ( z , z ) = σ y y B ( z , z ) = σ x x ( z , z ) [ = σ y y ( z , z ) ] ,
σ z z B ( z , z ) = QW σ z z ( z , z ) ɛ z z 1 ( z , z ) d z .
Γ x x ( z , z ) = δ ( z z ) + QW K x x ( z , z ) Γ x x ( z , z ) d z .
QW [ δ ( z z ) K z z ( z , z ) ] Γ z x ( z , z ) d z = QW K z x ( z , z ) Γ x x ( z , z ) d z .
Γ x z ( z , z ) = 0.
Γ z z ( z , z ) = δ ( z z ) + QW K z z ( z , z ) Γ z z ( z , z ) d z .
E x ( z ) = QW Γ x x ( z , z ) E x B ( z ) d z ,
E z ( z ) = QW [ Γ z x ( z , z ) E x B ( z ) + Γ z z ( z , z ) E z B ( z ) ] d z .
E x ( z ) = E x B ( z ) + QW K x x ( z , z ) E x ( z ) d z ,
E z ( z ) = E z B , eff ( z ) + QW K z z ( z , z ) E z ( z ) d z ,
E z B , eff ( z ) = E z B ( z ) + QW K z x ( z , z ) E x ( z ) d z
E x ( z ) = QW [ Γ x x ( z , z ) E x B ( z ) + Γ x z ( z , z ) E z B ( z ) ] d z ,
E z ( z ) = QW Γ z z ( z , z ) E z B ( z ) d z ,
E ( z ) = [ QW Γ ( z , z ) d z ] E B ( 0 ) ,
γ ( z ) QW Γ ( z , z ) d z ,
γ ( z ) = U + QW K ( z , z ) γ ( z ) d z ,
S ED ED = QW σ loc ( z ) γ ( z ) d z ,
σ loc ( z ) = QW σ ( z , z ) d z .
QW Γ 1 ( z , z ) Γ ( z , z ) d z = δ ( z z ) U ,
E B ( z ) = QW Γ 1 ( z , z ) E ( z ) d z .
QW Γ 1 ( z , z ) E RES ( z ) d z = 0 .
Γ 1 ( z , z ) = U δ ( z z ) K ( z , z ) .
σ ( z , z ; q 0 , ω ) = a ( ω ) ( e x e x + e y e y ) ϕ ( z ) ϕ ( z ) + b ( ω ) e z e z Φ ( z ) Φ ( z )
ϕ ( u ) = ψ 1 ( u ) ψ 2 ( u ) , u = z or z ,
Φ ( u ) = ψ 1 ( u ) d ψ 2 ( u ) d u ψ 2 ( u ) d ψ 1 ( u ) d u , u = z or z .
a ( ω ) = i e 2 π 2 ω ( ɛ 2 ɛ 1 ) ( ɛ F ɛ 1 ) 2 [ ( ω + i γ 12 ) ] 2 ( ɛ 2 ɛ 1 ) 2 ,
b ( ω ) = i e 2 2 π m ω ( ɛ 2 ɛ 1 ) ( ɛ F ɛ 1 ) [ ( ω + i γ 12 ) ] 2 ( ɛ 2 ɛ 1 ) 2 ,
F ( z ) i μ 0 ω QW G B ( z , z ) [ ( e x e x + e y e y ) a ( ω ) ϕ ( z ) + e z e z b ( ω ) Φ ( z ) ] d z
Ξ ( z ) = [ e x e x + e y e y ] ϕ ( z ) + e z e z Φ ( z ) .
K ( z , z ) = F ( z ) Ξ ( z ) .
Γ ( z , z ) = U δ ( z z ) + F ( z ) N ( z ) ,
N ( z ) = QW Ξ ( z ) Γ ( z , z ) d z .
N ( z ) = [ U QW Ξ ( z ) F ( z ) d z ] 1 Ξ ( z ) .
Γ ( z , z ) = U δ ( z z ) + F ( z ) [ U QW Ξ ( z ) F ( z ) d z ] 1 Ξ ( z ) .
S ED ED = QW σ ( z , z ) Γ ( z , z ) d z d z d z = QW σ ( z , z ) d z d z + [ QW σ ( z , z ) F ( z ) d z d z ] [ U QW Ξ ( z ) F ( z ) d z ] 1 [ QW Ξ ( z ) d z ] .
QW ϕ ( z ) d z = 0 ,
η E z [ QW F ( z ) Φ ( z ) d z ] [ U QW Ξ ( z ) F ( z ) d z ] 1 e z ,
S ED ED = b ( ω ) ( 1 + η ) e z e z [ QW Φ ( z ) d z ] 2 .
J S = b ( ω ) ( 1 + η ) [ QW Φ ( z ) d z ] 2 E z B ( 0 ) e z .
D z ( 0 + ) D z ( 0 ) = 0 ,
E x ( 0 + ) E x ( 0 ) = 1 ɛ 0 q ω J z S ,
QW [ U δ ( z z ) K ( z , z ) ] E RES ( z ) d z = 0 ,
E RES ( z ) = F ( z ) R ,
R = QW Ξ ( z ) E RES ( z ) d z .
[ U QW Ξ ( z ) F ( z ) d z ] R = 0 .
Det [ U QW Ξ ( z ) F ( z ) d z ] = 0 ,
F ( z ) = b ( ω ) i ɛ 0 ω Φ ( z ) e z e z
QW Ξ ( z ) F ( z ) d z = b ( ω ) i ɛ 0 ω e z e z QW Φ 2 ( z ) d z .
b ( ω ) i ɛ 0 ω QW Φ 2 ( z ) d z = 1 .
S z z ED ED = b ( ω ) [ QW Φ ( z ) d z ] 2 1 [ b ( ω ) / i ɛ 0 ω ] QW Φ 2 ( z ) d z ,
Γ ( z , z ) = U δ ( z z ) + [ b ( ω ) / i ɛ 0 ω ] Φ ( z ) Φ ( z ) 1 [ b ( ω ) / i ɛ 0 ω ] QW Φ 2 ( z ) d z e z e z .
ɛ z z ( z , z ) = Γ z z 1 ( z , z ) = δ ( z z ) + i b ( ω ) ɛ 0 ω Φ ( z ) Φ ( z ) ,

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