Abstract

We study the nonlinear resonant reflection of an intense linearly polarized plane wave from a vacuum-dense two-level-medium interface under normal-incidence conditions. A domain of parameters is specially selected for which one needs to take into account strong atom–field coupling, which results in the appearance of a gap in the spectrum of mixed states (polaritons). For the linear problem, the presence of the gap causes a strong reflection of an incident signal with a frequency within the gap. The near-zone dipole–dipole interaction is also included within the framework of the local-field approach. By performing the time-domain analysis of the reflectivity at different spectral points, we observe certain peculiarities, such as the possibility of a steady-state high-contrast optical switching with low-level operation, stable and unstable hysteresis loops, and an auto-oscillation regime of reflectivity for a certain range of the parameters driving the evolution of the system.

© 1997 Optical Society of America

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  1. F. A. Hopf, C. M. Bowden, and W. H. Louisell, Phys. Rev. A 29, 2591 (1984).
    [CrossRef]
  2. L. Roso-Franco, Phys. Rev. Lett. 55, 2149 (1985).
    [CrossRef] [PubMed]
  3. Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Phys. Rev. A 34, 3917 (1986).
    [CrossRef] [PubMed]
  4. Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Opt. Commun. 61, 147 (1987).
    [CrossRef]
  5. L. Roso-Franco, J. Opt. Soc. Am. B 4, 1878 (1987).
    [CrossRef]
  6. C. R. Stroud, C. M. Bowden, and L. Allen, Opt. Commun. 67, 387 (1988).
    [CrossRef]
  7. M. G. Benedict and E. D. Trifonov, Phys. Rev. A 38, 2854 (1988).
    [CrossRef] [PubMed]
  8. M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 66, 726 (1989) [English translation: Opt. Spectrosc. (USSR) 66, 424 (1989)].
  9. R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 39, 3444 (1989).
    [CrossRef] [PubMed]
  10. L. Roso-Franco and M. Ll. Pons, J. Mod. Opt. 37, 1645 (1990).
    [CrossRef]
  11. M. Ll. Pons and L. Roso-Franco, Opt. Lett. 15, 1230 (1990).
    [CrossRef]
  12. M. Ll. Pons and L. Roso-Franco, Europhys. Lett. 12, 507 (1990).
    [CrossRef]
  13. M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 68, 812 (1990) [English translation: Opt. Spectrosc. (USSR) 68, 473 (1990)].
  14. R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 42, 5573 (1990).
    [CrossRef] [PubMed]
  15. R. Inguva and C. M. Bowden, Phys. Rev. A 41, 1670 (1990).
    [CrossRef] [PubMed]
  16. M. G. Benedict, V. Malyshev, E. D. Trifonov, and A. I. Zaitsev, Phys. Rev. A 43, 3845 (1991).
    [CrossRef] [PubMed]
  17. C. M. Bowden, A. Postan, and R. Inguva, J. Opt. Soc. Am. B 8, 1081 (1991).
    [CrossRef]
  18. M. E. Crenshaw, M. Scalora, and C. M. Bowden, Phys. Rev. Lett. 68, 911 (1992).
    [CrossRef] [PubMed]
  19. M. E. Crenshaw and C. M. Bowden, Phys. Rev. Lett. 69, 3475 (1992).
    [CrossRef] [PubMed]
  20. M. Scalora and C. M. Bowden, Phys. Rev. A 51, 4048 (1995).
    [CrossRef] [PubMed]
  21. V. Malyshev and E. Conejero Jarque, J. Opt. Soc. Am. B 12, 1868 (1995).
    [CrossRef]
  22. R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rep. 7C, 101 (1973).
    [CrossRef]
  23. V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Wiley, New York, 1975).
  24. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford U. Press, London, 1954).
  25. J. J. Hopfield, Phys. Rev. 112, 1555 (1958).
    [CrossRef]
  26. V. M. Agranovich, Zh. Eksp. Teor. Fiz. 37, 430 (1959) [English translation: Sov. Phys. JETP 10, 307 (1960)].
  27. J. W. Haus, L. Wang, M. Scalora, and C. M. Bowden, Phys. Rev. A 38, 4043 (1988).
    [CrossRef] [PubMed]
  28. H. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985).
  29. J. A. Goldstone and E. Garmiere, Phys. Rev. Lett. 53, 910 (1984).
    [CrossRef]
  30. A. S. Davydov, Theory of Molecular Excitons (Plenum, New York, 1971).
  31. A. I. Rashba and M. D. Sturge, eds. Excitons (North-Holland, Amsterdam, 1982).
  32. M. Lindberg, S. W. Koch, and H. Haug, Phys. Rev. A 33, 407 (1986).
    [CrossRef] [PubMed]
  33. A. Knorr, Th. Östereich, K. Schönhammer, R. Binder, and S. W. Koch, Phys. Rev. B 33, 407 (1986).
    [CrossRef]
  34. A. N. Oraevsky, D. J. Jones, and D. K. Bandy, Opt. Commun. 111, 163 (1994).
    [CrossRef]
  35. M. P. Helen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, Phys. Rev. Lett. 73, 1103 (1994).
    [CrossRef]
  36. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 843.

1995 (2)

1994 (2)

A. N. Oraevsky, D. J. Jones, and D. K. Bandy, Opt. Commun. 111, 163 (1994).
[CrossRef]

M. P. Helen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, Phys. Rev. Lett. 73, 1103 (1994).
[CrossRef]

1992 (2)

M. E. Crenshaw, M. Scalora, and C. M. Bowden, Phys. Rev. Lett. 68, 911 (1992).
[CrossRef] [PubMed]

M. E. Crenshaw and C. M. Bowden, Phys. Rev. Lett. 69, 3475 (1992).
[CrossRef] [PubMed]

1991 (2)

M. G. Benedict, V. Malyshev, E. D. Trifonov, and A. I. Zaitsev, Phys. Rev. A 43, 3845 (1991).
[CrossRef] [PubMed]

C. M. Bowden, A. Postan, and R. Inguva, J. Opt. Soc. Am. B 8, 1081 (1991).
[CrossRef]

1990 (6)

L. Roso-Franco and M. Ll. Pons, J. Mod. Opt. 37, 1645 (1990).
[CrossRef]

M. Ll. Pons and L. Roso-Franco, Opt. Lett. 15, 1230 (1990).
[CrossRef]

M. Ll. Pons and L. Roso-Franco, Europhys. Lett. 12, 507 (1990).
[CrossRef]

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 68, 812 (1990) [English translation: Opt. Spectrosc. (USSR) 68, 473 (1990)].

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 42, 5573 (1990).
[CrossRef] [PubMed]

R. Inguva and C. M. Bowden, Phys. Rev. A 41, 1670 (1990).
[CrossRef] [PubMed]

1989 (2)

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 66, 726 (1989) [English translation: Opt. Spectrosc. (USSR) 66, 424 (1989)].

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 39, 3444 (1989).
[CrossRef] [PubMed]

1988 (3)

C. R. Stroud, C. M. Bowden, and L. Allen, Opt. Commun. 67, 387 (1988).
[CrossRef]

M. G. Benedict and E. D. Trifonov, Phys. Rev. A 38, 2854 (1988).
[CrossRef] [PubMed]

J. W. Haus, L. Wang, M. Scalora, and C. M. Bowden, Phys. Rev. A 38, 4043 (1988).
[CrossRef] [PubMed]

1987 (2)

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Opt. Commun. 61, 147 (1987).
[CrossRef]

L. Roso-Franco, J. Opt. Soc. Am. B 4, 1878 (1987).
[CrossRef]

1986 (3)

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Phys. Rev. A 34, 3917 (1986).
[CrossRef] [PubMed]

M. Lindberg, S. W. Koch, and H. Haug, Phys. Rev. A 33, 407 (1986).
[CrossRef] [PubMed]

A. Knorr, Th. Östereich, K. Schönhammer, R. Binder, and S. W. Koch, Phys. Rev. B 33, 407 (1986).
[CrossRef]

1985 (1)

L. Roso-Franco, Phys. Rev. Lett. 55, 2149 (1985).
[CrossRef] [PubMed]

1984 (2)

F. A. Hopf, C. M. Bowden, and W. H. Louisell, Phys. Rev. A 29, 2591 (1984).
[CrossRef]

J. A. Goldstone and E. Garmiere, Phys. Rev. Lett. 53, 910 (1984).
[CrossRef]

1973 (1)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rep. 7C, 101 (1973).
[CrossRef]

1959 (1)

V. M. Agranovich, Zh. Eksp. Teor. Fiz. 37, 430 (1959) [English translation: Sov. Phys. JETP 10, 307 (1960)].

1958 (1)

J. J. Hopfield, Phys. Rev. 112, 1555 (1958).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, Zh. Eksp. Teor. Fiz. 37, 430 (1959) [English translation: Sov. Phys. JETP 10, 307 (1960)].

V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Wiley, New York, 1975).

Allen, L.

C. R. Stroud, C. M. Bowden, and L. Allen, Opt. Commun. 67, 387 (1988).
[CrossRef]

Bandy, D. K.

A. N. Oraevsky, D. J. Jones, and D. K. Bandy, Opt. Commun. 111, 163 (1994).
[CrossRef]

Ben-Aryeh, Y.

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Opt. Commun. 61, 147 (1987).
[CrossRef]

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Phys. Rev. A 34, 3917 (1986).
[CrossRef] [PubMed]

Benedict, M. G.

M. G. Benedict, V. Malyshev, E. D. Trifonov, and A. I. Zaitsev, Phys. Rev. A 43, 3845 (1991).
[CrossRef] [PubMed]

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 68, 812 (1990) [English translation: Opt. Spectrosc. (USSR) 68, 473 (1990)].

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 66, 726 (1989) [English translation: Opt. Spectrosc. (USSR) 66, 424 (1989)].

M. G. Benedict and E. D. Trifonov, Phys. Rev. A 38, 2854 (1988).
[CrossRef] [PubMed]

Binder, R.

A. Knorr, Th. Östereich, K. Schönhammer, R. Binder, and S. W. Koch, Phys. Rev. B 33, 407 (1986).
[CrossRef]

Born, M.

M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford U. Press, London, 1954).

Bowden, C. M.

M. Scalora and C. M. Bowden, Phys. Rev. A 51, 4048 (1995).
[CrossRef] [PubMed]

M. E. Crenshaw and C. M. Bowden, Phys. Rev. Lett. 69, 3475 (1992).
[CrossRef] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, Phys. Rev. Lett. 68, 911 (1992).
[CrossRef] [PubMed]

C. M. Bowden, A. Postan, and R. Inguva, J. Opt. Soc. Am. B 8, 1081 (1991).
[CrossRef]

R. Inguva and C. M. Bowden, Phys. Rev. A 41, 1670 (1990).
[CrossRef] [PubMed]

C. R. Stroud, C. M. Bowden, and L. Allen, Opt. Commun. 67, 387 (1988).
[CrossRef]

J. W. Haus, L. Wang, M. Scalora, and C. M. Bowden, Phys. Rev. A 38, 4043 (1988).
[CrossRef] [PubMed]

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Opt. Commun. 61, 147 (1987).
[CrossRef]

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Phys. Rev. A 34, 3917 (1986).
[CrossRef] [PubMed]

F. A. Hopf, C. M. Bowden, and W. H. Louisell, Phys. Rev. A 29, 2591 (1984).
[CrossRef]

Conejero Jarque, E.

Crenshaw, M. E.

M. E. Crenshaw and C. M. Bowden, Phys. Rev. Lett. 69, 3475 (1992).
[CrossRef] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, Phys. Rev. Lett. 68, 911 (1992).
[CrossRef] [PubMed]

Davydov, A. S.

A. S. Davydov, Theory of Molecular Excitons (Plenum, New York, 1971).

Englund, J. C.

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Opt. Commun. 61, 147 (1987).
[CrossRef]

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Phys. Rev. A 34, 3917 (1986).
[CrossRef] [PubMed]

Feshbach, H.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 843.

Friedberg, R.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 42, 5573 (1990).
[CrossRef] [PubMed]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 39, 3444 (1989).
[CrossRef] [PubMed]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rep. 7C, 101 (1973).
[CrossRef]

Garmiere, E.

J. A. Goldstone and E. Garmiere, Phys. Rev. Lett. 53, 910 (1984).
[CrossRef]

Gibbs, H. H.

H. H. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985).

Ginzburg, V. L.

V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in Crystal Optics and the Theory of Excitons (Wiley, New York, 1975).

Goldstone, J. A.

J. A. Goldstone and E. Garmiere, Phys. Rev. Lett. 53, 910 (1984).
[CrossRef]

Güdel, H. U.

M. P. Helen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, Phys. Rev. Lett. 73, 1103 (1994).
[CrossRef]

Hartmann, S. R.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 42, 5573 (1990).
[CrossRef] [PubMed]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 39, 3444 (1989).
[CrossRef] [PubMed]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rep. 7C, 101 (1973).
[CrossRef]

Haug, H.

M. Lindberg, S. W. Koch, and H. Haug, Phys. Rev. A 33, 407 (1986).
[CrossRef] [PubMed]

Haus, J. W.

J. W. Haus, L. Wang, M. Scalora, and C. M. Bowden, Phys. Rev. A 38, 4043 (1988).
[CrossRef] [PubMed]

Helen, M. P.

M. P. Helen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, Phys. Rev. Lett. 73, 1103 (1994).
[CrossRef]

Hopf, F. A.

F. A. Hopf, C. M. Bowden, and W. H. Louisell, Phys. Rev. A 29, 2591 (1984).
[CrossRef]

Hopfield, J. J.

J. J. Hopfield, Phys. Rev. 112, 1555 (1958).
[CrossRef]

Huang, K.

M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Oxford U. Press, London, 1954).

Inguva, R.

Jones, D. J.

A. N. Oraevsky, D. J. Jones, and D. K. Bandy, Opt. Commun. 111, 163 (1994).
[CrossRef]

Knorr, A.

A. Knorr, Th. Östereich, K. Schönhammer, R. Binder, and S. W. Koch, Phys. Rev. B 33, 407 (1986).
[CrossRef]

Koch, S. W.

M. Lindberg, S. W. Koch, and H. Haug, Phys. Rev. A 33, 407 (1986).
[CrossRef] [PubMed]

A. Knorr, Th. Östereich, K. Schönhammer, R. Binder, and S. W. Koch, Phys. Rev. B 33, 407 (1986).
[CrossRef]

Lindberg, M.

M. Lindberg, S. W. Koch, and H. Haug, Phys. Rev. A 33, 407 (1986).
[CrossRef] [PubMed]

Louisell, W. H.

F. A. Hopf, C. M. Bowden, and W. H. Louisell, Phys. Rev. A 29, 2591 (1984).
[CrossRef]

Malyshev, V.

V. Malyshev and E. Conejero Jarque, J. Opt. Soc. Am. B 12, 1868 (1995).
[CrossRef]

M. G. Benedict, V. Malyshev, E. D. Trifonov, and A. I. Zaitsev, Phys. Rev. A 43, 3845 (1991).
[CrossRef] [PubMed]

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 68, 812 (1990) [English translation: Opt. Spectrosc. (USSR) 68, 473 (1990)].

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 66, 726 (1989) [English translation: Opt. Spectrosc. (USSR) 66, 424 (1989)].

Manassah, J. T.

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 42, 5573 (1990).
[CrossRef] [PubMed]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 39, 3444 (1989).
[CrossRef] [PubMed]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rep. 7C, 101 (1973).
[CrossRef]

Morse, P. M.

P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 843.

Oraevsky, A. N.

A. N. Oraevsky, D. J. Jones, and D. K. Bandy, Opt. Commun. 111, 163 (1994).
[CrossRef]

Östereich, Th.

A. Knorr, Th. Östereich, K. Schönhammer, R. Binder, and S. W. Koch, Phys. Rev. B 33, 407 (1986).
[CrossRef]

Pons, M. Ll.

L. Roso-Franco and M. Ll. Pons, J. Mod. Opt. 37, 1645 (1990).
[CrossRef]

M. Ll. Pons and L. Roso-Franco, Europhys. Lett. 12, 507 (1990).
[CrossRef]

M. Ll. Pons and L. Roso-Franco, Opt. Lett. 15, 1230 (1990).
[CrossRef]

Postan, A.

Rai, J.

M. P. Helen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, Phys. Rev. Lett. 73, 1103 (1994).
[CrossRef]

Rai, S.

M. P. Helen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, Phys. Rev. Lett. 73, 1103 (1994).
[CrossRef]

Rand, S. C.

M. P. Helen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, Phys. Rev. Lett. 73, 1103 (1994).
[CrossRef]

Roso-Franco, L.

M. Ll. Pons and L. Roso-Franco, Europhys. Lett. 12, 507 (1990).
[CrossRef]

L. Roso-Franco and M. Ll. Pons, J. Mod. Opt. 37, 1645 (1990).
[CrossRef]

M. Ll. Pons and L. Roso-Franco, Opt. Lett. 15, 1230 (1990).
[CrossRef]

L. Roso-Franco, J. Opt. Soc. Am. B 4, 1878 (1987).
[CrossRef]

L. Roso-Franco, Phys. Rev. Lett. 55, 2149 (1985).
[CrossRef] [PubMed]

Scalora, M.

M. Scalora and C. M. Bowden, Phys. Rev. A 51, 4048 (1995).
[CrossRef] [PubMed]

M. E. Crenshaw, M. Scalora, and C. M. Bowden, Phys. Rev. Lett. 68, 911 (1992).
[CrossRef] [PubMed]

J. W. Haus, L. Wang, M. Scalora, and C. M. Bowden, Phys. Rev. A 38, 4043 (1988).
[CrossRef] [PubMed]

Schönhammer, K.

A. Knorr, Th. Östereich, K. Schönhammer, R. Binder, and S. W. Koch, Phys. Rev. B 33, 407 (1986).
[CrossRef]

Shu, Q.

M. P. Helen, H. U. Güdel, Q. Shu, J. Rai, S. Rai, and S. C. Rand, Phys. Rev. Lett. 73, 1103 (1994).
[CrossRef]

Stroud, C. R.

C. R. Stroud, C. M. Bowden, and L. Allen, Opt. Commun. 67, 387 (1988).
[CrossRef]

Trifonov, E. D.

M. G. Benedict, V. Malyshev, E. D. Trifonov, and A. I. Zaitsev, Phys. Rev. A 43, 3845 (1991).
[CrossRef] [PubMed]

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 68, 812 (1990) [English translation: Opt. Spectrosc. (USSR) 68, 473 (1990)].

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 66, 726 (1989) [English translation: Opt. Spectrosc. (USSR) 66, 424 (1989)].

M. G. Benedict and E. D. Trifonov, Phys. Rev. A 38, 2854 (1988).
[CrossRef] [PubMed]

Wang, L.

J. W. Haus, L. Wang, M. Scalora, and C. M. Bowden, Phys. Rev. A 38, 4043 (1988).
[CrossRef] [PubMed]

Zaitsev, A. I.

M. G. Benedict, V. Malyshev, E. D. Trifonov, and A. I. Zaitsev, Phys. Rev. A 43, 3845 (1991).
[CrossRef] [PubMed]

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 68, 812 (1990) [English translation: Opt. Spectrosc. (USSR) 68, 473 (1990)].

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 66, 726 (1989) [English translation: Opt. Spectrosc. (USSR) 66, 424 (1989)].

Europhys. Lett. (1)

M. Ll. Pons and L. Roso-Franco, Europhys. Lett. 12, 507 (1990).
[CrossRef]

J. Mod. Opt. (1)

L. Roso-Franco and M. Ll. Pons, J. Mod. Opt. 37, 1645 (1990).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (3)

A. N. Oraevsky, D. J. Jones, and D. K. Bandy, Opt. Commun. 111, 163 (1994).
[CrossRef]

C. R. Stroud, C. M. Bowden, and L. Allen, Opt. Commun. 67, 387 (1988).
[CrossRef]

Y. Ben-Aryeh, C. M. Bowden, and J. C. Englund, Opt. Commun. 61, 147 (1987).
[CrossRef]

Opt. Lett. (1)

Opt. Spektrosk. (2)

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 68, 812 (1990) [English translation: Opt. Spectrosc. (USSR) 68, 473 (1990)].

M. G. Benedict, A. I. Zaitsev, V. Malyshev, and E. D. Trifonov, Opt. Spektrosk. 66, 726 (1989) [English translation: Opt. Spectrosc. (USSR) 66, 424 (1989)].

Phys. Rep. (1)

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rep. 7C, 101 (1973).
[CrossRef]

Phys. Rev. (1)

J. J. Hopfield, Phys. Rev. 112, 1555 (1958).
[CrossRef]

Phys. Rev. A (10)

J. W. Haus, L. Wang, M. Scalora, and C. M. Bowden, Phys. Rev. A 38, 4043 (1988).
[CrossRef] [PubMed]

M. Scalora and C. M. Bowden, Phys. Rev. A 51, 4048 (1995).
[CrossRef] [PubMed]

M. Lindberg, S. W. Koch, and H. Haug, Phys. Rev. A 33, 407 (1986).
[CrossRef] [PubMed]

R. Friedberg, S. R. Hartmann, and J. T. Manassah, Phys. Rev. A 39, 3444 (1989).
[CrossRef] [PubMed]

M. G. Benedict and E. D. Trifonov, Phys. Rev. A 38, 2854 (1988).
[CrossRef] [PubMed]

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Figures (12)

Fig. 1
Fig. 1

Family of solutions of Eq. (8) above the threshold of local-field bistability (δL=T2ΔL=12) demonstrating (a) the appearance and (b) the disappearance of the three-valued solution of Eq. (8) with the dimensionless frequency detuning δ=T2Δ. e =(μT2/)E and τ1=T1/T2.

Fig. 2
Fig. 2

Schematic representation of the polariton branches in the vicinity of an atom–light resonance (a) without and (b) with local-field correction.

Fig. 3
Fig. 3

Appearance and disappearance of the domain wall inside the medium, with (a) the increase and (b) the decrease, respectively, in the dimensionless incident-field amplitude e0=(μT2/)E0 (δL=6, δ=-4.5). In the calculations the amplitude e0 was changed stepwise, and then the stationary values of all the functions were waited for. The critical value when the field goes up is different than when it goes down.

Fig. 4
Fig. 4

Hysteresis loop of reflectivity at δL=6 and δ=-4.5 calculated on the basis of Eqs. (3) by adiabatic up-and-down scanning of the external field amplitude e0 with a constant velocity v=0.0005 (solid curve). The circles and the triangles represent the results of calculations made under steady-state conditions, which we obtained by using as W(|e|2) the low branch of the three-valued field dependence of the population difference up to |e|<e2 and then the upper branch of this dependence when |e|>e2 [see inset in which the corresponding dependence W(|e|2) is depicted] and by using as W(|e|2) the low branch up to |e|<e1 and then the upper branch when |e|>e1 (see also inset), respectively.

Fig. 5
Fig. 5

Field behaviors of reflectivity that we calculated on the basis of stationary Eqs. (5) by using as W(|e|) the low branch of the three-valued solution of Eq. (8) for |e|<e2 and then the upper branch of this solution when |e|>e2 (see Fig. 1). The top curve is calculated at δ=-3.5, giving the highest slope of its descent part. The middle curve corresponds to the critical values of δL and δ, δLc=8.08 and δc=-4.93, respectively. The bottom curve is calculated at δ=-5.95, giving the widest range of the three-valued solution. We carried out all the calculations by following Eqs. (6) and (8) (see Ref. 5) for the method of solution.

Fig. 6
Fig. 6

Dynamics of the appearance and the disappearance of (a) the population domain wall and (b) the hysteresis loop of reflectivity calculated by the linear up-and-down variation of the external field amplitude with a constant velocity v=0.0005 when δL=12, δ=-5. The circles and the triangles represent the results of calculations made under steady-state conditions, which we obtained by using as W(|e|2) the low branch of the three-valued solution of Eq. (8) at |e|<e2 (see Fig. 1) and then the upper branch of this solution when |e|>e2 and by using as W(|e|2) the low branch for |e|<e1 (see also Fig. 1) and then the upper branch when |e|>e1, respectively.

Fig. 7
Fig. 7

Time dependence of reflectivity (dashed curve) and the internal boundary positions (solid curve) that we obtained by solving Eqs. (3) with stepwise changes of the external field amplitude e0.

Fig. 8
Fig. 8

Reflection coefficient of a modeled system composed of a slab whose refraction index ns=3.67+1.42i and a semi-infinite medium with nr=0.27+2.37i versus the slab thickness ξw=k0xw.

Fig. 9
Fig. 9

Spatial dependence of the internal field amplitude |e(ξ)| (solid curves) and the population difference W(ξ) (dashed curves) calculated with (thick curves) and without (thin curves) the local-field correction under steady-state conditions. Ψ =2πμ2N0T2/=4, δ=-4.

Fig. 10
Fig. 10

Field dependence of the reflectivity calculated with (solid curve) and without (dashed curve) the local-field correction under steady-state conditions. Ψ=4, δ=-4.

Fig. 11
Fig. 11

(a) Appearance of internal reflection bistability in the presence of the local field. The critical values of Ψ and δ are Ψc=5.64 and δc=-7.74, respectively (analogous values without the local-field correction are Ψc=4.66 and δc=-Ψc; see Ref. 21). (b) Sample of the multivalued (more than three) behavior of the reflectivity at Ψ=25 and δ=-35. We carried out all the calculations by following Eqs. (6) and (8).

Fig. 12
Fig. 12

Hysteresis loop of reflectivity for parameters (a) Ψ =7, δ=-9.48; and (b) Ψ=12, δ=-16. The solid curves were obtained by adiabatic up-and-down scanning of the external field amplitude e0 at a constant velocity v=0.0005. The dotted curves represent the stationary calculation on the basis of Eqs. (6) and (8).

Equations (27)

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E(x, t)=E0t-xcexp(ik0x)+2πik0μN0×0exp(ik0|x-x|)×Rx, t-|x-x|cdx,
Rt=-i(Δ+ΔLW)+1T2R-i μEW,
Wt=i μ2(ER*-E*R)-1T1(1+W),
Er(t)=E(0, t)-E0(t)=2πik0μN00 exp(ik0x)Rx, t-xcdx.
e(ξ, τ)=e0(τ)exp(iξ)+iΨ0 exp(i|ξ-ξ|)×R(ξ,τ)dξ,
Rτ=-[i(δ+δLW)+1]R-ieW,
Wτ=i2(eR*-e*R)-1τ1(1+W),
2eξ2+e=-2ΨR.
e(ξ)=e0 exp(iξ)+i20 exp(i|ξ-ξ|)×[(|e|2)-1]e(ξ)dξ.
d2edξ2+(|e|2)e=0.
(|e|2)=1+2Ψ i+δ+δLW1+(δ+δLW)2+|e|2τ1
1+WW{[δ+δL(W+1)]2+1}=-|e|2τ1,
2ρ22[(δ+2ρ22δL)2+1]=|e|2τ1,
(δ+2ρ22δL)1,2=13{δ±[(δ)2-3]1/2}.
ρ22c=1δL3,
|ec|2τ1=83δL3.
r=(ns+nr)(1-ns)+(ns-nr)(1+ns)exp(2insξw)(ns+nr)(1+ns)+(ns-nr)(1-ns)exp(2insξw),
2Ex2-1c22Et2=4πc22Pt2.
G(x, t)=c2Θt-|x|c,
E(x, t)=Ei(x, t)-0dx-dtG(x-x, t-t)×4πc22Pt2=Ei(x, t)-2πc0dx t×Px, t-|x-x|c.
E(x, t)=12E(x, t)exp(-iω0t)+c.c.,
Ei(x, t)=12E0[t-(x/c)]exp(-iω0t+ik0x)+c.c.,
P(x, t)=12μN0R(x, t)exp(-iω0t)+c.c.
E(x, t)=E0t-xcexp(ik0x)+2πik0μN0×0 exp(ik0|x-x|)×Rx, t-|x-x|cdx.
2Ex2+k02E+2ik0 1cEt-1c22Et2
=-4πk02μN0R-4πik0μN0 1cRt.
2Ex2+k02E+2ik0 1cEt=-4πk02μN0R,

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