Abstract

We propose an original method for analytically solving the propagation equation in a resonant dense medium, and we give explicit solutions, using a parametric formulation under the thin-sample approximation. We then use the knowledge of the field transformation in a single-pass process to study the transmission of a resonant dense medium inserted into a ring cavity. Implicit analytical results are given, together with an explicit formula under the thin-film approximation. The nonlinear phase shift that is associated with propagation through the medium is shown to have a great influence on the cavity transmission. Optical bistability is obtained in the most general case. We can easily adjust the switching intensities and the intensity shift by modifying the initial cavity detuning ϕ0. For positive cavity detunings, perfect optical limiting can be obtained: Induced absorptive and dispersive losses limit the output intensity. This device can lead to the stabilization of a noisy incident continuous wave or to the realization of optical limiters.

© 1999 Optical Society of America

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References

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  1. H. Gibbs, Optical Bistability (Academic, Orlando, Fla., 1985); L. Lugiato, “Theory of optical bistability,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. XXI.
  2. F. Hopf, C. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591–2596 (1984).
    [CrossRef]
  3. Y. Ben-Aryeh, C. Bowden, and J. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917–3926 (1986).
    [CrossRef] [PubMed]
  4. Y. Ben-Aryeh, C. Bowden, and J. Englund, “Longitudinal spatial first-order phase transition in a system of coherently-driven two-level atoms,” Opt. Commun. 61, 147–150 (1987).
    [CrossRef]
  5. J. Haus, L. Wang, M. Scalora, and C. Bowden, “Spatial effects in intrinsic optical bistability,” Phys. Rev. A 38, 4043–4053 (1988).
    [CrossRef] [PubMed]
  6. B. Samson and W. Gawlik, “Light-induced gain and directional energy flow with counterpropagating light beams in dense media,” Phys. Rev. A 52, R4352–R4355 (1995).
    [CrossRef] [PubMed]
  7. A. Afanas’ev, R. Vlasov, N. Gubar, and V. Volkov, “Hysteresis behavior in light reflection from a dense resonant medium with intrinsic optical bistability,” J. Opt. Soc. Am. B 15, 1160–1167 (1998).
    [CrossRef]
  8. R. Inguva and C. Bowden, “Spatial and temporal evolution of the first-order phase transition in intrinsic optical bistability,” Phys. Rev. A 41, 1670–1676 (1990).
    [CrossRef] [PubMed]
  9. F. Sanchez, “Optical bistability in a 2×2 coupler fiber ring resonator: parametric formulation,” Opt. Commun. 142, 211–214 (1997).
    [CrossRef]
  10. M. Brunel, C. Özkul, K. A. Ameur, and F. Sanchez, “Limiting effects in absorptive bistability,” Opt. Commun. 153, 99–105 (1998).
    [CrossRef]
  11. M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond switching of the solid-state phase transition in the smart system material VO2,” Appl. Phys. Lett. 65, 1507–1510 (1994).
    [CrossRef]
  12. M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation dynamics of the semiconductor–metal phase transition in VO2,” J. Appl. Phys. 79, 2404–2408 (1996).
    [CrossRef]
  13. M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
    [CrossRef]
  14. B. L. Justus, A. L. Huston, and A. J. Campillo, “Broadband thermal optical limiter,” Appl. Phys. Lett. 63, 1483–1486 (1993).
    [CrossRef]
  15. K. Mansour, M. J. Soileau, and E. W. Van Stryland, “Nonlinear optical properties of carbon-black suspensions (ink),” J. Opt. Soc. Am. B 9, 1100–1109 (1992).
    [CrossRef]
  16. M. Lindberg, S. W. Koch, and H. Haug, “Oscillatory instability of an induced absorber in a ring cavity,” J. Opt. Soc. Am. B 3, 751–758 (1986).
    [CrossRef]
  17. M. Scalora, J. W. Haus, and C. M. Bowden, “Intrinsic optical bistability in a cavity,” Phys. Rev. A 41, 6320–6330 (1990).
    [CrossRef] [PubMed]
  18. P. R. Hemmer, N. P. Bigelow, D. P. Katz, M. S. Shahriar, L. DeSalvo, and R. Bonifacio, “Self-organization, broken symmetry, and lasing in an atomic vapor: the interdependence of gratings and gain,” Phys. Rev. Lett. 77, 1468–1471 (1996).
    [CrossRef] [PubMed]

1998

1997

F. Sanchez, “Optical bistability in a 2×2 coupler fiber ring resonator: parametric formulation,” Opt. Commun. 142, 211–214 (1997).
[CrossRef]

1996

P. R. Hemmer, N. P. Bigelow, D. P. Katz, M. S. Shahriar, L. DeSalvo, and R. Bonifacio, “Self-organization, broken symmetry, and lasing in an atomic vapor: the interdependence of gratings and gain,” Phys. Rev. Lett. 77, 1468–1471 (1996).
[CrossRef] [PubMed]

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation dynamics of the semiconductor–metal phase transition in VO2,” J. Appl. Phys. 79, 2404–2408 (1996).
[CrossRef]

1995

B. Samson and W. Gawlik, “Light-induced gain and directional energy flow with counterpropagating light beams in dense media,” Phys. Rev. A 52, R4352–R4355 (1995).
[CrossRef] [PubMed]

1994

M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
[CrossRef]

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond switching of the solid-state phase transition in the smart system material VO2,” Appl. Phys. Lett. 65, 1507–1510 (1994).
[CrossRef]

1993

B. L. Justus, A. L. Huston, and A. J. Campillo, “Broadband thermal optical limiter,” Appl. Phys. Lett. 63, 1483–1486 (1993).
[CrossRef]

1992

1990

M. Scalora, J. W. Haus, and C. M. Bowden, “Intrinsic optical bistability in a cavity,” Phys. Rev. A 41, 6320–6330 (1990).
[CrossRef] [PubMed]

R. Inguva and C. Bowden, “Spatial and temporal evolution of the first-order phase transition in intrinsic optical bistability,” Phys. Rev. A 41, 1670–1676 (1990).
[CrossRef] [PubMed]

1988

J. Haus, L. Wang, M. Scalora, and C. Bowden, “Spatial effects in intrinsic optical bistability,” Phys. Rev. A 38, 4043–4053 (1988).
[CrossRef] [PubMed]

1987

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Longitudinal spatial first-order phase transition in a system of coherently-driven two-level atoms,” Opt. Commun. 61, 147–150 (1987).
[CrossRef]

1986

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917–3926 (1986).
[CrossRef] [PubMed]

M. Lindberg, S. W. Koch, and H. Haug, “Oscillatory instability of an induced absorber in a ring cavity,” J. Opt. Soc. Am. B 3, 751–758 (1986).
[CrossRef]

1984

F. Hopf, C. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591–2596 (1984).
[CrossRef]

Afanas’ev, A.

Ameur, K. A.

M. Brunel, C. Özkul, K. A. Ameur, and F. Sanchez, “Limiting effects in absorptive bistability,” Opt. Commun. 153, 99–105 (1998).
[CrossRef]

Becker, M.

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation dynamics of the semiconductor–metal phase transition in VO2,” J. Appl. Phys. 79, 2404–2408 (1996).
[CrossRef]

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond switching of the solid-state phase transition in the smart system material VO2,” Appl. Phys. Lett. 65, 1507–1510 (1994).
[CrossRef]

Ben-Aryeh, Y.

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Longitudinal spatial first-order phase transition in a system of coherently-driven two-level atoms,” Opt. Commun. 61, 147–150 (1987).
[CrossRef]

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917–3926 (1986).
[CrossRef] [PubMed]

Bigelow, N. P.

P. R. Hemmer, N. P. Bigelow, D. P. Katz, M. S. Shahriar, L. DeSalvo, and R. Bonifacio, “Self-organization, broken symmetry, and lasing in an atomic vapor: the interdependence of gratings and gain,” Phys. Rev. Lett. 77, 1468–1471 (1996).
[CrossRef] [PubMed]

Boilot, J. P.

M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
[CrossRef]

Bonifacio, R.

P. R. Hemmer, N. P. Bigelow, D. P. Katz, M. S. Shahriar, L. DeSalvo, and R. Bonifacio, “Self-organization, broken symmetry, and lasing in an atomic vapor: the interdependence of gratings and gain,” Phys. Rev. Lett. 77, 1468–1471 (1996).
[CrossRef] [PubMed]

Bowden, C.

R. Inguva and C. Bowden, “Spatial and temporal evolution of the first-order phase transition in intrinsic optical bistability,” Phys. Rev. A 41, 1670–1676 (1990).
[CrossRef] [PubMed]

J. Haus, L. Wang, M. Scalora, and C. Bowden, “Spatial effects in intrinsic optical bistability,” Phys. Rev. A 38, 4043–4053 (1988).
[CrossRef] [PubMed]

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Longitudinal spatial first-order phase transition in a system of coherently-driven two-level atoms,” Opt. Commun. 61, 147–150 (1987).
[CrossRef]

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917–3926 (1986).
[CrossRef] [PubMed]

F. Hopf, C. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591–2596 (1984).
[CrossRef]

Bowden, C. M.

M. Scalora, J. W. Haus, and C. M. Bowden, “Intrinsic optical bistability in a cavity,” Phys. Rev. A 41, 6320–6330 (1990).
[CrossRef] [PubMed]

Brun, A.

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation dynamics of the semiconductor–metal phase transition in VO2,” J. Appl. Phys. 79, 2404–2408 (1996).
[CrossRef]

M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
[CrossRef]

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond switching of the solid-state phase transition in the smart system material VO2,” Appl. Phys. Lett. 65, 1507–1510 (1994).
[CrossRef]

Brunel, M.

M. Brunel, C. Özkul, K. A. Ameur, and F. Sanchez, “Limiting effects in absorptive bistability,” Opt. Commun. 153, 99–105 (1998).
[CrossRef]

M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
[CrossRef]

Buckman, A.

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation dynamics of the semiconductor–metal phase transition in VO2,” J. Appl. Phys. 79, 2404–2408 (1996).
[CrossRef]

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond switching of the solid-state phase transition in the smart system material VO2,” Appl. Phys. Lett. 65, 1507–1510 (1994).
[CrossRef]

Campillo, A. J.

B. L. Justus, A. L. Huston, and A. J. Campillo, “Broadband thermal optical limiter,” Appl. Phys. Lett. 63, 1483–1486 (1993).
[CrossRef]

Canva, M.

M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
[CrossRef]

Chaput, F.

M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
[CrossRef]

DeSalvo, L.

P. R. Hemmer, N. P. Bigelow, D. P. Katz, M. S. Shahriar, L. DeSalvo, and R. Bonifacio, “Self-organization, broken symmetry, and lasing in an atomic vapor: the interdependence of gratings and gain,” Phys. Rev. Lett. 77, 1468–1471 (1996).
[CrossRef] [PubMed]

Englund, J.

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Longitudinal spatial first-order phase transition in a system of coherently-driven two-level atoms,” Opt. Commun. 61, 147–150 (1987).
[CrossRef]

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917–3926 (1986).
[CrossRef] [PubMed]

Gawlik, W.

B. Samson and W. Gawlik, “Light-induced gain and directional energy flow with counterpropagating light beams in dense media,” Phys. Rev. A 52, R4352–R4355 (1995).
[CrossRef] [PubMed]

Georges, P.

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation dynamics of the semiconductor–metal phase transition in VO2,” J. Appl. Phys. 79, 2404–2408 (1996).
[CrossRef]

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond switching of the solid-state phase transition in the smart system material VO2,” Appl. Phys. Lett. 65, 1507–1510 (1994).
[CrossRef]

Gubar, N.

Haug, H.

Haus, J.

J. Haus, L. Wang, M. Scalora, and C. Bowden, “Spatial effects in intrinsic optical bistability,” Phys. Rev. A 38, 4043–4053 (1988).
[CrossRef] [PubMed]

Haus, J. W.

M. Scalora, J. W. Haus, and C. M. Bowden, “Intrinsic optical bistability in a cavity,” Phys. Rev. A 41, 6320–6330 (1990).
[CrossRef] [PubMed]

Hemmer, P. R.

P. R. Hemmer, N. P. Bigelow, D. P. Katz, M. S. Shahriar, L. DeSalvo, and R. Bonifacio, “Self-organization, broken symmetry, and lasing in an atomic vapor: the interdependence of gratings and gain,” Phys. Rev. Lett. 77, 1468–1471 (1996).
[CrossRef] [PubMed]

Hopf, F.

F. Hopf, C. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591–2596 (1984).
[CrossRef]

Huston, A. L.

B. L. Justus, A. L. Huston, and A. J. Campillo, “Broadband thermal optical limiter,” Appl. Phys. Lett. 63, 1483–1486 (1993).
[CrossRef]

Inguva, R.

R. Inguva and C. Bowden, “Spatial and temporal evolution of the first-order phase transition in intrinsic optical bistability,” Phys. Rev. A 41, 1670–1676 (1990).
[CrossRef] [PubMed]

Justus, B. L.

B. L. Justus, A. L. Huston, and A. J. Campillo, “Broadband thermal optical limiter,” Appl. Phys. Lett. 63, 1483–1486 (1993).
[CrossRef]

Katz, D. P.

P. R. Hemmer, N. P. Bigelow, D. P. Katz, M. S. Shahriar, L. DeSalvo, and R. Bonifacio, “Self-organization, broken symmetry, and lasing in an atomic vapor: the interdependence of gratings and gain,” Phys. Rev. Lett. 77, 1468–1471 (1996).
[CrossRef] [PubMed]

Koch, S. W.

Le Luyer, F.

M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
[CrossRef]

Lépine, T.

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation dynamics of the semiconductor–metal phase transition in VO2,” J. Appl. Phys. 79, 2404–2408 (1996).
[CrossRef]

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond switching of the solid-state phase transition in the smart system material VO2,” Appl. Phys. Lett. 65, 1507–1510 (1994).
[CrossRef]

Lindberg, M.

Louisell, W.

F. Hopf, C. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591–2596 (1984).
[CrossRef]

Malier, L.

M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
[CrossRef]

Mansour, K.

Özkul, C.

M. Brunel, C. Özkul, K. A. Ameur, and F. Sanchez, “Limiting effects in absorptive bistability,” Opt. Commun. 153, 99–105 (1998).
[CrossRef]

Samson, B.

B. Samson and W. Gawlik, “Light-induced gain and directional energy flow with counterpropagating light beams in dense media,” Phys. Rev. A 52, R4352–R4355 (1995).
[CrossRef] [PubMed]

Sanchez, F.

M. Brunel, C. Özkul, K. A. Ameur, and F. Sanchez, “Limiting effects in absorptive bistability,” Opt. Commun. 153, 99–105 (1998).
[CrossRef]

F. Sanchez, “Optical bistability in a 2×2 coupler fiber ring resonator: parametric formulation,” Opt. Commun. 142, 211–214 (1997).
[CrossRef]

Scalora, M.

M. Scalora, J. W. Haus, and C. M. Bowden, “Intrinsic optical bistability in a cavity,” Phys. Rev. A 41, 6320–6330 (1990).
[CrossRef] [PubMed]

J. Haus, L. Wang, M. Scalora, and C. Bowden, “Spatial effects in intrinsic optical bistability,” Phys. Rev. A 38, 4043–4053 (1988).
[CrossRef] [PubMed]

Shahriar, M. S.

P. R. Hemmer, N. P. Bigelow, D. P. Katz, M. S. Shahriar, L. DeSalvo, and R. Bonifacio, “Self-organization, broken symmetry, and lasing in an atomic vapor: the interdependence of gratings and gain,” Phys. Rev. Lett. 77, 1468–1471 (1996).
[CrossRef] [PubMed]

Soileau, M. J.

Van Stryland, E. W.

Vlasov, R.

Volkov, V.

Walser, R.

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation dynamics of the semiconductor–metal phase transition in VO2,” J. Appl. Phys. 79, 2404–2408 (1996).
[CrossRef]

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond switching of the solid-state phase transition in the smart system material VO2,” Appl. Phys. Lett. 65, 1507–1510 (1994).
[CrossRef]

Wang, L.

J. Haus, L. Wang, M. Scalora, and C. Bowden, “Spatial effects in intrinsic optical bistability,” Phys. Rev. A 38, 4043–4053 (1988).
[CrossRef] [PubMed]

Appl. Phys. B:

M. Brunel, F. Le Luyer, M. Canva, A. Brun, F. Chaput, L. Malier, and J. P. Boilot, “Reverse saturable absorption in aluminophthalocyanine doped xerogels,” Appl. Phys. B: 58, 443–445 (1994).
[CrossRef]

Appl. Phys. Lett.

B. L. Justus, A. L. Huston, and A. J. Campillo, “Broadband thermal optical limiter,” Appl. Phys. Lett. 63, 1483–1486 (1993).
[CrossRef]

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond switching of the solid-state phase transition in the smart system material VO2,” Appl. Phys. Lett. 65, 1507–1510 (1994).
[CrossRef]

J. Appl. Phys.

M. Becker, A. Buckman, R. Walser, T. Lépine, P. Georges, and A. Brun, “Femtosecond laser excitation dynamics of the semiconductor–metal phase transition in VO2,” J. Appl. Phys. 79, 2404–2408 (1996).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

F. Sanchez, “Optical bistability in a 2×2 coupler fiber ring resonator: parametric formulation,” Opt. Commun. 142, 211–214 (1997).
[CrossRef]

M. Brunel, C. Özkul, K. A. Ameur, and F. Sanchez, “Limiting effects in absorptive bistability,” Opt. Commun. 153, 99–105 (1998).
[CrossRef]

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Longitudinal spatial first-order phase transition in a system of coherently-driven two-level atoms,” Opt. Commun. 61, 147–150 (1987).
[CrossRef]

Phys. Rev. A

J. Haus, L. Wang, M. Scalora, and C. Bowden, “Spatial effects in intrinsic optical bistability,” Phys. Rev. A 38, 4043–4053 (1988).
[CrossRef] [PubMed]

B. Samson and W. Gawlik, “Light-induced gain and directional energy flow with counterpropagating light beams in dense media,” Phys. Rev. A 52, R4352–R4355 (1995).
[CrossRef] [PubMed]

F. Hopf, C. Bowden, and W. Louisell, “Mirrorless optical bistability with the use of the local-field correction,” Phys. Rev. A 29, 2591–2596 (1984).
[CrossRef]

Y. Ben-Aryeh, C. Bowden, and J. Englund, “Intrinsic optical bistability in collections of spatially distributed two-level atoms,” Phys. Rev. A 34, 3917–3926 (1986).
[CrossRef] [PubMed]

R. Inguva and C. Bowden, “Spatial and temporal evolution of the first-order phase transition in intrinsic optical bistability,” Phys. Rev. A 41, 1670–1676 (1990).
[CrossRef] [PubMed]

M. Scalora, J. W. Haus, and C. M. Bowden, “Intrinsic optical bistability in a cavity,” Phys. Rev. A 41, 6320–6330 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett.

P. R. Hemmer, N. P. Bigelow, D. P. Katz, M. S. Shahriar, L. DeSalvo, and R. Bonifacio, “Self-organization, broken symmetry, and lasing in an atomic vapor: the interdependence of gratings and gain,” Phys. Rev. Lett. 77, 1468–1471 (1996).
[CrossRef] [PubMed]

Other

H. Gibbs, Optical Bistability (Academic, Orlando, Fla., 1985); L. Lugiato, “Theory of optical bistability,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. XXI.

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Figures (7)

Fig. 1
Fig. 1

Representation of the population difference between the ground state and the excited state in a resonant dense medium as a function of the intensity for δ=0 and b=15.

Fig. 2
Fig. 2

Representation of the output intensity relative to the incident intensity through a resonant dense medium in a single-pass configuration. The results are given for δ=0 and b=15 for two values of the normalized length l for the parametric formulation and the exact calculation.

Fig. 3
Fig. 3

Configuration considered in this paper: The resonant dense medium is inserted inside a resonant ring cavity.

Fig. 4
Fig. 4

Evolution of the output intensity relative to the incident intensity for the parametric formulation and the exact calculation. The parameters used are δ=0, b=15, and l=0.001.

Fig. 5
Fig. 5

Evolution of the output intensity relative to the incident intensity. The curves were obtained with δ=0, b=15, l=0.001, and ϕ0=2 kπ-0.0005π.

Fig. 6
Fig. 6

Evolution of the switching intensity Is and the intensity shift ΔI as a function of ϕ0. The other parameters were δ=0, b=15, and l=0.001.

Fig. 7
Fig. 7

Evolution of the output intensity relative to the incident intensity. The curves were obtained with δ=0, b=15, l=0.001, and ϕ0=2 kπ+0.0005π.

Equations (32)

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

dNdt=i 2µ(E*P-EP*)-N-1T1,
dPdt=i μEN-1T2[1-i(δ+bN)]P,
b=4π3μ2N0T2
χ=3i4πbN1-i(δ+bN),
1-NN[1+(δ+bN)2]=|ξ|2,
ξ(z)exp[i(kz-ωt)],
dξdς=i4π2χξ,
ς=(ω/c)z.
dξdς=-(α+iβ)ξ,
α=123bN1+(δ+bN)2,
β=123bN(δ+bN)1+(δ+bN)2,
d|ξ|2dς=-2α|ξ|2.
2b(δ+bN)N-1+(δ+bN)2N2(1-N) dNdς=-3b,
A logNout-1N0-1-B logNoutN0+B1Nout-1N0
+C(Nout-N0)=-3bl,
A logN1-1N0-1-B logN1N0+B1N1-1N0
+C(N1-N0)=-3bls.
ξ(l)=ξ(0)exp(-αl-iβl),
|ξ(0)|2=1-NN[1+(δ+bN)2],
Iin=1-NN[1+(δ+bN)2],
Iout=1-NN[1+(δ+bN)2]exp(-2αl),
ξ1=τξin+ρ2ξ2 exp(iϕ0),
ξout=τξ2,
|ξin|2=1τ2|ξ1|2{1-2ρ2 exp[-α(ξ1)l]cos[ϕ0-β(ξ1)l]+ρ4 exp[-2α(ξ1)l]},
|ξout|2=τ2|ξ1|2 exp[-2α(ξ1)l].
dϕdς=123bN(δ+bN)1+(δ+bN)2.
dϕdN=123bN(δ+bN)1+(δ+bN)21dNdς.
dϕdN=-122b(δ+bN)21+(δ+bN)2-δ+bNN(1-N),
Δϕ=-122b(Nout-N0)-2 arctan b(Nout-N0)1+(δ+bNout)(δ+bN0)+(δ+b)log1-Nout1-N0-δ logNoutN0.
|ξ1|2=1-NN[1+(δ+bN)2].
Iin=1τ21-NN[1+(δ+bN)2][1-2ρ2×exp(-αl)cos(βl-ϕ0)+ρ4 exp(-2αl)],
Iout=τ2 1-NN[1+(δ+bN)2]exp(-2αl).

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