Abstract

We report on the observation of frequency multistability in a semiconductor laser emission. We experimentally study the spectral behavior of a semiconductor laser under a spectrally filtered orthogonal-polarization feedback and show that using a reinjected signal having both absorptive and dispersive lineshapes, we are able to control the laser spectral response exhibiting bistability or multistability. We describe all the observed spectra, considering only the linear response of the laser and both the amplitude and phase filtering of the reinjected orthogonal field.

© 2007 Optical Society of America

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  1. L. A. Lugiato, "Theory of optical bistability," in Progress in Optics, E.Wolf, ed. (North-Holland, 1984), vol. 21, p. 71, and references therein.
    [CrossRef]
  2. H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled fabry-perot interferometer," Phys. Rev. Lett. 36, 1135-1138 (1976).
    [CrossRef]
  3. A. T. Rosenberger, L. A. Orozco, and H. J. Kimble, "Observation of absorptive bistability with two-level atoms in a ring cavity," Phys. Rev. A 28, 2569-2572 (1983).
    [CrossRef]
  4. A. Joshi and M. Xiao, "Optical multistability in three-level atoms inside an optical ring cavity," Phys. Rev. Lett. 91, 143904 (2003).
    [CrossRef] [PubMed]
  5. B. Farias, T. Passerat de Silans, M. Chevrollier, and M. Oriá, "Frequency bistability of a semiconductor laser under a frequency-dependent feedback," Phys. Rev. Lett. 94, 173902 1-4 (2005).
    [CrossRef]
  6. G. H. M. Van Tartwijk and D. Lenstra, "Semiconductor lasers with optical injection and feedback," J. Opt. B: Quantum Semiclassical Opt. 7, 87-143 (1995).
    [CrossRef]
  7. R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
    [CrossRef]
  8. G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. R. Tredicce, "Low frequency fluctuations and multimode operation of a semiconductor laser with optical feedback," Opt. Commun. 149, 341-347 (1998).
    [CrossRef]
  9. D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, "Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection," Phys. Rev. A 72, 043818 (2005).
    [CrossRef]
  10. H. Erzgraber, B. Krauskopf, D. Lenstra, A. P. A. Fischer, and G. Vemuri, "Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback," Phys. Rev. E 73, 055201(R) (2006).
    [CrossRef]
  11. P. Saboureau, J.-P. Foing, and P. Schanne, "Injection-locked semiconductor lasers with delayed optoelectronic feedback," IEEE J. Quantum Electron. 33, 1582-1591 (1997).
    [CrossRef]
  12. R. Badii, N. Matuschek, T. Pliska, J. Troger, and B. Schmidt, "Dynamics of multimode diode lasers with strong, frequency-selective optical feedback," Phys. Rev. E 68, 036605 (2003).
    [CrossRef]
  13. O. K. Andersen, A. P. A. Fischer, I. C. Lane, E. Louvergneaux, S. Stolte, and D. Lenstra, "Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell," IEEE J. Quantum Electron. 35, 577-582 (1999).
    [CrossRef]
  14. M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, "Dynamical behavior of semiconductor lasers with frequency selective optical feedback," Chaos, Solitons Fractals 10, 811-818 (1999).
    [CrossRef]
  15. A. P. A. Fischer, M. Yousefi, D. Lenstra, M. Carter, and G. Vemuri, "Filtered optical feedback induced frequency dynamics in semiconductor lasers," Phys. Rev. Lett. 92, 023901 (2004).
    [CrossRef] [PubMed]
  16. A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonettev, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
    [CrossRef] [PubMed]
  17. R. Ju, Y. Hong, and P. Spencer, "Semiconductor lasers subject to polarization-rotated optical feedback," IEE Proc.: Optoelectron. 153, 131-137 (2006).
    [CrossRef]
  18. D. Cheng, T. Yen, E. Liu, and K. Chuang, "Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback," IEEE Photonics Technol. Lett. 16, 1435-1437 (2004).
    [CrossRef]
  19. T. Heil, A. Uchida, P. Davis, and T. Aida, "TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback," Phys. Rev. A 68, 033811 (2003).
    [CrossRef]
  20. J. Houlihan, G. Huyet, and J. G. McInerney, "Dynamics of a semiconductor laser with incoherent optical feedback," Opt. Commun. 199, 175-179 (2001).
    [CrossRef]
  21. H. Yasaka, Y. Yoshikuni, and M. Watanabe, "Measurement of gain saturation coefficient of a DFB laser for lasing mode control by orthogonal polarization light," IEEE J. Quantum Electron. 27, 2248-2255 (1991).
    [CrossRef]
  22. H. Yasaka and H. Kawaguchi, "Linewidth reduction and optical frequency stabilization of a distributed feedback laser by incoherent optical negative feedback," Appl. Phys. Lett. 53, 1360-1362 (1988).
    [CrossRef]
  23. H. Chang, H. Wu, C. Xie, and H. Wang, "Controlled shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system," Phys. Rev. Lett. 93, 213901 (2004).
    [CrossRef] [PubMed]
  24. C. Masoller, T. Sorrentino, M. Chevrollier, and M. Oriá, "Bistability in semiconductor lasers with polarization-rotated frequency-dependent," IEEE J. Quantum Electron. 43, 261-268 (2007).
    [CrossRef]
  25. The amplitude stability of the laser under orthogonal feedback occurs for operation above about the double of the threshold current, see .
  26. M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, "Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback," IEE Proc.: Optoelectron. 148, 233-237 (2001).
    [CrossRef]
  27. A. F. A. da Rocha, P. C. S. Segundo, M. Chevrollier, and M. Oriá, "Diode laser coupled to an atomic line by incoherent optical negative feedback," Appl. Phys. Lett. 84, 179-181 (2004).
    [CrossRef]
  28. J. E. Bjorkholm and A. Ashkin, "cw self-focusing and self-trapping of light in sodium vapor," Phys. Rev. Lett. 32, 129-132 (1974).
    [CrossRef]
  29. See, e. g., T. Ackemann, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, and G. L. Lippi, "Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping," Opt. Commun. 147, 411-428 (1998), and references therein.
    [CrossRef]
  30. Equation only gives the new frequency (ν) as a function of the free-laser frequency (νo). In order to reproduce the experimental transmission of the analysis filter (absorption cell, external to the feedback loop), which converts the emitted frequency ν into an amplitude signal fp(ν), we plot the lineshape fp(ν) as a function of νo.
  31. M. Kitano, T. Yabuzaki, and T. Ogawa, "Optical tristability," Phys. Rev. Lett. 46, 926-929 (1981).
    [CrossRef]
  32. S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, "Observation of optical tristability in sodium vapors," Phys. Rev. Lett. 49, 1928-1931 (1982).
    [CrossRef]
  33. The hysteresis cycles are either counterclockwise, as in the pure absorptive hysteresis, or clockwise, occurring when the two mechanisms provoking hysteresis are present. See, for instance, A. Joshi, W. Yang, and M. Xiao, "Hysteresis loop with controllable shape and direction in an optical ring cavity," Phys. Rev. A 70, 041802(R) (2004).
    [CrossRef]

2007

C. Masoller, T. Sorrentino, M. Chevrollier, and M. Oriá, "Bistability in semiconductor lasers with polarization-rotated frequency-dependent," IEEE J. Quantum Electron. 43, 261-268 (2007).
[CrossRef]

2006

H. Erzgraber, B. Krauskopf, D. Lenstra, A. P. A. Fischer, and G. Vemuri, "Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback," Phys. Rev. E 73, 055201(R) (2006).
[CrossRef]

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonettev, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

R. Ju, Y. Hong, and P. Spencer, "Semiconductor lasers subject to polarization-rotated optical feedback," IEE Proc.: Optoelectron. 153, 131-137 (2006).
[CrossRef]

2005

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, "Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection," Phys. Rev. A 72, 043818 (2005).
[CrossRef]

B. Farias, T. Passerat de Silans, M. Chevrollier, and M. Oriá, "Frequency bistability of a semiconductor laser under a frequency-dependent feedback," Phys. Rev. Lett. 94, 173902 1-4 (2005).
[CrossRef]

2004

A. P. A. Fischer, M. Yousefi, D. Lenstra, M. Carter, and G. Vemuri, "Filtered optical feedback induced frequency dynamics in semiconductor lasers," Phys. Rev. Lett. 92, 023901 (2004).
[CrossRef] [PubMed]

D. Cheng, T. Yen, E. Liu, and K. Chuang, "Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback," IEEE Photonics Technol. Lett. 16, 1435-1437 (2004).
[CrossRef]

A. F. A. da Rocha, P. C. S. Segundo, M. Chevrollier, and M. Oriá, "Diode laser coupled to an atomic line by incoherent optical negative feedback," Appl. Phys. Lett. 84, 179-181 (2004).
[CrossRef]

H. Chang, H. Wu, C. Xie, and H. Wang, "Controlled shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system," Phys. Rev. Lett. 93, 213901 (2004).
[CrossRef] [PubMed]

The hysteresis cycles are either counterclockwise, as in the pure absorptive hysteresis, or clockwise, occurring when the two mechanisms provoking hysteresis are present. See, for instance, A. Joshi, W. Yang, and M. Xiao, "Hysteresis loop with controllable shape and direction in an optical ring cavity," Phys. Rev. A 70, 041802(R) (2004).
[CrossRef]

2003

T. Heil, A. Uchida, P. Davis, and T. Aida, "TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback," Phys. Rev. A 68, 033811 (2003).
[CrossRef]

R. Badii, N. Matuschek, T. Pliska, J. Troger, and B. Schmidt, "Dynamics of multimode diode lasers with strong, frequency-selective optical feedback," Phys. Rev. E 68, 036605 (2003).
[CrossRef]

A. Joshi and M. Xiao, "Optical multistability in three-level atoms inside an optical ring cavity," Phys. Rev. Lett. 91, 143904 (2003).
[CrossRef] [PubMed]

2001

J. Houlihan, G. Huyet, and J. G. McInerney, "Dynamics of a semiconductor laser with incoherent optical feedback," Opt. Commun. 199, 175-179 (2001).
[CrossRef]

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, "Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback," IEE Proc.: Optoelectron. 148, 233-237 (2001).
[CrossRef]

1999

O. K. Andersen, A. P. A. Fischer, I. C. Lane, E. Louvergneaux, S. Stolte, and D. Lenstra, "Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell," IEEE J. Quantum Electron. 35, 577-582 (1999).
[CrossRef]

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, "Dynamical behavior of semiconductor lasers with frequency selective optical feedback," Chaos, Solitons Fractals 10, 811-818 (1999).
[CrossRef]

1998

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. R. Tredicce, "Low frequency fluctuations and multimode operation of a semiconductor laser with optical feedback," Opt. Commun. 149, 341-347 (1998).
[CrossRef]

See, e. g., T. Ackemann, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, and G. L. Lippi, "Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping," Opt. Commun. 147, 411-428 (1998), and references therein.
[CrossRef]

1997

P. Saboureau, J.-P. Foing, and P. Schanne, "Injection-locked semiconductor lasers with delayed optoelectronic feedback," IEEE J. Quantum Electron. 33, 1582-1591 (1997).
[CrossRef]

1995

G. H. M. Van Tartwijk and D. Lenstra, "Semiconductor lasers with optical injection and feedback," J. Opt. B: Quantum Semiclassical Opt. 7, 87-143 (1995).
[CrossRef]

1991

H. Yasaka, Y. Yoshikuni, and M. Watanabe, "Measurement of gain saturation coefficient of a DFB laser for lasing mode control by orthogonal polarization light," IEEE J. Quantum Electron. 27, 2248-2255 (1991).
[CrossRef]

1988

H. Yasaka and H. Kawaguchi, "Linewidth reduction and optical frequency stabilization of a distributed feedback laser by incoherent optical negative feedback," Appl. Phys. Lett. 53, 1360-1362 (1988).
[CrossRef]

1983

A. T. Rosenberger, L. A. Orozco, and H. J. Kimble, "Observation of absorptive bistability with two-level atoms in a ring cavity," Phys. Rev. A 28, 2569-2572 (1983).
[CrossRef]

1982

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, "Observation of optical tristability in sodium vapors," Phys. Rev. Lett. 49, 1928-1931 (1982).
[CrossRef]

1981

M. Kitano, T. Yabuzaki, and T. Ogawa, "Optical tristability," Phys. Rev. Lett. 46, 926-929 (1981).
[CrossRef]

1980

R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

1976

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled fabry-perot interferometer," Phys. Rev. Lett. 36, 1135-1138 (1976).
[CrossRef]

1974

J. E. Bjorkholm and A. Ashkin, "cw self-focusing and self-trapping of light in sodium vapor," Phys. Rev. Lett. 32, 129-132 (1974).
[CrossRef]

Ackemann, T.

See, e. g., T. Ackemann, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, and G. L. Lippi, "Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping," Opt. Commun. 147, 411-428 (1998), and references therein.
[CrossRef]

Aida, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, "TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback," Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Amonettev, J.

Andersen, O. K.

O. K. Andersen, A. P. A. Fischer, I. C. Lane, E. Louvergneaux, S. Stolte, and D. Lenstra, "Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell," IEEE J. Quantum Electron. 35, 577-582 (1999).
[CrossRef]

Ashkin, A.

J. E. Bjorkholm and A. Ashkin, "cw self-focusing and self-trapping of light in sodium vapor," Phys. Rev. Lett. 32, 129-132 (1974).
[CrossRef]

Badii, R.

R. Badii, N. Matuschek, T. Pliska, J. Troger, and B. Schmidt, "Dynamics of multimode diode lasers with strong, frequency-selective optical feedback," Phys. Rev. E 68, 036605 (2003).
[CrossRef]

Balle, S.

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. R. Tredicce, "Low frequency fluctuations and multimode operation of a semiconductor laser with optical feedback," Opt. Commun. 149, 341-347 (1998).
[CrossRef]

Baracco, M. J.

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, "Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection," Phys. Rev. A 72, 043818 (2005).
[CrossRef]

Bjorkholm, J. E.

J. E. Bjorkholm and A. Ashkin, "cw self-focusing and self-trapping of light in sodium vapor," Phys. Rev. Lett. 32, 129-132 (1974).
[CrossRef]

Blackburn, K. L.

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, "Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection," Phys. Rev. A 72, 043818 (2005).
[CrossRef]

Burner, G.

Carter, M.

A. P. A. Fischer, M. Yousefi, D. Lenstra, M. Carter, and G. Vemuri, "Filtered optical feedback induced frequency dynamics in semiconductor lasers," Phys. Rev. Lett. 92, 023901 (2004).
[CrossRef] [PubMed]

Cecchi, S.

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, "Observation of optical tristability in sodium vapors," Phys. Rev. Lett. 49, 1928-1931 (1982).
[CrossRef]

Chang, H.

H. Chang, H. Wu, C. Xie, and H. Wang, "Controlled shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system," Phys. Rev. Lett. 93, 213901 (2004).
[CrossRef] [PubMed]

Cheng, D.

D. Cheng, T. Yen, E. Liu, and K. Chuang, "Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback," IEEE Photonics Technol. Lett. 16, 1435-1437 (2004).
[CrossRef]

Chevrollier, M.

C. Masoller, T. Sorrentino, M. Chevrollier, and M. Oriá, "Bistability in semiconductor lasers with polarization-rotated frequency-dependent," IEEE J. Quantum Electron. 43, 261-268 (2007).
[CrossRef]

B. Farias, T. Passerat de Silans, M. Chevrollier, and M. Oriá, "Frequency bistability of a semiconductor laser under a frequency-dependent feedback," Phys. Rev. Lett. 94, 173902 1-4 (2005).
[CrossRef]

A. F. A. da Rocha, P. C. S. Segundo, M. Chevrollier, and M. Oriá, "Diode laser coupled to an atomic line by incoherent optical negative feedback," Appl. Phys. Lett. 84, 179-181 (2004).
[CrossRef]

Chuang, K.

D. Cheng, T. Yen, E. Liu, and K. Chuang, "Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback," IEEE Photonics Technol. Lett. 16, 1435-1437 (2004).
[CrossRef]

da Rocha, A. F. A.

A. F. A. da Rocha, P. C. S. Segundo, M. Chevrollier, and M. Oriá, "Diode laser coupled to an atomic line by incoherent optical negative feedback," Appl. Phys. Lett. 84, 179-181 (2004).
[CrossRef]

Davis, P.

T. Heil, A. Uchida, P. Davis, and T. Aida, "TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback," Phys. Rev. A 68, 033811 (2003).
[CrossRef]

de Silans, T. Passerat

B. Farias, T. Passerat de Silans, M. Chevrollier, and M. Oriá, "Frequency bistability of a semiconductor laser under a frequency-dependent feedback," Phys. Rev. Lett. 94, 173902 1-4 (2005).
[CrossRef]

Erneux, T.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonettev, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, "Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection," Phys. Rev. A 72, 043818 (2005).
[CrossRef]

Erzgraber, H.

H. Erzgraber, B. Krauskopf, D. Lenstra, A. P. A. Fischer, and G. Vemuri, "Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback," Phys. Rev. E 73, 055201(R) (2006).
[CrossRef]

Farias, B.

B. Farias, T. Passerat de Silans, M. Chevrollier, and M. Oriá, "Frequency bistability of a semiconductor laser under a frequency-dependent feedback," Phys. Rev. Lett. 94, 173902 1-4 (2005).
[CrossRef]

Fischer, A.

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, "Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback," IEE Proc.: Optoelectron. 148, 233-237 (2001).
[CrossRef]

Fischer, A. P. A.

H. Erzgraber, B. Krauskopf, D. Lenstra, A. P. A. Fischer, and G. Vemuri, "Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback," Phys. Rev. E 73, 055201(R) (2006).
[CrossRef]

A. P. A. Fischer, M. Yousefi, D. Lenstra, M. Carter, and G. Vemuri, "Filtered optical feedback induced frequency dynamics in semiconductor lasers," Phys. Rev. Lett. 92, 023901 (2004).
[CrossRef] [PubMed]

O. K. Andersen, A. P. A. Fischer, I. C. Lane, E. Louvergneaux, S. Stolte, and D. Lenstra, "Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell," IEEE J. Quantum Electron. 35, 577-582 (1999).
[CrossRef]

Foing, J.-P.

P. Saboureau, J.-P. Foing, and P. Schanne, "Injection-locked semiconductor lasers with delayed optoelectronic feedback," IEEE J. Quantum Electron. 33, 1582-1591 (1997).
[CrossRef]

Gavrielides, A.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonettev, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, "Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection," Phys. Rev. A 72, 043818 (2005).
[CrossRef]

Giacomelli, G.

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. R. Tredicce, "Low frequency fluctuations and multimode operation of a semiconductor laser with optical feedback," Opt. Commun. 149, 341-347 (1998).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled fabry-perot interferometer," Phys. Rev. Lett. 36, 1135-1138 (1976).
[CrossRef]

Giudici, M.

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, "Dynamical behavior of semiconductor lasers with frequency selective optical feedback," Chaos, Solitons Fractals 10, 811-818 (1999).
[CrossRef]

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. R. Tredicce, "Low frequency fluctuations and multimode operation of a semiconductor laser with optical feedback," Opt. Commun. 149, 341-347 (1998).
[CrossRef]

Giuggioli, L.

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, "Dynamical behavior of semiconductor lasers with frequency selective optical feedback," Chaos, Solitons Fractals 10, 811-818 (1999).
[CrossRef]

Giusfredi, G.

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, "Observation of optical tristability in sodium vapors," Phys. Rev. Lett. 49, 1928-1931 (1982).
[CrossRef]

Green, C.

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, "Dynamical behavior of semiconductor lasers with frequency selective optical feedback," Chaos, Solitons Fractals 10, 811-818 (1999).
[CrossRef]

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. R. Tredicce, "Low frequency fluctuations and multimode operation of a semiconductor laser with optical feedback," Opt. Commun. 149, 341-347 (1998).
[CrossRef]

Heil, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, "TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback," Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Hoffer, L. M.

See, e. g., T. Ackemann, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, and G. L. Lippi, "Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping," Opt. Commun. 147, 411-428 (1998), and references therein.
[CrossRef]

Hong, Y.

R. Ju, Y. Hong, and P. Spencer, "Semiconductor lasers subject to polarization-rotated optical feedback," IEE Proc.: Optoelectron. 153, 131-137 (2006).
[CrossRef]

Houlihan, J.

J. Houlihan, G. Huyet, and J. G. McInerney, "Dynamics of a semiconductor laser with incoherent optical feedback," Opt. Commun. 199, 175-179 (2001).
[CrossRef]

Huyet, G.

J. Houlihan, G. Huyet, and J. G. McInerney, "Dynamics of a semiconductor laser with incoherent optical feedback," Opt. Commun. 199, 175-179 (2001).
[CrossRef]

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. R. Tredicce, "Low frequency fluctuations and multimode operation of a semiconductor laser with optical feedback," Opt. Commun. 149, 341-347 (1998).
[CrossRef]

Joshi, A.

The hysteresis cycles are either counterclockwise, as in the pure absorptive hysteresis, or clockwise, occurring when the two mechanisms provoking hysteresis are present. See, for instance, A. Joshi, W. Yang, and M. Xiao, "Hysteresis loop with controllable shape and direction in an optical ring cavity," Phys. Rev. A 70, 041802(R) (2004).
[CrossRef]

A. Joshi and M. Xiao, "Optical multistability in three-level atoms inside an optical ring cavity," Phys. Rev. Lett. 91, 143904 (2003).
[CrossRef] [PubMed]

Ju, R.

R. Ju, Y. Hong, and P. Spencer, "Semiconductor lasers subject to polarization-rotated optical feedback," IEE Proc.: Optoelectron. 153, 131-137 (2006).
[CrossRef]

Kawaguchi, H.

H. Yasaka and H. Kawaguchi, "Linewidth reduction and optical frequency stabilization of a distributed feedback laser by incoherent optical negative feedback," Appl. Phys. Lett. 53, 1360-1362 (1988).
[CrossRef]

Kimble, H. J.

A. T. Rosenberger, L. A. Orozco, and H. J. Kimble, "Observation of absorptive bistability with two-level atoms in a ring cavity," Phys. Rev. A 28, 2569-2572 (1983).
[CrossRef]

Kitano, M.

M. Kitano, T. Yabuzaki, and T. Ogawa, "Optical tristability," Phys. Rev. Lett. 46, 926-929 (1981).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Krauskopf, B.

H. Erzgraber, B. Krauskopf, D. Lenstra, A. P. A. Fischer, and G. Vemuri, "Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback," Phys. Rev. E 73, 055201(R) (2006).
[CrossRef]

Lane, I. C.

O. K. Andersen, A. P. A. Fischer, I. C. Lane, E. Louvergneaux, S. Stolte, and D. Lenstra, "Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell," IEEE J. Quantum Electron. 35, 577-582 (1999).
[CrossRef]

Lang, R.

R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

Lenstra, D.

H. Erzgraber, B. Krauskopf, D. Lenstra, A. P. A. Fischer, and G. Vemuri, "Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback," Phys. Rev. E 73, 055201(R) (2006).
[CrossRef]

A. P. A. Fischer, M. Yousefi, D. Lenstra, M. Carter, and G. Vemuri, "Filtered optical feedback induced frequency dynamics in semiconductor lasers," Phys. Rev. Lett. 92, 023901 (2004).
[CrossRef] [PubMed]

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, "Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback," IEE Proc.: Optoelectron. 148, 233-237 (2001).
[CrossRef]

O. K. Andersen, A. P. A. Fischer, I. C. Lane, E. Louvergneaux, S. Stolte, and D. Lenstra, "Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell," IEEE J. Quantum Electron. 35, 577-582 (1999).
[CrossRef]

G. H. M. Van Tartwijk and D. Lenstra, "Semiconductor lasers with optical injection and feedback," J. Opt. B: Quantum Semiclassical Opt. 7, 87-143 (1995).
[CrossRef]

Lippi, G. L.

See, e. g., T. Ackemann, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, and G. L. Lippi, "Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping," Opt. Commun. 147, 411-428 (1998), and references therein.
[CrossRef]

Liu, E.

D. Cheng, T. Yen, E. Liu, and K. Chuang, "Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback," IEEE Photonics Technol. Lett. 16, 1435-1437 (2004).
[CrossRef]

Louvergneaux, E.

O. K. Andersen, A. P. A. Fischer, I. C. Lane, E. Louvergneaux, S. Stolte, and D. Lenstra, "Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell," IEEE J. Quantum Electron. 35, 577-582 (1999).
[CrossRef]

Lugiato, L. A.

L. A. Lugiato, "Theory of optical bistability," in Progress in Optics, E.Wolf, ed. (North-Holland, 1984), vol. 21, p. 71, and references therein.
[CrossRef]

Masoller, C.

C. Masoller, T. Sorrentino, M. Chevrollier, and M. Oriá, "Bistability in semiconductor lasers with polarization-rotated frequency-dependent," IEEE J. Quantum Electron. 43, 261-268 (2007).
[CrossRef]

Matuschek, N.

R. Badii, N. Matuschek, T. Pliska, J. Troger, and B. Schmidt, "Dynamics of multimode diode lasers with strong, frequency-selective optical feedback," Phys. Rev. E 68, 036605 (2003).
[CrossRef]

McCall, S. L.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled fabry-perot interferometer," Phys. Rev. Lett. 36, 1135-1138 (1976).
[CrossRef]

McInerney, J. G.

J. Houlihan, G. Huyet, and J. G. McInerney, "Dynamics of a semiconductor laser with incoherent optical feedback," Opt. Commun. 199, 175-179 (2001).
[CrossRef]

McLachlan, T.

Miller, J.

Nalik, J.

See, e. g., T. Ackemann, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, and G. L. Lippi, "Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping," Opt. Commun. 147, 411-428 (1998), and references therein.
[CrossRef]

Ogawa, T.

M. Kitano, T. Yabuzaki, and T. Ogawa, "Optical tristability," Phys. Rev. Lett. 46, 926-929 (1981).
[CrossRef]

Oriá, M.

C. Masoller, T. Sorrentino, M. Chevrollier, and M. Oriá, "Bistability in semiconductor lasers with polarization-rotated frequency-dependent," IEEE J. Quantum Electron. 43, 261-268 (2007).
[CrossRef]

B. Farias, T. Passerat de Silans, M. Chevrollier, and M. Oriá, "Frequency bistability of a semiconductor laser under a frequency-dependent feedback," Phys. Rev. Lett. 94, 173902 1-4 (2005).
[CrossRef]

A. F. A. da Rocha, P. C. S. Segundo, M. Chevrollier, and M. Oriá, "Diode laser coupled to an atomic line by incoherent optical negative feedback," Appl. Phys. Lett. 84, 179-181 (2004).
[CrossRef]

Orozco, L. A.

A. T. Rosenberger, L. A. Orozco, and H. J. Kimble, "Observation of absorptive bistability with two-level atoms in a ring cavity," Phys. Rev. A 28, 2569-2572 (1983).
[CrossRef]

Parmenter, Z. A.

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, "Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection," Phys. Rev. A 72, 043818 (2005).
[CrossRef]

Petriella, E.

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, "Observation of optical tristability in sodium vapors," Phys. Rev. Lett. 49, 1928-1931 (1982).
[CrossRef]

Pliska, T.

R. Badii, N. Matuschek, T. Pliska, J. Troger, and B. Schmidt, "Dynamics of multimode diode lasers with strong, frequency-selective optical feedback," Phys. Rev. E 68, 036605 (2003).
[CrossRef]

Rosenberger, A. T.

A. T. Rosenberger, L. A. Orozco, and H. J. Kimble, "Observation of absorptive bistability with two-level atoms in a ring cavity," Phys. Rev. A 28, 2569-2572 (1983).
[CrossRef]

Saboureau, P.

P. Saboureau, J.-P. Foing, and P. Schanne, "Injection-locked semiconductor lasers with delayed optoelectronic feedback," IEEE J. Quantum Electron. 33, 1582-1591 (1997).
[CrossRef]

Salieri, P.

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, "Observation of optical tristability in sodium vapors," Phys. Rev. Lett. 49, 1928-1931 (1982).
[CrossRef]

Schanne, P.

P. Saboureau, J.-P. Foing, and P. Schanne, "Injection-locked semiconductor lasers with delayed optoelectronic feedback," IEEE J. Quantum Electron. 33, 1582-1591 (1997).
[CrossRef]

Schmidt, B.

R. Badii, N. Matuschek, T. Pliska, J. Troger, and B. Schmidt, "Dynamics of multimode diode lasers with strong, frequency-selective optical feedback," Phys. Rev. E 68, 036605 (2003).
[CrossRef]

Scholz, T.

See, e. g., T. Ackemann, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, and G. L. Lippi, "Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping," Opt. Commun. 147, 411-428 (1998), and references therein.
[CrossRef]

Segundo, P. C. S.

A. F. A. da Rocha, P. C. S. Segundo, M. Chevrollier, and M. Oriá, "Diode laser coupled to an atomic line by incoherent optical negative feedback," Appl. Phys. Lett. 84, 179-181 (2004).
[CrossRef]

Sorrentino, T.

C. Masoller, T. Sorrentino, M. Chevrollier, and M. Oriá, "Bistability in semiconductor lasers with polarization-rotated frequency-dependent," IEEE J. Quantum Electron. 43, 261-268 (2007).
[CrossRef]

Spencer, P.

R. Ju, Y. Hong, and P. Spencer, "Semiconductor lasers subject to polarization-rotated optical feedback," IEE Proc.: Optoelectron. 153, 131-137 (2006).
[CrossRef]

Stolte, S.

O. K. Andersen, A. P. A. Fischer, I. C. Lane, E. Louvergneaux, S. Stolte, and D. Lenstra, "Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell," IEEE J. Quantum Electron. 35, 577-582 (1999).
[CrossRef]

Sukow, D. W.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonettev, "Square-wave self-modulation in diode lasers with polarization-rotated optical feedback," Opt. Lett. 31, 2006-2008 (2006).
[CrossRef] [PubMed]

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, "Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection," Phys. Rev. A 72, 043818 (2005).
[CrossRef]

Tredicce, J. R.

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, "Dynamical behavior of semiconductor lasers with frequency selective optical feedback," Chaos, Solitons Fractals 10, 811-818 (1999).
[CrossRef]

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. R. Tredicce, "Low frequency fluctuations and multimode operation of a semiconductor laser with optical feedback," Opt. Commun. 149, 341-347 (1998).
[CrossRef]

Troger, J.

R. Badii, N. Matuschek, T. Pliska, J. Troger, and B. Schmidt, "Dynamics of multimode diode lasers with strong, frequency-selective optical feedback," Phys. Rev. E 68, 036605 (2003).
[CrossRef]

Uchida, A.

T. Heil, A. Uchida, P. Davis, and T. Aida, "TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback," Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Van Tartwijk, G. H. M.

G. H. M. Van Tartwijk and D. Lenstra, "Semiconductor lasers with optical injection and feedback," J. Opt. B: Quantum Semiclassical Opt. 7, 87-143 (1995).
[CrossRef]

Vemuri, G.

H. Erzgraber, B. Krauskopf, D. Lenstra, A. P. A. Fischer, and G. Vemuri, "Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback," Phys. Rev. E 73, 055201(R) (2006).
[CrossRef]

A. P. A. Fischer, M. Yousefi, D. Lenstra, M. Carter, and G. Vemuri, "Filtered optical feedback induced frequency dynamics in semiconductor lasers," Phys. Rev. Lett. 92, 023901 (2004).
[CrossRef] [PubMed]

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, "Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback," IEE Proc.: Optoelectron. 148, 233-237 (2001).
[CrossRef]

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled fabry-perot interferometer," Phys. Rev. Lett. 36, 1135-1138 (1976).
[CrossRef]

Vorgerd, Ch.

See, e. g., T. Ackemann, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, and G. L. Lippi, "Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping," Opt. Commun. 147, 411-428 (1998), and references therein.
[CrossRef]

Wang, H.

H. Chang, H. Wu, C. Xie, and H. Wang, "Controlled shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system," Phys. Rev. Lett. 93, 213901 (2004).
[CrossRef] [PubMed]

Watanabe, M.

H. Yasaka, Y. Yoshikuni, and M. Watanabe, "Measurement of gain saturation coefficient of a DFB laser for lasing mode control by orthogonal polarization light," IEEE J. Quantum Electron. 27, 2248-2255 (1991).
[CrossRef]

Wu, H.

H. Chang, H. Wu, C. Xie, and H. Wang, "Controlled shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system," Phys. Rev. Lett. 93, 213901 (2004).
[CrossRef] [PubMed]

Xiao, M.

The hysteresis cycles are either counterclockwise, as in the pure absorptive hysteresis, or clockwise, occurring when the two mechanisms provoking hysteresis are present. See, for instance, A. Joshi, W. Yang, and M. Xiao, "Hysteresis loop with controllable shape and direction in an optical ring cavity," Phys. Rev. A 70, 041802(R) (2004).
[CrossRef]

A. Joshi and M. Xiao, "Optical multistability in three-level atoms inside an optical ring cavity," Phys. Rev. Lett. 91, 143904 (2003).
[CrossRef] [PubMed]

Xie, C.

H. Chang, H. Wu, C. Xie, and H. Wang, "Controlled shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system," Phys. Rev. Lett. 93, 213901 (2004).
[CrossRef] [PubMed]

Yabuzaki, T.

M. Kitano, T. Yabuzaki, and T. Ogawa, "Optical tristability," Phys. Rev. Lett. 46, 926-929 (1981).
[CrossRef]

Yang, W.

The hysteresis cycles are either counterclockwise, as in the pure absorptive hysteresis, or clockwise, occurring when the two mechanisms provoking hysteresis are present. See, for instance, A. Joshi, W. Yang, and M. Xiao, "Hysteresis loop with controllable shape and direction in an optical ring cavity," Phys. Rev. A 70, 041802(R) (2004).
[CrossRef]

Yasaka, H.

H. Yasaka, Y. Yoshikuni, and M. Watanabe, "Measurement of gain saturation coefficient of a DFB laser for lasing mode control by orthogonal polarization light," IEEE J. Quantum Electron. 27, 2248-2255 (1991).
[CrossRef]

H. Yasaka and H. Kawaguchi, "Linewidth reduction and optical frequency stabilization of a distributed feedback laser by incoherent optical negative feedback," Appl. Phys. Lett. 53, 1360-1362 (1988).
[CrossRef]

Yen, T.

D. Cheng, T. Yen, E. Liu, and K. Chuang, "Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback," IEEE Photonics Technol. Lett. 16, 1435-1437 (2004).
[CrossRef]

Yoshikuni, Y.

H. Yasaka, Y. Yoshikuni, and M. Watanabe, "Measurement of gain saturation coefficient of a DFB laser for lasing mode control by orthogonal polarization light," IEEE J. Quantum Electron. 27, 2248-2255 (1991).
[CrossRef]

Yousefi, M.

A. P. A. Fischer, M. Yousefi, D. Lenstra, M. Carter, and G. Vemuri, "Filtered optical feedback induced frequency dynamics in semiconductor lasers," Phys. Rev. Lett. 92, 023901 (2004).
[CrossRef] [PubMed]

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, "Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback," IEE Proc.: Optoelectron. 148, 233-237 (2001).
[CrossRef]

Appl. Phys. Lett.

H. Yasaka and H. Kawaguchi, "Linewidth reduction and optical frequency stabilization of a distributed feedback laser by incoherent optical negative feedback," Appl. Phys. Lett. 53, 1360-1362 (1988).
[CrossRef]

A. F. A. da Rocha, P. C. S. Segundo, M. Chevrollier, and M. Oriá, "Diode laser coupled to an atomic line by incoherent optical negative feedback," Appl. Phys. Lett. 84, 179-181 (2004).
[CrossRef]

Chaos, Solitons Fractals

M. Giudici, L. Giuggioli, C. Green, and J. R. Tredicce, "Dynamical behavior of semiconductor lasers with frequency selective optical feedback," Chaos, Solitons Fractals 10, 811-818 (1999).
[CrossRef]

IEE Proc.: Optoelectron.

R. Ju, Y. Hong, and P. Spencer, "Semiconductor lasers subject to polarization-rotated optical feedback," IEE Proc.: Optoelectron. 153, 131-137 (2006).
[CrossRef]

M. Yousefi, D. Lenstra, G. Vemuri, and A. Fischer, "Control of nonlinear dynamics of a semiconductor laser with filtered optical feedback," IEE Proc.: Optoelectron. 148, 233-237 (2001).
[CrossRef]

IEEE J. Quantum Electron.

H. Yasaka, Y. Yoshikuni, and M. Watanabe, "Measurement of gain saturation coefficient of a DFB laser for lasing mode control by orthogonal polarization light," IEEE J. Quantum Electron. 27, 2248-2255 (1991).
[CrossRef]

C. Masoller, T. Sorrentino, M. Chevrollier, and M. Oriá, "Bistability in semiconductor lasers with polarization-rotated frequency-dependent," IEEE J. Quantum Electron. 43, 261-268 (2007).
[CrossRef]

P. Saboureau, J.-P. Foing, and P. Schanne, "Injection-locked semiconductor lasers with delayed optoelectronic feedback," IEEE J. Quantum Electron. 33, 1582-1591 (1997).
[CrossRef]

O. K. Andersen, A. P. A. Fischer, I. C. Lane, E. Louvergneaux, S. Stolte, and D. Lenstra, "Experimental stability diagram of a diode laser subject to weak phase-conjugate feedback from a rubidium vapor cell," IEEE J. Quantum Electron. 35, 577-582 (1999).
[CrossRef]

R. Lang and K. Kobayashi, "External optical feedback effects on semiconductor injection laser properties," IEEE J. Quantum Electron. 16, 347-355 (1980).
[CrossRef]

IEEE Photonics Technol. Lett.

D. Cheng, T. Yen, E. Liu, and K. Chuang, "Suppressing mode hopping in semiconductor lasers by orthogonal-polarization optical feedback," IEEE Photonics Technol. Lett. 16, 1435-1437 (2004).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt.

G. H. M. Van Tartwijk and D. Lenstra, "Semiconductor lasers with optical injection and feedback," J. Opt. B: Quantum Semiclassical Opt. 7, 87-143 (1995).
[CrossRef]

Opt. Commun.

G. Huyet, S. Balle, M. Giudici, C. Green, G. Giacomelli, and J. R. Tredicce, "Low frequency fluctuations and multimode operation of a semiconductor laser with optical feedback," Opt. Commun. 149, 341-347 (1998).
[CrossRef]

J. Houlihan, G. Huyet, and J. G. McInerney, "Dynamics of a semiconductor laser with incoherent optical feedback," Opt. Commun. 199, 175-179 (2001).
[CrossRef]

See, e. g., T. Ackemann, T. Scholz, Ch. Vorgerd, J. Nalik, L. M. Hoffer, and G. L. Lippi, "Self-lensing in sodium vapor: influence of saturation, atomic diffusion and radiation trapping," Opt. Commun. 147, 411-428 (1998), and references therein.
[CrossRef]

Opt. Lett.

Phys. Rev. A

The hysteresis cycles are either counterclockwise, as in the pure absorptive hysteresis, or clockwise, occurring when the two mechanisms provoking hysteresis are present. See, for instance, A. Joshi, W. Yang, and M. Xiao, "Hysteresis loop with controllable shape and direction in an optical ring cavity," Phys. Rev. A 70, 041802(R) (2004).
[CrossRef]

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, "Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection," Phys. Rev. A 72, 043818 (2005).
[CrossRef]

A. T. Rosenberger, L. A. Orozco, and H. J. Kimble, "Observation of absorptive bistability with two-level atoms in a ring cavity," Phys. Rev. A 28, 2569-2572 (1983).
[CrossRef]

T. Heil, A. Uchida, P. Davis, and T. Aida, "TE-TM dynamics in a semiconductor laser subject to polarization-rotated optical feedback," Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Phys. Rev. E

R. Badii, N. Matuschek, T. Pliska, J. Troger, and B. Schmidt, "Dynamics of multimode diode lasers with strong, frequency-selective optical feedback," Phys. Rev. E 68, 036605 (2003).
[CrossRef]

H. Erzgraber, B. Krauskopf, D. Lenstra, A. P. A. Fischer, and G. Vemuri, "Frequency versus relaxation oscillations in a semiconductor laser with coherent filtered optical feedback," Phys. Rev. E 73, 055201(R) (2006).
[CrossRef]

Phys. Rev. Lett.

A. Joshi and M. Xiao, "Optical multistability in three-level atoms inside an optical ring cavity," Phys. Rev. Lett. 91, 143904 (2003).
[CrossRef] [PubMed]

B. Farias, T. Passerat de Silans, M. Chevrollier, and M. Oriá, "Frequency bistability of a semiconductor laser under a frequency-dependent feedback," Phys. Rev. Lett. 94, 173902 1-4 (2005).
[CrossRef]

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, "Differential gain and bistability using a sodium-filled fabry-perot interferometer," Phys. Rev. Lett. 36, 1135-1138 (1976).
[CrossRef]

A. P. A. Fischer, M. Yousefi, D. Lenstra, M. Carter, and G. Vemuri, "Filtered optical feedback induced frequency dynamics in semiconductor lasers," Phys. Rev. Lett. 92, 023901 (2004).
[CrossRef] [PubMed]

M. Kitano, T. Yabuzaki, and T. Ogawa, "Optical tristability," Phys. Rev. Lett. 46, 926-929 (1981).
[CrossRef]

S. Cecchi, G. Giusfredi, E. Petriella, and P. Salieri, "Observation of optical tristability in sodium vapors," Phys. Rev. Lett. 49, 1928-1931 (1982).
[CrossRef]

J. E. Bjorkholm and A. Ashkin, "cw self-focusing and self-trapping of light in sodium vapor," Phys. Rev. Lett. 32, 129-132 (1974).
[CrossRef]

H. Chang, H. Wu, C. Xie, and H. Wang, "Controlled shift of optical bistability hysteresis curve and storage of optical signals in a four-level atomic system," Phys. Rev. Lett. 93, 213901 (2004).
[CrossRef] [PubMed]

Other

The amplitude stability of the laser under orthogonal feedback occurs for operation above about the double of the threshold current, see .

Equation only gives the new frequency (ν) as a function of the free-laser frequency (νo). In order to reproduce the experimental transmission of the analysis filter (absorption cell, external to the feedback loop), which converts the emitted frequency ν into an amplitude signal fp(ν), we plot the lineshape fp(ν) as a function of νo.

L. A. Lugiato, "Theory of optical bistability," in Progress in Optics, E.Wolf, ed. (North-Holland, 1984), vol. 21, p. 71, and references therein.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Scheme of the optical feedback into the diode laser (DL).

Fig. 2
Fig. 2

Filter lineshape: (a) absorptive, (b) dispersive. (c) Frequency of the laser under filtered orthogonal-polarization feedback as a function of the solitary laser frequency. The arrows indicate the frequency jumps when the path followed by the system is the absorptive (I) or the dispersive (II) curve (See text). These curves correspond to experimental parameters: β = 1.5 GHz mW ; α f = 5.8 × 10 18 Hz 2 (filter cell); ϵ a = 0.32 (absorption amplitude coefficient) and ϵ d = 0.37 (dispersion amplitude coefficient); κ o = 5.4 × 10 2 .

Fig. 3
Fig. 3

Scheme of the feedback loop. A beam with orthogonal polarization, filtered by a resonant atomic vapor, is sent back into the diode laser (DL). The feedback beam is analyzed by a photodetector ( PD 1 ) , and by a 3 μ m aperture (MA) followed by a photodetector ( PD 2 ) . See, at left, the respective spectra, without feedback. PD 3 measures the probe cell (out of the feedback loop) transmission. PM, power meter; G-F, Glan–Foucault polarizer; M, mirror; OI, optical isolator; λ 2 , half-wave plate; BS, beam-spliter; ☉ (↔) stands for orthogonal (parallel) laser polarization.

Fig. 4
Fig. 4

(a) Multistability curve probed by the out-of-the-loop Cs cell; (b) Theoretical fit, laser frequency analyzed by a Gaussian-shaped frequency discriminator ( α p = 2.1 × 10 17 Hz 2 , used for the fit). The width of the large arrows accounts for the laser frequency jitter and indicates regions for the jumps to occur. The experimental parameters as well as the positions in the spectra (indicated by capital letters) are the same as in Fig. 2. A small scaling factor is used to adjust the horizontal scale of the spectrum (b) to the experimental one (a) (see text).

Fig. 5
Fig. 5

Hysteretic cycles when both absorptive and dispersive effects are important. (a), (b) Different cycles observed when limiting the scanning around the frequency jump BC. β = 1.3 GHz mW ; α f = 6.56 × 10 18 Hz 2 , κ o = 46.2 × 10 3 ; α a = 0.3 . (c) Complete cycle; (d) Superposition of the (a)–(c) cycles. Inset, Detail of the calculated spectra [33].

Fig. 6
Fig. 6

Bistable hysteretic cycle as a function of the feedback power. Left, probe cell transmission; right, calculated spectra, with β = 0.80 GHz mW and ϵ a = 0.34 .

Fig. 7
Fig. 7

Multistable hysteretic cycle as a function of the feedback power. Left, probe cell transmission; right, calculated spectra, where the dotted lines indicate the frequency jumps.

Fig. 8
Fig. 8

Calculated spectra for different values of the feedback power and of the filter coefficient α f due to the (a) imaginary and (b) real parts of the atomic vapor index of refraction. Note the linear displacement of the resonant frequency, related to the free laser ν o central resonance. For each power we show three spectra for different values of the α f coefficient. For clarity, we omitted the arrows indicating the frequency jumps. (c) Hysteresis range [measured in the spectra of (a) and (b)] in the frequency of the laser under orthogonal-polarization filtered-feedback, probef by an absorptive frequency discriminator. The values of the α f coefficient are 11.75 (circles) and 8.75 (squares) owing to absorptive (full symbols) or dispersive filter response (empty symbols).

Equations (1)

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ν = ν 0 β κ 0 [ 1 ϵ i f i ( ν ) ] P ,

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