Abstract

We theoretically discuss the impact of the cavity configuration on the possible longitudinal mode multistability in homogeneously broadened lasers. Our analysis is based on the most general form of a Travelling-Wave Model for which we present a method that allows us to evaluate the monochromatic solutions as well as their eigenvalue spectrum. We find, in agreement with recent experimental reports, that multistability is more easily reached in Ring than in Fabry-Pérot cavities which we attribute to the different amount of Spatial-Hole Burning in each configuration.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. J. Born, S. Yu, M. Sorel, and P. J. R. Laybourn, "Controllable and stable mode selection in a semiconductor ring laser by injection locking," in CLEO Proceedings, paper CWK4, (2003).
  2. C. J. Born, M. Hill, S. Yu, and M. Sorel, "Study of longitudinal mode coupling in a semiconductor ring laser," in Proceedings of the 17th Annual Meeting of the IEEE-LEOS, pp. 27-28 (2004).
  3. C. J. Born, M. Sorel, and S. Yu, "Linear and nonlinear mode interactions in a semiconductor ring laser," IEEE J. Quantum Electron. 41, 261 (2005).
    [CrossRef]
  4. Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, "A novel semiconductor ring laser device aimed for all-optical signal processing," in ECOC Proceedings, paper Th.1.C.4 (2008).
  5. M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, "Unidirectional bistability in semiconductor waveguides lasers," Appl. Phys. Lett. 80(17), 3051-3053 (2002).
    [CrossRef]
  6. K. Huybrechts, B. Maes, G. Morthier, and R. Baets, "Tristable all-optical flip-flop using coupled non linear cavities," in Winter Topical Meeting Series (IEEE, New York, 2008), p. 1617.
  7. L. M. Narducci, J. R. Tredicce, L. A. Lugiato, N. B. Abraham, and D. K. Bandy, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33, 1842 (1986).
    [CrossRef] [PubMed]
  8. L. A. Kotomtseva, "Steady states for longitudinal modes and dynamics of a laser with a saturable absorbent," Quantum Semiclass. Opt. 10, 331 (1998).
    [CrossRef]
  9. R. Lang, and K. Kobayashi, "External optical feedback effects on semiconductor injection-laser properties," IEEE J. Quantum Electron. 16, 347 (1980).
    [CrossRef]
  10. A. Loose, B. K. Goswami, H.-J. Wünsche, and F. Henneberger, "Tristability of a semiconductor laser due to time-delayed optical feedback," Phys. Rev. E 79, 036211 (2009).
    [CrossRef]
  11. K. P. Komarov, "Multistable single-mode emission from solid-state state lasers," Quantum Electron. 24(11), 975-976 (1994).
    [CrossRef]
  12. J. R. Tredicce, L. M. Narducci, N. B. Abraham, D. K. Bandy, and L. A. Lugiato, "Experimental-evidence of mode competition leading to optical bistability in homogenously broadened lasers," Opt. Commun. 56, 435 (1986).
    [CrossRef]
  13. M. Yamada, "Theory of mode competition noise in semiconductor injection-lasers," IEEE J. Quantum Electron. 22, 1052 (1986).
    [CrossRef]
  14. F. Pedaci, S. Lepri, S. Balle, G. Giacomelli, M. Giudici, and J. R. Tredicce, "Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser," Phys. Rev. E 73, 041101 (2006).
    [CrossRef]
  15. T. Acsente, "Laser diode intensity noise induced by mode hopping," Romanian Rep. Phys. 59, 87 (2007).
  16. Ya. I. Khanin, Fundamentals of Laser Dynamics, Cambridge Int. Sci. Pub. Ltd., Cambridge, UK (2006).
  17. H. Fu, and H. Haken, "Multifrequency operations in a short-cavity standing-wave laser," Phys. Rev. A 43, 2446-2454 (1991).
    [CrossRef] [PubMed]
  18. L. A. Lugiato, L. M. Narducci, and M. F. Squicciarini, "Exact linear-stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser," Phys. Rev. A 34, 3101 (1986).
    [CrossRef] [PubMed]
  19. G. J. de Valcárcel, E. Roldán, and F. Prati, "Risken-Nummedal-Graham-Haken instability in class B lasers," Opt. Commun. 163, 5-8 (1999).
    [CrossRef]
  20. H. Risken, and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662 (1968).
    [CrossRef]
  21. R. Graham, and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420 (1968).
    [CrossRef]
  22. A. Pérez-Serrano, J. Javaloyes, and S. Balle, "Bichromatic emission and multimode dynamics in bidirectional Ring Lasers," Phys. Rev. A 81, 043817 (2010).
    [CrossRef]
  23. J. Javaloyes, and S. Balle, "Quasiequilibrium time-domain susceptibility of semiconductor quantum wells," Phys. Rev. A 81, 062505 (2010).
    [CrossRef]
  24. S. Fürst, A. Pérez-Serrano, A. Scirè, M. Sorel, and S. Balle, "Modal structure, directional and wavelength jumps of integrated semiconductor ring lasers: Experiments and theory," Appl. Phys. Lett. 93, 251109 (2008).
    [CrossRef]
  25. R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, (2007).
    [CrossRef] [PubMed]
  26. J. W. Eaton, GNU Octave Manual, Network Theory Limited, (2002).

2010 (2)

A. Pérez-Serrano, J. Javaloyes, and S. Balle, "Bichromatic emission and multimode dynamics in bidirectional Ring Lasers," Phys. Rev. A 81, 043817 (2010).
[CrossRef]

J. Javaloyes, and S. Balle, "Quasiequilibrium time-domain susceptibility of semiconductor quantum wells," Phys. Rev. A 81, 062505 (2010).
[CrossRef]

2009 (1)

A. Loose, B. K. Goswami, H.-J. Wünsche, and F. Henneberger, "Tristability of a semiconductor laser due to time-delayed optical feedback," Phys. Rev. E 79, 036211 (2009).
[CrossRef]

2008 (1)

S. Fürst, A. Pérez-Serrano, A. Scirè, M. Sorel, and S. Balle, "Modal structure, directional and wavelength jumps of integrated semiconductor ring lasers: Experiments and theory," Appl. Phys. Lett. 93, 251109 (2008).
[CrossRef]

2007 (1)

T. Acsente, "Laser diode intensity noise induced by mode hopping," Romanian Rep. Phys. 59, 87 (2007).

2006 (1)

F. Pedaci, S. Lepri, S. Balle, G. Giacomelli, M. Giudici, and J. R. Tredicce, "Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser," Phys. Rev. E 73, 041101 (2006).
[CrossRef]

2005 (1)

C. J. Born, M. Sorel, and S. Yu, "Linear and nonlinear mode interactions in a semiconductor ring laser," IEEE J. Quantum Electron. 41, 261 (2005).
[CrossRef]

2002 (1)

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, "Unidirectional bistability in semiconductor waveguides lasers," Appl. Phys. Lett. 80(17), 3051-3053 (2002).
[CrossRef]

1999 (1)

G. J. de Valcárcel, E. Roldán, and F. Prati, "Risken-Nummedal-Graham-Haken instability in class B lasers," Opt. Commun. 163, 5-8 (1999).
[CrossRef]

1998 (1)

L. A. Kotomtseva, "Steady states for longitudinal modes and dynamics of a laser with a saturable absorbent," Quantum Semiclass. Opt. 10, 331 (1998).
[CrossRef]

1994 (1)

K. P. Komarov, "Multistable single-mode emission from solid-state state lasers," Quantum Electron. 24(11), 975-976 (1994).
[CrossRef]

1991 (1)

H. Fu, and H. Haken, "Multifrequency operations in a short-cavity standing-wave laser," Phys. Rev. A 43, 2446-2454 (1991).
[CrossRef] [PubMed]

1986 (4)

L. A. Lugiato, L. M. Narducci, and M. F. Squicciarini, "Exact linear-stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser," Phys. Rev. A 34, 3101 (1986).
[CrossRef] [PubMed]

J. R. Tredicce, L. M. Narducci, N. B. Abraham, D. K. Bandy, and L. A. Lugiato, "Experimental-evidence of mode competition leading to optical bistability in homogenously broadened lasers," Opt. Commun. 56, 435 (1986).
[CrossRef]

M. Yamada, "Theory of mode competition noise in semiconductor injection-lasers," IEEE J. Quantum Electron. 22, 1052 (1986).
[CrossRef]

L. M. Narducci, J. R. Tredicce, L. A. Lugiato, N. B. Abraham, and D. K. Bandy, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33, 1842 (1986).
[CrossRef] [PubMed]

1980 (1)

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

1968 (2)

H. Risken, and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662 (1968).
[CrossRef]

R. Graham, and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420 (1968).
[CrossRef]

Abraham, N. B.

L. M. Narducci, J. R. Tredicce, L. A. Lugiato, N. B. Abraham, and D. K. Bandy, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33, 1842 (1986).
[CrossRef] [PubMed]

J. R. Tredicce, L. M. Narducci, N. B. Abraham, D. K. Bandy, and L. A. Lugiato, "Experimental-evidence of mode competition leading to optical bistability in homogenously broadened lasers," Opt. Commun. 56, 435 (1986).
[CrossRef]

Acsente, T.

T. Acsente, "Laser diode intensity noise induced by mode hopping," Romanian Rep. Phys. 59, 87 (2007).

Balle, S.

J. Javaloyes, and S. Balle, "Quasiequilibrium time-domain susceptibility of semiconductor quantum wells," Phys. Rev. A 81, 062505 (2010).
[CrossRef]

A. Pérez-Serrano, J. Javaloyes, and S. Balle, "Bichromatic emission and multimode dynamics in bidirectional Ring Lasers," Phys. Rev. A 81, 043817 (2010).
[CrossRef]

S. Fürst, A. Pérez-Serrano, A. Scirè, M. Sorel, and S. Balle, "Modal structure, directional and wavelength jumps of integrated semiconductor ring lasers: Experiments and theory," Appl. Phys. Lett. 93, 251109 (2008).
[CrossRef]

F. Pedaci, S. Lepri, S. Balle, G. Giacomelli, M. Giudici, and J. R. Tredicce, "Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser," Phys. Rev. E 73, 041101 (2006).
[CrossRef]

Bandy, D. K.

J. R. Tredicce, L. M. Narducci, N. B. Abraham, D. K. Bandy, and L. A. Lugiato, "Experimental-evidence of mode competition leading to optical bistability in homogenously broadened lasers," Opt. Commun. 56, 435 (1986).
[CrossRef]

L. M. Narducci, J. R. Tredicce, L. A. Lugiato, N. B. Abraham, and D. K. Bandy, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33, 1842 (1986).
[CrossRef] [PubMed]

Born, C. J.

C. J. Born, M. Sorel, and S. Yu, "Linear and nonlinear mode interactions in a semiconductor ring laser," IEEE J. Quantum Electron. 41, 261 (2005).
[CrossRef]

de Valcárcel, G. J.

G. J. de Valcárcel, E. Roldán, and F. Prati, "Risken-Nummedal-Graham-Haken instability in class B lasers," Opt. Commun. 163, 5-8 (1999).
[CrossRef]

Donati, S.

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, "Unidirectional bistability in semiconductor waveguides lasers," Appl. Phys. Lett. 80(17), 3051-3053 (2002).
[CrossRef]

Fu, H.

H. Fu, and H. Haken, "Multifrequency operations in a short-cavity standing-wave laser," Phys. Rev. A 43, 2446-2454 (1991).
[CrossRef] [PubMed]

Fürst, S.

S. Fürst, A. Pérez-Serrano, A. Scirè, M. Sorel, and S. Balle, "Modal structure, directional and wavelength jumps of integrated semiconductor ring lasers: Experiments and theory," Appl. Phys. Lett. 93, 251109 (2008).
[CrossRef]

Giacomelli, G.

F. Pedaci, S. Lepri, S. Balle, G. Giacomelli, M. Giudici, and J. R. Tredicce, "Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser," Phys. Rev. E 73, 041101 (2006).
[CrossRef]

Giudici, M.

F. Pedaci, S. Lepri, S. Balle, G. Giacomelli, M. Giudici, and J. R. Tredicce, "Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser," Phys. Rev. E 73, 041101 (2006).
[CrossRef]

Giuliani, G.

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, "Unidirectional bistability in semiconductor waveguides lasers," Appl. Phys. Lett. 80(17), 3051-3053 (2002).
[CrossRef]

Goswami, B. K.

A. Loose, B. K. Goswami, H.-J. Wünsche, and F. Henneberger, "Tristability of a semiconductor laser due to time-delayed optical feedback," Phys. Rev. E 79, 036211 (2009).
[CrossRef]

Graham, R.

R. Graham, and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420 (1968).
[CrossRef]

Haken, H.

H. Fu, and H. Haken, "Multifrequency operations in a short-cavity standing-wave laser," Phys. Rev. A 43, 2446-2454 (1991).
[CrossRef] [PubMed]

R. Graham, and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420 (1968).
[CrossRef]

Henneberger, F.

A. Loose, B. K. Goswami, H.-J. Wünsche, and F. Henneberger, "Tristability of a semiconductor laser due to time-delayed optical feedback," Phys. Rev. E 79, 036211 (2009).
[CrossRef]

Javaloyes, J.

A. Pérez-Serrano, J. Javaloyes, and S. Balle, "Bichromatic emission and multimode dynamics in bidirectional Ring Lasers," Phys. Rev. A 81, 043817 (2010).
[CrossRef]

J. Javaloyes, and S. Balle, "Quasiequilibrium time-domain susceptibility of semiconductor quantum wells," Phys. Rev. A 81, 062505 (2010).
[CrossRef]

Kobayashi, K.

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

Komarov, K. P.

K. P. Komarov, "Multistable single-mode emission from solid-state state lasers," Quantum Electron. 24(11), 975-976 (1994).
[CrossRef]

Kotomtseva, L. A.

L. A. Kotomtseva, "Steady states for longitudinal modes and dynamics of a laser with a saturable absorbent," Quantum Semiclass. Opt. 10, 331 (1998).
[CrossRef]

Lang, R.

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

Laybourn, P. J. R.

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, "Unidirectional bistability in semiconductor waveguides lasers," Appl. Phys. Lett. 80(17), 3051-3053 (2002).
[CrossRef]

Lepri, S.

F. Pedaci, S. Lepri, S. Balle, G. Giacomelli, M. Giudici, and J. R. Tredicce, "Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser," Phys. Rev. E 73, 041101 (2006).
[CrossRef]

Loose, A.

A. Loose, B. K. Goswami, H.-J. Wünsche, and F. Henneberger, "Tristability of a semiconductor laser due to time-delayed optical feedback," Phys. Rev. E 79, 036211 (2009).
[CrossRef]

Lugiato, L. A.

L. M. Narducci, J. R. Tredicce, L. A. Lugiato, N. B. Abraham, and D. K. Bandy, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33, 1842 (1986).
[CrossRef] [PubMed]

J. R. Tredicce, L. M. Narducci, N. B. Abraham, D. K. Bandy, and L. A. Lugiato, "Experimental-evidence of mode competition leading to optical bistability in homogenously broadened lasers," Opt. Commun. 56, 435 (1986).
[CrossRef]

L. A. Lugiato, L. M. Narducci, and M. F. Squicciarini, "Exact linear-stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser," Phys. Rev. A 34, 3101 (1986).
[CrossRef] [PubMed]

Narducci, L. M.

L. A. Lugiato, L. M. Narducci, and M. F. Squicciarini, "Exact linear-stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser," Phys. Rev. A 34, 3101 (1986).
[CrossRef] [PubMed]

J. R. Tredicce, L. M. Narducci, N. B. Abraham, D. K. Bandy, and L. A. Lugiato, "Experimental-evidence of mode competition leading to optical bistability in homogenously broadened lasers," Opt. Commun. 56, 435 (1986).
[CrossRef]

L. M. Narducci, J. R. Tredicce, L. A. Lugiato, N. B. Abraham, and D. K. Bandy, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33, 1842 (1986).
[CrossRef] [PubMed]

Nummedal, K.

H. Risken, and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662 (1968).
[CrossRef]

Pedaci, F.

F. Pedaci, S. Lepri, S. Balle, G. Giacomelli, M. Giudici, and J. R. Tredicce, "Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser," Phys. Rev. E 73, 041101 (2006).
[CrossRef]

Pérez-Serrano, A.

A. Pérez-Serrano, J. Javaloyes, and S. Balle, "Bichromatic emission and multimode dynamics in bidirectional Ring Lasers," Phys. Rev. A 81, 043817 (2010).
[CrossRef]

S. Fürst, A. Pérez-Serrano, A. Scirè, M. Sorel, and S. Balle, "Modal structure, directional and wavelength jumps of integrated semiconductor ring lasers: Experiments and theory," Appl. Phys. Lett. 93, 251109 (2008).
[CrossRef]

Prati, F.

G. J. de Valcárcel, E. Roldán, and F. Prati, "Risken-Nummedal-Graham-Haken instability in class B lasers," Opt. Commun. 163, 5-8 (1999).
[CrossRef]

Risken, H.

H. Risken, and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662 (1968).
[CrossRef]

Roldán, E.

G. J. de Valcárcel, E. Roldán, and F. Prati, "Risken-Nummedal-Graham-Haken instability in class B lasers," Opt. Commun. 163, 5-8 (1999).
[CrossRef]

Scirè, A.

S. Fürst, A. Pérez-Serrano, A. Scirè, M. Sorel, and S. Balle, "Modal structure, directional and wavelength jumps of integrated semiconductor ring lasers: Experiments and theory," Appl. Phys. Lett. 93, 251109 (2008).
[CrossRef]

Sorel, M.

S. Fürst, A. Pérez-Serrano, A. Scirè, M. Sorel, and S. Balle, "Modal structure, directional and wavelength jumps of integrated semiconductor ring lasers: Experiments and theory," Appl. Phys. Lett. 93, 251109 (2008).
[CrossRef]

C. J. Born, M. Sorel, and S. Yu, "Linear and nonlinear mode interactions in a semiconductor ring laser," IEEE J. Quantum Electron. 41, 261 (2005).
[CrossRef]

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, "Unidirectional bistability in semiconductor waveguides lasers," Appl. Phys. Lett. 80(17), 3051-3053 (2002).
[CrossRef]

Squicciarini, M. F.

L. A. Lugiato, L. M. Narducci, and M. F. Squicciarini, "Exact linear-stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser," Phys. Rev. A 34, 3101 (1986).
[CrossRef] [PubMed]

Tredicce, J. R.

F. Pedaci, S. Lepri, S. Balle, G. Giacomelli, M. Giudici, and J. R. Tredicce, "Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser," Phys. Rev. E 73, 041101 (2006).
[CrossRef]

J. R. Tredicce, L. M. Narducci, N. B. Abraham, D. K. Bandy, and L. A. Lugiato, "Experimental-evidence of mode competition leading to optical bistability in homogenously broadened lasers," Opt. Commun. 56, 435 (1986).
[CrossRef]

L. M. Narducci, J. R. Tredicce, L. A. Lugiato, N. B. Abraham, and D. K. Bandy, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33, 1842 (1986).
[CrossRef] [PubMed]

Wünsche, H.-J.

A. Loose, B. K. Goswami, H.-J. Wünsche, and F. Henneberger, "Tristability of a semiconductor laser due to time-delayed optical feedback," Phys. Rev. E 79, 036211 (2009).
[CrossRef]

Yamada, M.

M. Yamada, "Theory of mode competition noise in semiconductor injection-lasers," IEEE J. Quantum Electron. 22, 1052 (1986).
[CrossRef]

Yu, S.

C. J. Born, M. Sorel, and S. Yu, "Linear and nonlinear mode interactions in a semiconductor ring laser," IEEE J. Quantum Electron. 41, 261 (2005).
[CrossRef]

Appl. Phys. Lett. (2)

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, "Unidirectional bistability in semiconductor waveguides lasers," Appl. Phys. Lett. 80(17), 3051-3053 (2002).
[CrossRef]

S. Fürst, A. Pérez-Serrano, A. Scirè, M. Sorel, and S. Balle, "Modal structure, directional and wavelength jumps of integrated semiconductor ring lasers: Experiments and theory," Appl. Phys. Lett. 93, 251109 (2008).
[CrossRef]

IEEE J. Quantum Electron. (3)

C. J. Born, M. Sorel, and S. Yu, "Linear and nonlinear mode interactions in a semiconductor ring laser," IEEE J. Quantum Electron. 41, 261 (2005).
[CrossRef]

M. Yamada, "Theory of mode competition noise in semiconductor injection-lasers," IEEE J. Quantum Electron. 22, 1052 (1986).
[CrossRef]

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

J. Appl. Phys. (1)

H. Risken, and K. Nummedal, "Self-pulsing in lasers," J. Appl. Phys. 39, 4662 (1968).
[CrossRef]

Opt. Commun. (2)

J. R. Tredicce, L. M. Narducci, N. B. Abraham, D. K. Bandy, and L. A. Lugiato, "Experimental-evidence of mode competition leading to optical bistability in homogenously broadened lasers," Opt. Commun. 56, 435 (1986).
[CrossRef]

G. J. de Valcárcel, E. Roldán, and F. Prati, "Risken-Nummedal-Graham-Haken instability in class B lasers," Opt. Commun. 163, 5-8 (1999).
[CrossRef]

Phys. Rev. A (5)

A. Pérez-Serrano, J. Javaloyes, and S. Balle, "Bichromatic emission and multimode dynamics in bidirectional Ring Lasers," Phys. Rev. A 81, 043817 (2010).
[CrossRef]

J. Javaloyes, and S. Balle, "Quasiequilibrium time-domain susceptibility of semiconductor quantum wells," Phys. Rev. A 81, 062505 (2010).
[CrossRef]

H. Fu, and H. Haken, "Multifrequency operations in a short-cavity standing-wave laser," Phys. Rev. A 43, 2446-2454 (1991).
[CrossRef] [PubMed]

L. A. Lugiato, L. M. Narducci, and M. F. Squicciarini, "Exact linear-stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser," Phys. Rev. A 34, 3101 (1986).
[CrossRef] [PubMed]

L. M. Narducci, J. R. Tredicce, L. A. Lugiato, N. B. Abraham, and D. K. Bandy, "Mode-mode competition and unstable behavior in a homogeneously broadened ring laser," Phys. Rev. A 33, 1842 (1986).
[CrossRef] [PubMed]

Phys. Rev. E (2)

A. Loose, B. K. Goswami, H.-J. Wünsche, and F. Henneberger, "Tristability of a semiconductor laser due to time-delayed optical feedback," Phys. Rev. E 79, 036211 (2009).
[CrossRef]

F. Pedaci, S. Lepri, S. Balle, G. Giacomelli, M. Giudici, and J. R. Tredicce, "Multiplicative noise in the longitudinal mode dynamics of a bulk semiconductor laser," Phys. Rev. E 73, 041101 (2006).
[CrossRef]

Quantum Electron. (1)

K. P. Komarov, "Multistable single-mode emission from solid-state state lasers," Quantum Electron. 24(11), 975-976 (1994).
[CrossRef]

Quantum Semiclass. Opt. (1)

L. A. Kotomtseva, "Steady states for longitudinal modes and dynamics of a laser with a saturable absorbent," Quantum Semiclass. Opt. 10, 331 (1998).
[CrossRef]

Romanian Rep. Phys. (1)

T. Acsente, "Laser diode intensity noise induced by mode hopping," Romanian Rep. Phys. 59, 87 (2007).

Z. Phys. (1)

R. Graham, and H. Haken, "Quantum theory of light propagation in a fluctuating laser-active medium," Z. Phys. 213, 420 (1968).
[CrossRef]

Other (7)

R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, (2007).
[CrossRef] [PubMed]

J. W. Eaton, GNU Octave Manual, Network Theory Limited, (2002).

Ya. I. Khanin, Fundamentals of Laser Dynamics, Cambridge Int. Sci. Pub. Ltd., Cambridge, UK (2006).

K. Huybrechts, B. Maes, G. Morthier, and R. Baets, "Tristable all-optical flip-flop using coupled non linear cavities," in Winter Topical Meeting Series (IEEE, New York, 2008), p. 1617.

Z. Wang, G. Yuan, G. Verschaffelt, J. Danckaert, and S. Yu, "A novel semiconductor ring laser device aimed for all-optical signal processing," in ECOC Proceedings, paper Th.1.C.4 (2008).

C. J. Born, S. Yu, M. Sorel, and P. J. R. Laybourn, "Controllable and stable mode selection in a semiconductor ring laser by injection locking," in CLEO Proceedings, paper CWK4, (2003).

C. J. Born, M. Hill, S. Yu, and M. Sorel, "Study of longitudinal mode coupling in a semiconductor ring laser," in Proceedings of the 17th Annual Meeting of the IEEE-LEOS, pp. 27-28 (2004).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

General cavity structure and boundary conditions.

Fig. 2
Fig. 2

(a) Numerical bifurcation diagram for mode m = 2 for a ring laser, g = 4, γ = 250, α = 2.03, ɛ = 0.05, η = 10, t+ = t = 0.98 and r+ = r = 0.01. The threshold value is Jth = 0.51. (b) Real versus imaginary part of the eigenvalues for J = 3. Eigenvalues in blue (red) have Re(λ) < 0 (Re(λ) > 0). (c) Same as panel (b) for J = 4.

Fig. 3
Fig. 3

Bifurcation diagram for the first modes of a ring laser (a) with the parameters of Fig. 2 and for an equivalent FP laser (b), g = 2, γ = 125, α = 1.01, ɛ = 0.025, η = 5, t± = 0 and r± = 0.99. (c) <|D2|> is the average of |D2| along the cavity for cases (a) and (b).

Fig. 4
Fig. 4

Bifurcation diagram for: (a) ring laser with parameters g = 4, t± = 0.6, r± = 0.01, γ = 250, α = 1.55, ɛ = 0.05, η = 10; (b) equivalent symmetric FP with α = 0.51, η = 5 and r± = 0.6; (c) equivalent asymmetric FP with α = 0.21, η = 5 and r+ = 0.99 and r = 0.2. The threshold value is Jth = 0.51. (d) <|D2|> vs J for these lasers.

Fig. 5
Fig. 5

Bifurcation diagram for the first three modes for a symmetric (a) and asymmetric (b) Fabry-Pérot lasers. In both cases η = 10, for other parameters see Fig. 4. (c) <|D2|> vs J for the FPs (a) and (b).

Equations (6)

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

( ± s + τ ) A ± = B ± α A ± ,
γ 1 τ B ± = ( 1 + i δ ) B ± + g ( D 0 A ± + D ± 2 A ) ,
ɛ 1 τ D 0 = J D 0 ( A + B + * + A B * + c . c . ) ,
η 1 τ D ± 2 = D ± 2 ɛ η 1 ( A ± B * + A * B ± ) ,
ω m ± = 2 π m 1 + α tot ± / γ , J m ± = α tot ± g [ 1 + ( ω m ± γ ) 2 ] ,
ω m = π m 1 + α tot / γ , J m = α tot g [ 1 + ( ω m γ ) 2 ] .

Metrics