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 OSA

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References

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  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]

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]

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).

Baets, R.

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.

Balle, S.

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]

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, 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).

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]

Danckaert, J.

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).

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]

Eaton, J. W.

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

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]

Hill, M.

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).

Huybrechts, K.

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.

Javaloyes, J.

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]

Khanin, Ya. I.

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

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]

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).

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]

LeVeque, R. J.

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]

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]

Maes, B.

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.

Morthier, G.

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.

Narducci, L. M.

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]

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]

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]

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]

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).

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. Sorel, and S. Yu, “Linear and nonlinear mode interactions in a semiconductor ring laser,” IEEE J. Quantum Electron.41, 261 (2005).
[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]

Verschaffelt, G.

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).

Wang, Z.

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).

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.

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, M. Sorel, and S. Yu, “Linear and nonlinear mode interactions in a semiconductor ring laser,” IEEE J. Quantum Electron.41, 261 (2005).
[Crossref]

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).

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).

Yuan, G.

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).

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]

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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)

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( ± 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 ] .

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