Abstract

Multimode dynamics in bidirectional laser cavities can be accurately described by folding space into time delay. This results in a set of delayed algebraic equations that preserve the dynamics of all cavity modes while drastically reducing number of degrees of freedom. This reduction allows for both linear stability analysis and bifurcation diagram reconstruction, as well as integration times reduced by orders of magnitude.

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  1. R. Linke, B. Kasper, C. Burrus, I. Kaminow, J.-S. Ko, and T. Lee, “Mode power partition events in nearly single-frequency lasers,” J. Lightwave Technol. 3, 706–712 (1985).
    [CrossRef]
  2. M. Ohtsu, Y. Teramachi, Y. Otsuka, and A. Osaki, “Analyses of mode-hopping phenomena in an AlGaAs laser,” IEEE J. Quantum. Elect. 22, 535–543 (1986).
    [CrossRef]
  3. L. Furfaro, F. Pedaci, M. Giudici, X. Hachair, J. Tredicce, and S. Balle, “Mode-switching in semiconductor lasers,” IEEE J. Quantum. Elect. 40, 1365–1376 (2004).
    [CrossRef]
  4. L. E. Hargrove, R. L. Fork, and M. A. Pollack, “Locking of he-ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
    [CrossRef]
  5. H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000).
    [CrossRef]
  6. E. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. Wang, “Auto97: Continuation and bifurcation software for ordinary differential equations,” (2011).
  7. K. Engelborghs, T. Luzyanina, and G. Samaey, “Dde-biftool v. 2.00: a matlab package for bifurcation analysis of delay differential equations,” Tech. Rep., Department of Computer Science, K.U.Leuven, Belgium. (2001).
  8. J. A. Fleck, “Emission of pulse trains by Q-switched lasers,” Phys. Rev. Lett. 21, 131–133 (1968).
    [CrossRef]
  9. J. Javaloyes and S. Balle, “Mode-locking in Fabry-Pérot lasers,” IEEE J. Quantum Electron. 46, 1023–1030 (2010).
    [CrossRef]
  10. A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers,” Phys. Rev. A 81, 043817 (2010).
    [CrossRef]
  11. J. Javaloyes and S. Balle, “Quasiequilibrium time-domain susceptibility of semiconductor quantum wells,” Phys. Rev. A 81, 062505 (2010).
    [CrossRef]
  12. P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
    [CrossRef]
  13. J. Javaloyes and S. Balle, “All-optical directional switching of bistable semiconductor ring lasers,” IEEE J. Quantum Electron 47, 1078 –1085 (2011).
    [CrossRef]
  14. A.G. Vladimirov, A.S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser,” IEEE J. Quantum Electron 45, 462 –468 (2009).
    [CrossRef]
  15. L. Narducci and N. B. Abraham, Laser Physics and Laser Instabilities (World Scientific, Singapore, 1988).
  16. J. Mulet and S. Balle, “Mode locking dynamics in electrically-driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148–1156 (2005).
    [CrossRef]
  17. L. A. Lugiato and F. Prati, “Difference differential equations for a resonator with a very thin nonlinear medium,” Phys. Rev. Lett. 104, 233902 (2010).
    [CrossRef] [PubMed]
  18. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16, 347–355 (1980).
    [CrossRef]
  19. A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72, 033808 (2005).
    [CrossRef]
  20. M. Rossetti, P. Bardella, and I. Montrosset, “Modeling passive mode-locking in quantum dot lasers: A comparison between a finite-difference traveling-wave model and a delayed differential equation approach,” IEEE J. Quantum. Electron 47, 569 –576 (2011).
    [CrossRef]
  21. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 2007.
  22. J. Javaloyes and S. Balle, “Freetwm: a simulation tool for semiconductor lasers.” (2012). Available at http://nova.uib.es/ONL/Softwares/Softwares.html .
  23. A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Pérot lasers: the effect of spatial hole burning,” Opt. Express 19, 3284–3289 (2011).
    [CrossRef] [PubMed]
  24. S. Balle, “Simple analytical approximations for the gain and refractive index spectra in quantum well lasers,” Phys. Rev. A 57, 1304–1312 (1998).
    [CrossRef]

2011

P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
[CrossRef]

J. Javaloyes and S. Balle, “All-optical directional switching of bistable semiconductor ring lasers,” IEEE J. Quantum Electron 47, 1078 –1085 (2011).
[CrossRef]

M. Rossetti, P. Bardella, and I. Montrosset, “Modeling passive mode-locking in quantum dot lasers: A comparison between a finite-difference traveling-wave model and a delayed differential equation approach,” IEEE J. Quantum. Electron 47, 569 –576 (2011).
[CrossRef]

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Pérot lasers: the effect of spatial hole burning,” Opt. Express 19, 3284–3289 (2011).
[CrossRef] [PubMed]

2010

L. A. Lugiato and F. Prati, “Difference differential equations for a resonator with a very thin nonlinear medium,” Phys. Rev. Lett. 104, 233902 (2010).
[CrossRef] [PubMed]

J. Javaloyes and S. Balle, “Mode-locking in Fabry-Pérot lasers,” IEEE J. Quantum Electron. 46, 1023–1030 (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]

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

2009

A.G. Vladimirov, A.S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser,” IEEE J. Quantum Electron 45, 462 –468 (2009).
[CrossRef]

2005

J. Mulet and S. Balle, “Mode locking dynamics in electrically-driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148–1156 (2005).
[CrossRef]

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72, 033808 (2005).
[CrossRef]

2004

L. Furfaro, F. Pedaci, M. Giudici, X. Hachair, J. Tredicce, and S. Balle, “Mode-switching in semiconductor lasers,” IEEE J. Quantum. Elect. 40, 1365–1376 (2004).
[CrossRef]

2000

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000).
[CrossRef]

1998

S. Balle, “Simple analytical approximations for the gain and refractive index spectra in quantum well lasers,” Phys. Rev. A 57, 1304–1312 (1998).
[CrossRef]

1986

M. Ohtsu, Y. Teramachi, Y. Otsuka, and A. Osaki, “Analyses of mode-hopping phenomena in an AlGaAs laser,” IEEE J. Quantum. Elect. 22, 535–543 (1986).
[CrossRef]

1985

R. Linke, B. Kasper, C. Burrus, I. Kaminow, J.-S. Ko, and T. Lee, “Mode power partition events in nearly single-frequency lasers,” J. Lightwave Technol. 3, 706–712 (1985).
[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]

1968

J. A. Fleck, “Emission of pulse trains by Q-switched lasers,” Phys. Rev. Lett. 21, 131–133 (1968).
[CrossRef]

1964

L. E. Hargrove, R. L. Fork, and M. A. Pollack, “Locking of he-ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[CrossRef]

Abraham, N. B.

L. Narducci and N. B. Abraham, Laser Physics and Laser Instabilities (World Scientific, Singapore, 1988).

Balle, S.

J. Javaloyes and S. Balle, “All-optical directional switching of bistable semiconductor ring lasers,” IEEE J. Quantum Electron 47, 1078 –1085 (2011).
[CrossRef]

P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
[CrossRef]

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Pérot lasers: the effect of spatial hole burning,” Opt. Express 19, 3284–3289 (2011).
[CrossRef] [PubMed]

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]

J. Javaloyes and S. Balle, “Mode-locking in Fabry-Pérot lasers,” IEEE J. Quantum Electron. 46, 1023–1030 (2010).
[CrossRef]

J. Mulet and S. Balle, “Mode locking dynamics in electrically-driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148–1156 (2005).
[CrossRef]

L. Furfaro, F. Pedaci, M. Giudici, X. Hachair, J. Tredicce, and S. Balle, “Mode-switching in semiconductor lasers,” IEEE J. Quantum. Elect. 40, 1365–1376 (2004).
[CrossRef]

S. Balle, “Simple analytical approximations for the gain and refractive index spectra in quantum well lasers,” Phys. Rev. A 57, 1304–1312 (1998).
[CrossRef]

Bardella, P.

M. Rossetti, P. Bardella, and I. Montrosset, “Modeling passive mode-locking in quantum dot lasers: A comparison between a finite-difference traveling-wave model and a delayed differential equation approach,” IEEE J. Quantum. Electron 47, 569 –576 (2011).
[CrossRef]

Bryce, A.

P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
[CrossRef]

Burrus, C.

R. Linke, B. Kasper, C. Burrus, I. Kaminow, J.-S. Ko, and T. Lee, “Mode power partition events in nearly single-frequency lasers,” J. Lightwave Technol. 3, 706–712 (1985).
[CrossRef]

Champneys, A. R.

E. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. Wang, “Auto97: Continuation and bifurcation software for ordinary differential equations,” (2011).

Doedel, E.

E. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. Wang, “Auto97: Continuation and bifurcation software for ordinary differential equations,” (2011).

Engelborghs, K.

K. Engelborghs, T. Luzyanina, and G. Samaey, “Dde-biftool v. 2.00: a matlab package for bifurcation analysis of delay differential equations,” Tech. Rep., Department of Computer Science, K.U.Leuven, Belgium. (2001).

Fairgrieve, T. F.

E. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. Wang, “Auto97: Continuation and bifurcation software for ordinary differential equations,” (2011).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 2007.

Fleck, J. A.

J. A. Fleck, “Emission of pulse trains by Q-switched lasers,” Phys. Rev. Lett. 21, 131–133 (1968).
[CrossRef]

Fork, R. L.

L. E. Hargrove, R. L. Fork, and M. A. Pollack, “Locking of he-ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[CrossRef]

Furfaro, L.

L. Furfaro, F. Pedaci, M. Giudici, X. Hachair, J. Tredicce, and S. Balle, “Mode-switching in semiconductor lasers,” IEEE J. Quantum. Elect. 40, 1365–1376 (2004).
[CrossRef]

Giudici, M.

L. Furfaro, F. Pedaci, M. Giudici, X. Hachair, J. Tredicce, and S. Balle, “Mode-switching in semiconductor lasers,” IEEE J. Quantum. Elect. 40, 1365–1376 (2004).
[CrossRef]

Hachair, X.

L. Furfaro, F. Pedaci, M. Giudici, X. Hachair, J. Tredicce, and S. Balle, “Mode-switching in semiconductor lasers,” IEEE J. Quantum. Elect. 40, 1365–1376 (2004).
[CrossRef]

Hargrove, L. E.

L. E. Hargrove, R. L. Fork, and M. A. Pollack, “Locking of he-ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[CrossRef]

Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000).
[CrossRef]

Hou, L.

P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
[CrossRef]

Ironside, C.

P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
[CrossRef]

Javaloyes, J.

P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
[CrossRef]

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Pérot lasers: the effect of spatial hole burning,” Opt. Express 19, 3284–3289 (2011).
[CrossRef] [PubMed]

J. Javaloyes and S. Balle, “All-optical directional switching of bistable semiconductor ring lasers,” IEEE J. Quantum Electron 47, 1078 –1085 (2011).
[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]

J. Javaloyes and S. Balle, “Mode-locking in Fabry-Pérot lasers,” IEEE J. Quantum Electron. 46, 1023–1030 (2010).
[CrossRef]

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

Kaminow, I.

R. Linke, B. Kasper, C. Burrus, I. Kaminow, J.-S. Ko, and T. Lee, “Mode power partition events in nearly single-frequency lasers,” J. Lightwave Technol. 3, 706–712 (1985).
[CrossRef]

Kasper, B.

R. Linke, B. Kasper, C. Burrus, I. Kaminow, J.-S. Ko, and T. Lee, “Mode power partition events in nearly single-frequency lasers,” J. Lightwave Technol. 3, 706–712 (1985).
[CrossRef]

Ko, J.-S.

R. Linke, B. Kasper, C. Burrus, I. Kaminow, J.-S. Ko, and T. Lee, “Mode power partition events in nearly single-frequency lasers,” J. Lightwave Technol. 3, 706–712 (1985).
[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]

Kuznetsov, Y. A.

E. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. Wang, “Auto97: Continuation and bifurcation software for ordinary differential equations,” (2011).

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]

Lee, T.

R. Linke, B. Kasper, C. Burrus, I. Kaminow, J.-S. Ko, and T. Lee, “Mode power partition events in nearly single-frequency lasers,” J. Lightwave Technol. 3, 706–712 (1985).
[CrossRef]

Linke, R.

R. Linke, B. Kasper, C. Burrus, I. Kaminow, J.-S. Ko, and T. Lee, “Mode power partition events in nearly single-frequency lasers,” J. Lightwave Technol. 3, 706–712 (1985).
[CrossRef]

Lugiato, L. A.

L. A. Lugiato and F. Prati, “Difference differential equations for a resonator with a very thin nonlinear medium,” Phys. Rev. Lett. 104, 233902 (2010).
[CrossRef] [PubMed]

Luzyanina, T.

K. Engelborghs, T. Luzyanina, and G. Samaey, “Dde-biftool v. 2.00: a matlab package for bifurcation analysis of delay differential equations,” Tech. Rep., Department of Computer Science, K.U.Leuven, Belgium. (2001).

Mezosi, G.

P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
[CrossRef]

Montrosset, I.

M. Rossetti, P. Bardella, and I. Montrosset, “Modeling passive mode-locking in quantum dot lasers: A comparison between a finite-difference traveling-wave model and a delayed differential equation approach,” IEEE J. Quantum. Electron 47, 569 –576 (2011).
[CrossRef]

Mulet, J.

J. Mulet and S. Balle, “Mode locking dynamics in electrically-driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148–1156 (2005).
[CrossRef]

Narducci, L.

L. Narducci and N. B. Abraham, Laser Physics and Laser Instabilities (World Scientific, Singapore, 1988).

Ohtsu, M.

M. Ohtsu, Y. Teramachi, Y. Otsuka, and A. Osaki, “Analyses of mode-hopping phenomena in an AlGaAs laser,” IEEE J. Quantum. Elect. 22, 535–543 (1986).
[CrossRef]

Osaki, A.

M. Ohtsu, Y. Teramachi, Y. Otsuka, and A. Osaki, “Analyses of mode-hopping phenomena in an AlGaAs laser,” IEEE J. Quantum. Elect. 22, 535–543 (1986).
[CrossRef]

Otsuka, Y.

M. Ohtsu, Y. Teramachi, Y. Otsuka, and A. Osaki, “Analyses of mode-hopping phenomena in an AlGaAs laser,” IEEE J. Quantum. Elect. 22, 535–543 (1986).
[CrossRef]

Pedaci, F.

L. Furfaro, F. Pedaci, M. Giudici, X. Hachair, J. Tredicce, and S. Balle, “Mode-switching in semiconductor lasers,” IEEE J. Quantum. Elect. 40, 1365–1376 (2004).
[CrossRef]

Pérez-Serrano, A.

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Longitudinal mode multistability in ring and Fabry-Pérot lasers: the effect of spatial hole burning,” Opt. Express 19, 3284–3289 (2011).
[CrossRef] [PubMed]

A. Pérez-Serrano, J. Javaloyes, and S. Balle, “Bichromatic emission and multimode dynamics in bidirectional ring lasers,” Phys. Rev. A 81, 043817 (2010).
[CrossRef]

Pimenov, A.S.

A.G. Vladimirov, A.S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser,” IEEE J. Quantum Electron 45, 462 –468 (2009).
[CrossRef]

Pollack, M. A.

L. E. Hargrove, R. L. Fork, and M. A. Pollack, “Locking of he-ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[CrossRef]

Prati, F.

L. A. Lugiato and F. Prati, “Difference differential equations for a resonator with a very thin nonlinear medium,” Phys. Rev. Lett. 104, 233902 (2010).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 2007.

Rachinskii, D.

A.G. Vladimirov, A.S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser,” IEEE J. Quantum Electron 45, 462 –468 (2009).
[CrossRef]

Rossetti, M.

M. Rossetti, P. Bardella, and I. Montrosset, “Modeling passive mode-locking in quantum dot lasers: A comparison between a finite-difference traveling-wave model and a delayed differential equation approach,” IEEE J. Quantum. Electron 47, 569 –576 (2011).
[CrossRef]

Samaey, G.

K. Engelborghs, T. Luzyanina, and G. Samaey, “Dde-biftool v. 2.00: a matlab package for bifurcation analysis of delay differential equations,” Tech. Rep., Department of Computer Science, K.U.Leuven, Belgium. (2001).

Sandstede, B.

E. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. Wang, “Auto97: Continuation and bifurcation software for ordinary differential equations,” (2011).

Sorel, M.

P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
[CrossRef]

Stolarz, P.

P. Stolarz, J. Javaloyes, G. Mezosi, L. Hou, C. Ironside, M. Sorel, A. Bryce, and S. Balle, “Spectral dynamical behavior in passively mode-locked semiconductor lasers,” IEEE Photon. J. 3, 1067–1082 (2011).
[CrossRef]

Teramachi, Y.

M. Ohtsu, Y. Teramachi, Y. Otsuka, and A. Osaki, “Analyses of mode-hopping phenomena in an AlGaAs laser,” IEEE J. Quantum. Elect. 22, 535–543 (1986).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 2007.

Tredicce, J.

L. Furfaro, F. Pedaci, M. Giudici, X. Hachair, J. Tredicce, and S. Balle, “Mode-switching in semiconductor lasers,” IEEE J. Quantum. Elect. 40, 1365–1376 (2004).
[CrossRef]

Turaev, D.

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72, 033808 (2005).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University Press, 2007.

Vladimirov, A. G.

A. G. Vladimirov and D. Turaev, “Model for passive mode locking in semiconductor lasers,” Phys. Rev. A 72, 033808 (2005).
[CrossRef]

Vladimirov, A.G.

A.G. Vladimirov, A.S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser,” IEEE J. Quantum Electron 45, 462 –468 (2009).
[CrossRef]

Wang, X.

E. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede, and X. Wang, “Auto97: Continuation and bifurcation software for ordinary differential equations,” (2011).

Appl. Phys. Lett.

L. E. Hargrove, R. L. Fork, and M. A. Pollack, “Locking of he-ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[CrossRef]

IEEE J. Quantum Electron

J. Javaloyes and S. Balle, “All-optical directional switching of bistable semiconductor ring lasers,” IEEE J. Quantum Electron 47, 1078 –1085 (2011).
[CrossRef]

A.G. Vladimirov, A.S. Pimenov, and D. Rachinskii, “Numerical Study of Dynamical Regimes in a Monolithic Passively Mode-Locked Semiconductor Laser,” IEEE J. Quantum Electron 45, 462 –468 (2009).
[CrossRef]

IEEE J. Quantum Electron.

J. Javaloyes and S. Balle, “Mode-locking in Fabry-Pérot lasers,” IEEE J. Quantum Electron. 46, 1023–1030 (2010).
[CrossRef]

J. Mulet and S. Balle, “Mode locking dynamics in electrically-driven vertical-external-cavity surface-emitting lasers,” IEEE J. Quantum Electron. 41, 1148–1156 (2005).
[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 J. Quantum. Elect.

M. Ohtsu, Y. Teramachi, Y. Otsuka, and A. Osaki, “Analyses of mode-hopping phenomena in an AlGaAs laser,” IEEE J. Quantum. Elect. 22, 535–543 (1986).
[CrossRef]

L. Furfaro, F. Pedaci, M. Giudici, X. Hachair, J. Tredicce, and S. Balle, “Mode-switching in semiconductor lasers,” IEEE J. Quantum. Elect. 40, 1365–1376 (2004).
[CrossRef]

IEEE J. Quantum. Electron

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Figures (4)

Fig. 1
Fig. 1

Lasing threshold and frequency of the modes of a FP cavity for different values of the mirror reflectivity. The red dots are the solutions of Eq. (5) while the blue dashed lines correspond to the solutions of Eq. (6)

Fig. 2
Fig. 2

The red and blue lines represent the advection of the forward and the backward waves, while the green line depicts the DOFs needed to determine the polarization.

Fig. 3
Fig. 3

Bifurcation diagram as a function of the bias current for a two section FP PML laser. The black (green) points depict the maxima (minima) of the intensity I+(L) at the right output facet (top) while the middle and bottom panels represent the pulse FWHM and its skewness. The left column corresponds to the full TWM, (N1, N2) = (513, 17), while the second and third columns have been obtained with (N1, N2) = (33, 5) and (9, 2).

Fig. 4
Fig. 4

Eigenvalues around the off solution. The gain peak develops on the blue side of the band-edge frequency, corresponding to negative imaginary parts. The insets show the the eigenvalues around the gain peak and in the absorption plateau.

Equations (7)

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( t ± z ) E ± ( z , t ) = S ± ( z , t ) , S ± = P ± α E ± ,
E ± ( z , t ) = E ± ( z τ , t τ ) + 𝒤 ± ( z , t ) , 𝒤 ± ( z , t ) = 0 τ S ± ( z τ ± s , t τ + s ) d s ,
𝒤 ± = τ S ± ( z τ , t τ ) + S ± ( z , t ) 2 + 𝒪 ( τ 3 2 S ± ξ ± 2 ) ,
( 1 + α τ 2 ) E ± ( z , t ) = ( 1 α τ 2 ) E ± ( z τ , t τ ) + τ 2 { P ± ( z τ , t τ ) + P ± ( z , t ) } .
R 1 R 2 e 2 i ω [ 1 + g ( ω ) / 2 1 g ( ω ) / 2 ] = 1 ,
R 1 R 2 e 2 i ω + g ( ω ) = 1.
( 1 + α j τ j 2 ) E ± j ( t ) = ( 1 α j τ j 2 ) E ± j 1 ( t τ j ) + τ j 2 { P ± j 1 ( t τ j ) + P ± j ( t ) } .

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