Abstract

We report on the existence, stability and dynamical properties of two-dimensional self-localized vortices with azimuthal numbers up to 4 in a simple model for lasers with frequency-selective feedback. We build the full bifurcation diagram for vortex solutions and characterize the different dynamical regimes. The mathematical model used, which consists of a laser rate equation coupled to a linear equation for the feedback field, can describe the spatiotemporal dynamics of broad area vertical cavity surface emitting lasers with external frequency selective feedback in the limit of zero delay.

© 2010 Optical Society of America

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  1. T. Ackemann, W. J. Firth, and G.-L. Oppo, "Fundamentals and applications of Spatial Dissipative Solitons in Photonic Devices," Adv. Atom. Mol. Opt. Phys. 57, 323 (2009).
  2. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).
  3. Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).
  4. P. Genevet, S. Barland, M. Guidici, and J. R. Tredicce, "Cavity soliton laser based on mutually coupled semiconductor microresonators," Phys. Rev. Let. 101, 123905 (2008).
  5. A. G. Vladimirov, N. N. Rosanov, S. V. Fedorov, and G. V. Khodova, "Bifurcation analysis of laser autosolitons," Quantum Electron. 27, 949-952 (1997).
  6. T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, "Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber," Appl. Phys. B 98, 327 (2010).
  7. P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, "Bistable and addressable localized vortices in semiconductor lasers," submitted (2009) http://hal.archives-ouvertes.fr/docs/00/43/59/20/PDF/localizedvortices.pdf.
  8. N. N. Rosanov, "Solitons in laser systems with saturable absorption," in Dissipative Solitons, edited by N. Akhmediev and A. Ankiewicz, Lect. Notes Phys. 661, 101-130 (2004).
  9. N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, "Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling," Phys. Rev. Lett. 95, 053903 (2005).
    [PubMed]
  10. L.-C. Crasovan, B. A. Malomed, and D. Michalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2000).
  11. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).
  12. W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450 (1997).
  13. J. R. Salgueiro and Y. S. Kivshar, "Single- and double-vortex vector solitons in self-focusing nonlinear media," Phys. Rev. E 70, 056613 (2004).
  14. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Progress in Optics, ed. E. Wolf, 47, 291 (2005).
  15. P. V. Paulau, D. Gomila, T. Ackemann, N. A. Loiko, and W. J. Firth, "Self-localized structures in vertical-cavity surface-emitting lasers with external feedback," Phys. Rev. E 78, 016212 (2008).
  16. P. V. Paulau, D. Gomila, P. Colet, M. A. Matias, N. A. Loiko, and W. J. Firth "Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 80, 023808 (2009).
  17. J. Atai, and B. A. Malomed, "Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations," Phys. Lett. A 246, 412 (1998).
  18. W. J. Firth and P. V. Paulau, "Soliton lasers stabilized by coupling to a resonant linear system," submitted (2009).
  19. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826 (1995).
    [PubMed]
  20. S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser. Photon Rev. 2, 299 (2008).
  21. G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305 (2007).
  22. A. P. A. Fisher, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, "Experimental and theoretical study of filtered optical feedback in a semiconductor laser," IEEE J. Quantum Electron. 36, 375 (2000).
  23. M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, "Spontaneous motion of cavity solitons induced by a delayed feedback," Phys. Rev. Lett,  103,103904 (2009).

2010 (1)

T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, "Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber," Appl. Phys. B 98, 327 (2010).

2009 (3)

T. Ackemann, W. J. Firth, and G.-L. Oppo, "Fundamentals and applications of Spatial Dissipative Solitons in Photonic Devices," Adv. Atom. Mol. Opt. Phys. 57, 323 (2009).

P. V. Paulau, D. Gomila, P. Colet, M. A. Matias, N. A. Loiko, and W. J. Firth "Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 80, 023808 (2009).

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, "Spontaneous motion of cavity solitons induced by a delayed feedback," Phys. Rev. Lett,  103,103904 (2009).

2008 (5)

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser. Photon Rev. 2, 299 (2008).

P. V. Paulau, D. Gomila, T. Ackemann, N. A. Loiko, and W. J. Firth, "Self-localized structures in vertical-cavity surface-emitting lasers with external feedback," Phys. Rev. E 78, 016212 (2008).

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).

P. Genevet, S. Barland, M. Guidici, and J. R. Tredicce, "Cavity soliton laser based on mutually coupled semiconductor microresonators," Phys. Rev. Let. 101, 123905 (2008).

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305 (2007).

2005 (1)

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, "Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling," Phys. Rev. Lett. 95, 053903 (2005).
[PubMed]

2004 (1)

J. R. Salgueiro and Y. S. Kivshar, "Single- and double-vortex vector solitons in self-focusing nonlinear media," Phys. Rev. E 70, 056613 (2004).

2002 (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

2000 (2)

L.-C. Crasovan, B. A. Malomed, and D. Michalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2000).

A. P. A. Fisher, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, "Experimental and theoretical study of filtered optical feedback in a semiconductor laser," IEEE J. Quantum Electron. 36, 375 (2000).

1998 (1)

J. Atai, and B. A. Malomed, "Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations," Phys. Lett. A 246, 412 (1998).

1997 (2)

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450 (1997).

A. G. Vladimirov, N. N. Rosanov, S. V. Fedorov, and G. V. Khodova, "Bifurcation analysis of laser autosolitons," Quantum Electron. 27, 949-952 (1997).

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

Ackemann, T.

T. Ackemann, W. J. Firth, and G.-L. Oppo, "Fundamentals and applications of Spatial Dissipative Solitons in Photonic Devices," Adv. Atom. Mol. Opt. Phys. 57, 323 (2009).

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).

P. V. Paulau, D. Gomila, T. Ackemann, N. A. Loiko, and W. J. Firth, "Self-localized structures in vertical-cavity surface-emitting lasers with external feedback," Phys. Rev. E 78, 016212 (2008).

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser. Photon Rev. 2, 299 (2008).

Andersen, O. K.

A. P. A. Fisher, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, "Experimental and theoretical study of filtered optical feedback in a semiconductor laser," IEEE J. Quantum Electron. 36, 375 (2000).

Atai, J.

J. Atai, and B. A. Malomed, "Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations," Phys. Lett. A 246, 412 (1998).

Balle, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Barbay, S.

T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, "Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber," Appl. Phys. B 98, 327 (2010).

Barland, S.

P. Genevet, S. Barland, M. Guidici, and J. R. Tredicce, "Cavity soliton laser based on mutually coupled semiconductor microresonators," Phys. Rev. Let. 101, 123905 (2008).

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Beaudoin, G.

T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, "Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber," Appl. Phys. B 98, 327 (2010).

Brambilla, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Colet, P.

P. V. Paulau, D. Gomila, P. Colet, M. A. Matias, N. A. Loiko, and W. J. Firth "Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 80, 023808 (2009).

Crasovan, L.-C.

L.-C. Crasovan, B. A. Malomed, and D. Michalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2000).

Elsass, T.

T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, "Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber," Appl. Phys. B 98, 327 (2010).

Fedorov, S. V.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, "Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling," Phys. Rev. Lett. 95, 053903 (2005).
[PubMed]

A. G. Vladimirov, N. N. Rosanov, S. V. Fedorov, and G. V. Khodova, "Bifurcation analysis of laser autosolitons," Quantum Electron. 27, 949-952 (1997).

Firth, W. J.

T. Ackemann, W. J. Firth, and G.-L. Oppo, "Fundamentals and applications of Spatial Dissipative Solitons in Photonic Devices," Adv. Atom. Mol. Opt. Phys. 57, 323 (2009).

P. V. Paulau, D. Gomila, P. Colet, M. A. Matias, N. A. Loiko, and W. J. Firth "Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 80, 023808 (2009).

P. V. Paulau, D. Gomila, T. Ackemann, N. A. Loiko, and W. J. Firth, "Self-localized structures in vertical-cavity surface-emitting lasers with external feedback," Phys. Rev. E 78, 016212 (2008).

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450 (1997).

Fisher, A. P. A.

A. P. A. Fisher, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, "Experimental and theoretical study of filtered optical feedback in a semiconductor laser," IEEE J. Quantum Electron. 36, 375 (2000).

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser. Photon Rev. 2, 299 (2008).

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

Gauthron, K.

T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, "Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber," Appl. Phys. B 98, 327 (2010).

Genevet, P.

P. Genevet, S. Barland, M. Guidici, and J. R. Tredicce, "Cavity soliton laser based on mutually coupled semiconductor microresonators," Phys. Rev. Let. 101, 123905 (2008).

Giudici, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Gomila, D.

P. V. Paulau, D. Gomila, P. Colet, M. A. Matias, N. A. Loiko, and W. J. Firth "Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 80, 023808 (2009).

P. V. Paulau, D. Gomila, T. Ackemann, N. A. Loiko, and W. J. Firth, "Self-localized structures in vertical-cavity surface-emitting lasers with external feedback," Phys. Rev. E 78, 016212 (2008).

Guidici, M.

P. Genevet, S. Barland, M. Guidici, and J. R. Tredicce, "Cavity soliton laser based on mutually coupled semiconductor microresonators," Phys. Rev. Let. 101, 123905 (2008).

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

Jäger, R.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).

Jagerk, R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Khodova, G. V.

A. G. Vladimirov, N. N. Rosanov, S. V. Fedorov, and G. V. Khodova, "Bifurcation analysis of laser autosolitons," Quantum Electron. 27, 949-952 (1997).

Kivshar, Y. S.

J. R. Salgueiro and Y. S. Kivshar, "Single- and double-vortex vector solitons in self-focusing nonlinear media," Phys. Rev. E 70, 056613 (2004).

Knodlk, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Kuszelewicz, R.

T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, "Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber," Appl. Phys. B 98, 327 (2010).

Leblond, H.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).

Lenstra, D.

A. P. A. Fisher, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, "Experimental and theoretical study of filtered optical feedback in a semiconductor laser," IEEE J. Quantum Electron. 36, 375 (2000).

Loiko, N. A.

P. V. Paulau, D. Gomila, P. Colet, M. A. Matias, N. A. Loiko, and W. J. Firth "Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 80, 023808 (2009).

P. V. Paulau, D. Gomila, T. Ackemann, N. A. Loiko, and W. J. Firth, "Self-localized structures in vertical-cavity surface-emitting lasers with external feedback," Phys. Rev. E 78, 016212 (2008).

Lugiato, L. A.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Maggipinto, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Malomed, B. A.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).

L.-C. Crasovan, B. A. Malomed, and D. Michalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2000).

J. Atai, and B. A. Malomed, "Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations," Phys. Lett. A 246, 412 (1998).

Matias, M. A.

P. V. Paulau, D. Gomila, P. Colet, M. A. Matias, N. A. Loiko, and W. J. Firth "Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 80, 023808 (2009).

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).

Michalache, D.

L.-C. Crasovan, B. A. Malomed, and D. Michalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2000).

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).

Millerk, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305 (2007).

Oppo, G.-L.

T. Ackemann, W. J. Firth, and G.-L. Oppo, "Fundamentals and applications of Spatial Dissipative Solitons in Photonic Devices," Adv. Atom. Mol. Opt. Phys. 57, 323 (2009).

Padgett, M.

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser. Photon Rev. 2, 299 (2008).

Paulau, P. V.

P. V. Paulau, D. Gomila, P. Colet, M. A. Matias, N. A. Loiko, and W. J. Firth "Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 80, 023808 (2009).

P. V. Paulau, D. Gomila, T. Ackemann, N. A. Loiko, and W. J. Firth, "Self-localized structures in vertical-cavity surface-emitting lasers with external feedback," Phys. Rev. E 78, 016212 (2008).

Pieroux, D.

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, "Spontaneous motion of cavity solitons induced by a delayed feedback," Phys. Rev. Lett,  103,103904 (2009).

Rosanov, N. N.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, "Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling," Phys. Rev. Lett. 95, 053903 (2005).
[PubMed]

A. G. Vladimirov, N. N. Rosanov, S. V. Fedorov, and G. V. Khodova, "Bifurcation analysis of laser autosolitons," Quantum Electron. 27, 949-952 (1997).

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

Sagnes, I.

T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, "Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber," Appl. Phys. B 98, 327 (2010).

Salgueiro, J. R.

J. R. Salgueiro and Y. S. Kivshar, "Single- and double-vortex vector solitons in self-focusing nonlinear media," Phys. Rev. E 70, 056613 (2004).

Shatsev, A. N.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, "Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling," Phys. Rev. Lett. 95, 053903 (2005).
[PubMed]

Skryabin, D. V.

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450 (1997).

Spinelli, L.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Stolte, S.

A. P. A. Fisher, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, "Experimental and theoretical study of filtered optical feedback in a semiconductor laser," IEEE J. Quantum Electron. 36, 375 (2000).

Tanguy, Y.

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).

Tissoni, G.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Tlidi, M.

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, "Spontaneous motion of cavity solitons induced by a delayed feedback," Phys. Rev. Lett,  103,103904 (2009).

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305 (2007).

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305 (2007).

Tredicce, J. R.

P. Genevet, S. Barland, M. Guidici, and J. R. Tredicce, "Cavity soliton laser based on mutually coupled semiconductor microresonators," Phys. Rev. Let. 101, 123905 (2008).

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Turaev, D.

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, "Spontaneous motion of cavity solitons induced by a delayed feedback," Phys. Rev. Lett,  103,103904 (2009).

Vladimirov, A. G.

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, "Spontaneous motion of cavity solitons induced by a delayed feedback," Phys. Rev. Lett,  103,103904 (2009).

A. G. Vladimirov, N. N. Rosanov, S. V. Fedorov, and G. V. Khodova, "Bifurcation analysis of laser autosolitons," Quantum Electron. 27, 949-952 (1997).

Yousefi, M.

A. P. A. Fisher, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, "Experimental and theoretical study of filtered optical feedback in a semiconductor laser," IEEE J. Quantum Electron. 36, 375 (2000).

Adv. Atom. Mol. Opt. Phys. (1)

T. Ackemann, W. J. Firth, and G.-L. Oppo, "Fundamentals and applications of Spatial Dissipative Solitons in Photonic Devices," Adv. Atom. Mol. Opt. Phys. 57, 323 (2009).

Appl. Phys. B (1)

T. Elsass, K. Gauthron, G. Beaudoin, I. Sagnes, R. Kuszelewicz, and S. Barbay, "Fast manipulation of laser localized structures in a monolithic vertical cavity with saturable absorber," Appl. Phys. B 98, 327 (2010).

IEEE J. Quantum Electron. (1)

A. P. A. Fisher, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, "Experimental and theoretical study of filtered optical feedback in a semiconductor laser," IEEE J. Quantum Electron. 36, 375 (2000).

Laser. Photon Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, "Advances in optical angular momentum," Laser. Photon Rev. 2, 299 (2008).

Nat. Phys. (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nat. Phys. 3, 305 (2007).

Nature (London) (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodlk, M. Millerk, and R. Jagerk, "Cavity solitons as pixels in semiconductor microcavities," Nature (London) 419, 699 (2002).

Phys. Lett. A (1)

J. Atai, and B. A. Malomed, "Exact stable pulses in asymmetric linearly coupled Ginzburg-Landau equations," Phys. Lett. A 246, 412 (1998).

Phys. Rev. A (2)

P. V. Paulau, D. Gomila, P. Colet, M. A. Matias, N. A. Loiko, and W. J. Firth "Drifting instabilities of cavity solitons in vertical-cavity surface-emitting lasers with frequency-selective feedback," Phys. Rev. A 80, 023808 (2009).

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).

Phys. Rev. E (3)

J. R. Salgueiro and Y. S. Kivshar, "Single- and double-vortex vector solitons in self-focusing nonlinear media," Phys. Rev. E 70, 056613 (2004).

P. V. Paulau, D. Gomila, T. Ackemann, N. A. Loiko, and W. J. Firth, "Self-localized structures in vertical-cavity surface-emitting lasers with external feedback," Phys. Rev. E 78, 016212 (2008).

L.-C. Crasovan, B. A. Malomed, and D. Michalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2000).

Phys. Rev. Let. (1)

P. Genevet, S. Barland, M. Guidici, and J. R. Tredicce, "Cavity soliton laser based on mutually coupled semiconductor microresonators," Phys. Rev. Let. 101, 123905 (2008).

Phys. Rev. Lett (1)

M. Tlidi, A. G. Vladimirov, D. Pieroux, and D. Turaev, "Spontaneous motion of cavity solitons induced by a delayed feedback," Phys. Rev. Lett,  103,103904 (2009).

Phys. Rev. Lett. (4)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826 (1995).
[PubMed]

Y. Tanguy, T. Ackemann, W. J. Firth, and R. Jäger, "Realization of a Semiconductor-Based Cavity Soliton Laser," Phys. Rev. Lett. 100, 013907 (2008).

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, "Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling," Phys. Rev. Lett. 95, 053903 (2005).
[PubMed]

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450 (1997).

Quantum Electron. (1)

A. G. Vladimirov, N. N. Rosanov, S. V. Fedorov, and G. V. Khodova, "Bifurcation analysis of laser autosolitons," Quantum Electron. 27, 949-952 (1997).

Other (4)

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, "Bistable and addressable localized vortices in semiconductor lasers," submitted (2009) http://hal.archives-ouvertes.fr/docs/00/43/59/20/PDF/localizedvortices.pdf.

N. N. Rosanov, "Solitons in laser systems with saturable absorption," in Dissipative Solitons, edited by N. Akhmediev and A. Ankiewicz, Lect. Notes Phys. 661, 101-130 (2004).

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," Progress in Optics, ed. E. Wolf, 47, 291 (2005).

W. J. Firth and P. V. Paulau, "Soliton lasers stabilized by coupling to a resonant linear system," submitted (2009).

Supplementary Material (5)

» Media 1: AVI (428 KB)     
» Media 2: AVI (705 KB)     
» Media 3: AVI (2455 KB)     
» Media 4: AVI (1622 KB)     
» Media 5: AVI (701 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Coexistence of the fundamental soliton and vortices with m = 1,2: (a) the stationary transverse amplitude distribution; and (b) the instantaneous distribution of real part of the field. Black (white) corresponds to the minimum (maximum) value. Here 1 2 T = 2.7 ns 1 , ω S = 250 2 π ns 1 , α=5.0, σ=60ns -1,κ=100ns -1, and μ=0.66.

Fig. 2.
Fig. 2.

Transverse sections through the center of stable self-localized states. (a) Amplitude in semi-logarithmic scale, and (b) phase. Parameters as in Fig. 1. Dots correspond to m = 0, circles to m = 1, asterisks to m = 2, triangles to m = 3, and crosses to m = 4.

Fig. 3.
Fig. 3.

Bifurcation diagrams of self-localized states with m = 0,1,2. Total power as a function of the pump current μ. Other parameters are as in Fig. 1 and symbols as in Fig. 2. Instabilities below bifurcation points M and M 1 are illustrated in movies (Media 1) and (Media 2) correspondingly. Other labeled dots are explained in Section 5. Dash-dotted vertical lines A,B indicate the bifurcation points of the homogeneous solutions.

Fig. 4.
Fig. 4.

Additional features of the m = 0 (dots), 1 (circles) branches presented in Fig. 3: (a) maximum intensity; (b) frequency; and (c) radius of the m = 1 vortex ring (in arbitrary units); as a function of the pump current μ. Dashed thin lines represent the homogeneous steady states. Dash-dotted vertical lines A,B indicate the bifurcation points of the homogeneous solutions.

Fig. 5.
Fig. 5.

Dependence on pump current of instability growth rates for the m = 2 vortex soliton. The real part of the relevant perturbation eigenvalues is plotted for that part of the upper m = 2 branch in Fig. 3 for which the E = 0 state is stable, i.e. between B and C 2. The thin line indicates the mode with bifurcation point G 1 in Fig. 3. The real part of this mode is shown in lower-right inset, and the corresponding dynamical evolution in (Media 3). The medium-thickness line indicates the mode with bifurcation point G 2 in Fig.3. The real part of this mode is shown in middle inset, and the corresponding dynamical evolution in (Media 4). The thickest line indicates the mode with bifurcation point G 3 in Fig. 3. The real part of this mode is shown in the upper-left inset, and the corresponding dynamical evolution in (Media 5).

Equations (3)

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E t = κ ( 1 + ) ( E μE 1 + | E 2 ) i Δ E + F + i ω s E ,
F dt = - 1 2 T F + σ 1 2 T E ,
A E 0 + B E 0 1 + E 0 2 + Δ E 0 = 0 ,

Metrics