Abstract

In [Phys. Rev. Lett. 110, 064103 (2013)], using the Swift-Hohenberg equation, we introduced a mechanism that allows to generate oscillatory and excitable soliton dynamics. This mechanism was based on a competition between a pinning force at inhomogeneities and a pulling force due to drift. Here, we study the effect of such inhomogeneities and drift on temporal solitons and Kerr frequency combs in fiber cavities and microresonators, described by the Lugiato-Lefever equation with periodic boundary conditions. We demonstrate that for low values of the frequency detuning the competition between inhomogeneities and drift leads to similar dynamics at the defect location, confirming the generality of the mechanism. The intrinsic periodic nature of ring cavities and microresonators introduces, however, some interesting differences in the final global states. For higher values of the detuning we observe that the dynamics is no longer described by the same mechanism and it is considerably more complex.

© 2014 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]

2014 (3)

2013 (3)

2012 (1)

2011 (2)

I. V. Barashenkov and E. V. Zemlyanaya, “Travelling solitons in the externally driven nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 44465211 (2011).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

2010 (3)

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nature Phot. 4, 471–476 (2010).
[Crossref]

A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of noise on excitable dissipative solitons,” Eur. Phys. J. D 59, 37–42 (2010).
[Crossref]

M. Tlidi and L. Gelens, “High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities,” Opt. Lett. 35, 306–308 (2010).
[Crossref] [PubMed]

2009 (1)

E. Caboche, F. Pedaci, P. Genevet, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Microresonator defects as sources of drifting cavity solitons,” Phys. Rev. Lett. 102, 163901 (2009); ;E. Caboche, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Cavity-soliton motion in the presence of device defects,” Phys. Rev. A 80, 053814 (2009).
[Crossref] [PubMed]

2008 (3)

A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of a localized beam on the dynamics of excitable cavity solitons,” Phys. Rev. A 78, 053821 (2008).
[Crossref]

L. Gelens, D. Gomila, G. Van der Sande, J. Danckaert, P. Colet, and M. A. Matías, “Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials,” Phys. Rev. A 77, 033841 (2008).
[Crossref]

F. Pedaci, G. Tissoni, S. Barland, M. Giudici, and J. Tredicce, “Mapping local defects of extended media using localized structures,” Appl. Phys. Lett. 93, 111104 (2008).
[Crossref]

2007 (2)

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

D. Gomila, A. J. Scroggie, and W. J. Firth, “Bifurcation structure of dissipative solitons,” Physica D 227, 70–77 (2007).
[Crossref]

2005 (1)

R. Richter and I. V. Barashenkov, “Two-dimensional solitons on the surface of magnetic fluids,” Phys. Rev. Lett. 94, 184503 (2005).
[Crossref] [PubMed]

2004 (2)

2003 (2)

K. Bold, C. Edwards, J. Guckenheimer, S. Guharay, K. Hoffman, J. Hubbard, R. Oliva, and W. Weckesser, “The Forced van der Pol Equation II: Canards in the Reduced System,” SIAM J. Appl. Dyn. Syst. 2, 570–608 (2003).
[Crossref]

B. Schapers, T. Ackemann, and W. Lange, “Properties of feedback solitons in a single-mirror experiment,” IEEE J.Quantum Electron. 39, 227–237 (2003).
[Crossref]

2002 (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

2000 (2)

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, “Interaction of localized structures in an optical pattern-forming system,” Phys. Rev. Lett. 85, 748–751 (2000).
[Crossref] [PubMed]

N. V. Alexeeva and I. V. Barashenkov, “Impurity-Induced Satabilization of Solitons in Arrays of Parametrically Driven Nonlinear Oscillators,” Phys. Rev. Lett. 84, 3053–3056 (2000).
[Crossref]

1998 (2)

H. Ward, M. N. Ouarzazi, M. Taki, and P. Glorieux, “Transverse dynamics of optical parametric oscillators in presence of walk-off,” Eur. Phys. J. D 3, 275–288 (1998).
[Crossref]

M. Santagiustina, P. Colet, M. S. Miguel, and D. Walgraef, “Walk-off and pattern selection in optical parametric oscillators,” Opt. Lett. 23, 1167–1169 (1998).
[Crossref]

1997 (1)

M. Santagiustina, P. Colet, M. S. Miguel, and D. Walgraef, “Noise-sustained convective structures in nonlinear optics,” Phys. Rev. Lett. 79, 3633–3636 (1997).
[Crossref]

1996 (2)

P. Umbanhowar, F. Melo, and H. L. Swinney, “Localized excitations in a vertically vibrated granular layer,” Nature 382, 793–796 (1996).
[Crossref]

I. V. Barashenkov and Y. S. Smirnov, “Existence and stability chart for the ac-driven, damped nonlinear Schrodinger solitons,” Phys. Rev. E 54, 5707–5725 (1996).
[Crossref]

1993 (1)

K. J. Lee, W. D. McCormick, Q. Ouyang, and H. L. Swinney, “Pattern formation by interacting chemical fronts,” Science 261, 192–194 (1993).
[Crossref] [PubMed]

1992 (1)

M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Comm. 91, 401–407 (1992).
[Crossref]

1988 (1)

O. Thual and S. Fauve, “Localized structures generated by subcritical instabilities,” J. Phys. 49, 1829–1833 (1988).
[Crossref]

1987 (1)

L. A. Lugiato and R. Lefever, “Spatial dissipative structures in passive optical systems,” Phys. Rev. Lett. 58, 2209–2211 (1987).
[Crossref] [PubMed]

Ackemann, T.

B. Schapers, T. Ackemann, and W. Lange, “Properties of feedback solitons in a single-mirror experiment,” IEEE J.Quantum Electron. 39, 227–237 (2003).
[Crossref]

B. Schäpers, M. Feldmann, T. Ackemann, and W. Lange, “Interaction of localized structures in an optical pattern-forming system,” Phys. Rev. Lett. 85, 748–751 (2000).
[Crossref] [PubMed]

Agez, G.

E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, “Experimental evidence of absolute and convective instabilities in optics,” Phys. Rev. Lett. 92, 043901 (2004).
[Crossref] [PubMed]

Alexeeva, N. V.

N. V. Alexeeva and I. V. Barashenkov, “Impurity-Induced Satabilization of Solitons in Arrays of Parametrically Driven Nonlinear Oscillators,” Phys. Rev. Lett. 84, 3053–3056 (2000).
[Crossref]

Balakireva, I. V.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

Balle, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Barashenkov, I. V.

I. V. Barashenkov and E. V. Zemlyanaya, “Travelling solitons in the externally driven nonlinear Schrödinger equation,” J. Phys. A: Math. Theor. 44465211 (2011).
[Crossref]

R. Richter and I. V. Barashenkov, “Two-dimensional solitons on the surface of magnetic fluids,” Phys. Rev. Lett. 94, 184503 (2005).
[Crossref] [PubMed]

N. V. Alexeeva and I. V. Barashenkov, “Impurity-Induced Satabilization of Solitons in Arrays of Parametrically Driven Nonlinear Oscillators,” Phys. Rev. Lett. 84, 3053–3056 (2000).
[Crossref]

I. V. Barashenkov and Y. S. Smirnov, “Existence and stability chart for the ac-driven, damped nonlinear Schrodinger solitons,” Phys. Rev. E 54, 5707–5725 (1996).
[Crossref]

Barland, S.

E. Caboche, F. Pedaci, P. Genevet, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Microresonator defects as sources of drifting cavity solitons,” Phys. Rev. Lett. 102, 163901 (2009); ;E. Caboche, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Cavity-soliton motion in the presence of device defects,” Phys. Rev. A 80, 053814 (2009).
[Crossref] [PubMed]

F. Pedaci, G. Tissoni, S. Barland, M. Giudici, and J. Tredicce, “Mapping local defects of extended media using localized structures,” Appl. Phys. Lett. 93, 111104 (2008).
[Crossref]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Biancalana, F.

Birner, A.

Bold, K.

K. Bold, C. Edwards, J. Guckenheimer, S. Guharay, K. Hoffman, J. Hubbard, R. Oliva, and W. Weckesser, “The Forced van der Pol Equation II: Canards in the Reduced System,” SIAM J. Appl. Dyn. Syst. 2, 570–608 (2003).
[Crossref]

Brambilla, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
[Crossref] [PubMed]

Caboche, E.

E. Caboche, F. Pedaci, P. Genevet, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Microresonator defects as sources of drifting cavity solitons,” Phys. Rev. Lett. 102, 163901 (2009); ;E. Caboche, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Cavity-soliton motion in the presence of device defects,” Phys. Rev. A 80, 053814 (2009).
[Crossref] [PubMed]

Chang, W.

Chembo, Y. K.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

Y. K. Chembo and C. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).
[Crossref]

Coen, S.

P. Parra-Rivas, D. Gomila, F. Leo, S. Coen, and L. Gelens, “Third-order chromatic dispersion stabilizes Kerr frequency combs,” Opt. Lett. 39, 2971–2974 (2014).
[Crossref] [PubMed]

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, “Modeling of octave-spanning Kerr frequency combs using a generalized mean-field Lugiato-Lefever model,” Opt. Lett. 38, 37–39 (2013).
[Crossref] [PubMed]

F. Leo, L. Gelens, P. Emplit, M. Haelterman, and S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).
[Crossref] [PubMed]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nature Phot. 4, 471–476 (2010).
[Crossref]

P. Parra-Rivas, D. Gomila, M. A. Matias, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A89, 043813 (1–12) (2014).
[Crossref]

Coillet, A.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, “Stability analysis of the spatiotemporal Lugiato-Lefever model for Kerr optical frequency combs in the anomalous and normal dispersion regimes,” Phys. Rev. A 89, 063814 (2014).
[Crossref]

Colet, P.

A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of noise on excitable dissipative solitons,” Eur. Phys. J. D 59, 37–42 (2010).
[Crossref]

A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of a localized beam on the dynamics of excitable cavity solitons,” Phys. Rev. A 78, 053821 (2008).
[Crossref]

L. Gelens, D. Gomila, G. Van der Sande, J. Danckaert, P. Colet, and M. A. Matías, “Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials,” Phys. Rev. A 77, 033841 (2008).
[Crossref]

M. Santagiustina, P. Colet, M. S. Miguel, and D. Walgraef, “Walk-off and pattern selection in optical parametric oscillators,” Opt. Lett. 23, 1167–1169 (1998).
[Crossref]

M. Santagiustina, P. Colet, M. S. Miguel, and D. Walgraef, “Noise-sustained convective structures in nonlinear optics,” Phys. Rev. Lett. 79, 3633–3636 (1997).
[Crossref]

P. Parra-Rivas, D. Gomila, M. A. Matías, and P. Colet, “Dissipative soliton excitability induced by spatial inhomogeneities and drift,” Phys. Rev. Lett.110, 064103 (1–5) (2013).
[Crossref] [PubMed]

P. Parra-Rivas, D. Gomila, M. A. Matías, and P. Colet, “On the drif-defect mechanism for dissipative soliton excitability,” (in preparation).

Danckaert, J.

L. Gelens, D. Gomila, G. Van der Sande, J. Danckaert, P. Colet, and M. A. Matías, “Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials,” Phys. Rev. A 77, 033841 (2008).
[Crossref]

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
[Crossref]

Diddams, S. A.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[Crossref] [PubMed]

Edwards, C.

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Emplit, P.

Emplit, Ph.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nature Phot. 4, 471–476 (2010).
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D. Gomila, A. J. Scroggie, and W. J. Firth, “Bifurcation structure of dissipative solitons,” Physica D 227, 70–77 (2007).
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Gelens, L.

P. Parra-Rivas, D. Gomila, F. Leo, S. Coen, and L. Gelens, “Third-order chromatic dispersion stabilizes Kerr frequency combs,” Opt. Lett. 39, 2971–2974 (2014).
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F. Leo, L. Gelens, P. Emplit, M. Haelterman, and S. Coen, “Dynamics of one-dimensional Kerr cavity solitons,” Opt. Express 21, 9180–9191 (2013).
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M. Tlidi and L. Gelens, “High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities,” Opt. Lett. 35, 306–308 (2010).
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L. Gelens, D. Gomila, G. Van der Sande, J. Danckaert, P. Colet, and M. A. Matías, “Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials,” Phys. Rev. A 77, 033841 (2008).
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L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
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G. Kozyreff and L. Gelens, “Cavity solitons and localized patterns in a finite-size optical cavity,” Phys. Rev. A84, 023819 (1–5) (2011).
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F. Pedaci, G. Tissoni, S. Barland, M. Giudici, and J. Tredicce, “Mapping local defects of extended media using localized structures,” Appl. Phys. Lett. 93, 111104 (2008).
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S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
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A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of a localized beam on the dynamics of excitable cavity solitons,” Phys. Rev. A 78, 053821 (2008).
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L. Gelens, D. Gomila, G. Van der Sande, J. Danckaert, P. Colet, and M. A. Matías, “Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials,” Phys. Rev. A 77, 033841 (2008).
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L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
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P. Parra-Rivas, D. Gomila, M. A. Matías, and P. Colet, “On the drif-defect mechanism for dissipative soliton excitability,” (in preparation).

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P. Parra-Rivas, D. Gomila, M. A. Matias, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A89, 043813 (1–12) (2014).
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F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nature Phot. 4, 471–476 (2010).
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A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of a localized beam on the dynamics of excitable cavity solitons,” Phys. Rev. A 78, 053821 (2008).
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F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, “Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer,” Nature Phot. 4, 471–476 (2010).
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L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
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E. Caboche, F. Pedaci, P. Genevet, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Microresonator defects as sources of drifting cavity solitons,” Phys. Rev. Lett. 102, 163901 (2009); ;E. Caboche, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Cavity-soliton motion in the presence of device defects,” Phys. Rev. A 80, 053814 (2009).
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S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
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S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
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P. Parra-Rivas, D. Gomila, M. A. Matias, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A89, 043813 (1–12) (2014).
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A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of noise on excitable dissipative solitons,” Eur. Phys. J. D 59, 37–42 (2010).
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A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of a localized beam on the dynamics of excitable cavity solitons,” Phys. Rev. A 78, 053821 (2008).
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L. Gelens, D. Gomila, G. Van der Sande, J. Danckaert, P. Colet, and M. A. Matías, “Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials,” Phys. Rev. A 77, 033841 (2008).
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P. Parra-Rivas, D. Gomila, M. A. Matías, and P. Colet, “Dissipative soliton excitability induced by spatial inhomogeneities and drift,” Phys. Rev. Lett.110, 064103 (1–5) (2013).
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P. Parra-Rivas, D. Gomila, M. A. Matías, and P. Colet, “On the drif-defect mechanism for dissipative soliton excitability,” (in preparation).

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Mlynek, J.

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K. Bold, C. Edwards, J. Guckenheimer, S. Guharay, K. Hoffman, J. Hubbard, R. Oliva, and W. Weckesser, “The Forced van der Pol Equation II: Canards in the Reduced System,” SIAM J. Appl. Dyn. Syst. 2, 570–608 (2003).
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H. Ward, M. N. Ouarzazi, M. Taki, and P. Glorieux, “Transverse dynamics of optical parametric oscillators in presence of walk-off,” Eur. Phys. J. D 3, 275–288 (1998).
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P. Parra-Rivas, D. Gomila, F. Leo, S. Coen, and L. Gelens, “Third-order chromatic dispersion stabilizes Kerr frequency combs,” Opt. Lett. 39, 2971–2974 (2014).
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P. Parra-Rivas, D. Gomila, M. A. Matías, and P. Colet, “On the drif-defect mechanism for dissipative soliton excitability,” (in preparation).

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B. Schapers, T. Ackemann, and W. Lange, “Properties of feedback solitons in a single-mirror experiment,” IEEE J.Quantum Electron. 39, 227–237 (2003).
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Schmidberger, M. J.

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D. Gomila, A. J. Scroggie, and W. J. Firth, “Bifurcation structure of dissipative solitons,” Physica D 227, 70–77 (2007).
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E. Louvergneaux, C. Szwaj, G. Agez, P. Glorieux, and M. Taki, “Experimental evidence of absolute and convective instabilities in optics,” Phys. Rev. Lett. 92, 043901 (2004).
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M. Tlidi and L. Gelens, “High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities,” Opt. Lett. 35, 306–308 (2010).
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L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
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E. Caboche, F. Pedaci, P. Genevet, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Microresonator defects as sources of drifting cavity solitons,” Phys. Rev. Lett. 102, 163901 (2009); ;E. Caboche, S. Barland, M. Giudici, J. Tredicce, G. Tissoni, and L. A. Lugiato, “Cavity-soliton motion in the presence of device defects,” Phys. Rev. A 80, 053814 (2009).
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P. Umbanhowar, F. Melo, and H. L. Swinney, “Localized excitations in a vertically vibrated granular layer,” Nature 382, 793–796 (1996).
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Van der Sande, G.

L. Gelens, D. Gomila, G. Van der Sande, J. Danckaert, P. Colet, and M. A. Matías, “Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials,” Phys. Rev. A 77, 033841 (2008).
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L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
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Veretennicoff, I.

L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
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M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Comm. 91, 401–407 (1992).
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A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of noise on excitable dissipative solitons,” Eur. Phys. J. D 59, 37–42 (2010).
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H. Ward, M. N. Ouarzazi, M. Taki, and P. Glorieux, “Transverse dynamics of optical parametric oscillators in presence of walk-off,” Eur. Phys. J. D 3, 275–288 (1998).
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P. Umbanhowar, F. Melo, and H. L. Swinney, “Localized excitations in a vertically vibrated granular layer,” Nature 382, 793–796 (1996).
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S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature 419, 699–702 (2002).
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Nature Phot. (1)

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M. Haelterman, S. Trillo, and S. Wabnitz, “Dissipative modulation instability in a nonlinear dispersive ring cavity,” Opt. Comm. 91, 401–407 (1992).
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Opt. Express (2)

Opt. Lett. (6)

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L. Gelens, G. Van der Sande, P. Tassin, M. Tlidi, P. Kockaert, D. Gomila, I. Veretennicoff, and J. Danckaert, “Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures,” Phys. Rev. A 75, 063812 (2007).
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Y. K. Chembo and C. Menyuk, “Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering-gallery-mode resonators,” Phys. Rev. A 87, 053852 (2013).
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A. Jacobo, D. Gomila, M. A. Matías, and P. Colet, “Effects of a localized beam on the dynamics of excitable cavity solitons,” Phys. Rev. A 78, 053821 (2008).
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K. Bold, C. Edwards, J. Guckenheimer, S. Guharay, K. Hoffman, J. Hubbard, R. Oliva, and W. Weckesser, “The Forced van der Pol Equation II: Canards in the Reduced System,” SIAM J. Appl. Dyn. Syst. 2, 570–608 (2003).
[Crossref]

Other (5)

“Dissipative Solitons: From Optics to Biology and Medicine,” Lecture Notes in Physics, Vol. 751 edited by N. Akhmediev and A. Ankiewicz, eds. (Springer, 2008).

P. Parra-Rivas, D. Gomila, M. A. Matias, S. Coen, and L. Gelens, “Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs,” Phys. Rev. A89, 043813 (1–12) (2014).
[Crossref]

G. Kozyreff and L. Gelens, “Cavity solitons and localized patterns in a finite-size optical cavity,” Phys. Rev. A84, 023819 (1–5) (2011).
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P. Parra-Rivas, D. Gomila, M. A. Matías, and P. Colet, “Dissipative soliton excitability induced by spatial inhomogeneities and drift,” Phys. Rev. Lett.110, 064103 (1–5) (2013).
[Crossref] [PubMed]

P. Parra-Rivas, D. Gomila, M. A. Matías, and P. Colet, “On the drif-defect mechanism for dissipative soliton excitability,” (in preparation).

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Figures (9)

Figure 1
Figure 1 A synchronously pumped fiber cavity. R and T are the reflection and transmission coefficients of the beam splitter. L is the length of the fiber.
Figure 2
Figure 2 Effect of a defect on drifting CS solutions. Parameters for t = 0–1800 are h = 0.6, c = 0.1. At t = 1800, h is set to 0 and then the soliton starts drifting. The time evolution is shown in the middle panel, while the initial and final CS profiles are plotted in the bottom and top panels in black. The corresponding profile of the inhomogeneity is added in blue. Other parameters are θ = 1.56, u0 = 1.137, σ = 0.2727 and τ0 = tR/2.
Figure 3
Figure 3 Bifurcation diagrams of the different steady-state state solutions in function of h with c = 0. The solid (dashed) lines represent the energy of the stable (unstable) states. Other parameters are as in Fig. 2.
Figure 4
Figure 4 Profiles of the different steady-state state solutions corresponding to the branches shown in Fig. 3. The panels on the left depict the absolute value of the field u inside the cavity (black) and the corresponding profile of the defect (blue), while the panels on the right show the corresponding KFC in dB scale. (a) h = 0.052, (b) h = 0.556, and (c) h = −0.196. Other parameters are as in Fig. 2 and c = 0.
Figure 5
Figure 5 Bifurcation diagrams of the different steady-state state solutions in function of h for different values of the the drift strength c: (a) c = 0.025, (b) c = 0.06 and (c) c = 0.1. The solid (dashed) lines represent the energy of the stable (unstable) states. The + markers correspond to the extrema of oscillatory solutions, and the vertical dashed line shows the location of the Fold of Cycles (FC). Other parameters are as in Fig. 2.
Figure 6
Figure 6 Evolution of a CS at (a) c = 0.1, h = 0.3 (large-amplitude oscillations), (b) c = 0.1, h = 0.49, (small-amplitude oscillations), and (c) c = 0.1, h = 0.3 (excitability). The top two panels depict the evolution and final profile of the absolute value of the field u inside the cavity, while the bottom two panels show the corresponding evolution and final profile of the corresponding KFC in dB scale. Other parameters are as in Fig. 2. In panel (a), a periodic train of solitons is created at the inhomogeneity. In panel (b), a soliton is pinned at the inhomogeneity and locally oscillates with small amplitude. In panel (c), the system is excited by transiently (Δt = 30) changing the parameter values by hh + Δh, with Δh = −0.3. Such a parametric excitation leads to the emission of a CS form the defect location that continues to circulate in the cavity.
Figure 7
Figure 7 Temporal evolution of the field u at the defect position τ0 for two different boundary conditions: 1) absorbing boundary conditions (black solid line), 2) periodic boundary conditions (red dashed line). The train of solitons generated in the cavity corresponds to 9 peaks that circulate (branch H in Fig. 8). In panel (a) the domain width Lτ = 78, while in panel (b) Lτ = 84.8. h = 0.3 and c = 0.1, while other parameters are as in Fig. 2.
Figure 8
Figure 8 The top panel shows the oscillation period T of the various solutions of train of solitons (A–H) in the system with periodic boundary conditions. The natural period T0 in the system with absorbing boundary conditions is plotted in dashed lines as reference. The bottom panel shows the amount of CSs within the train of solitons corresponding to the branches shown in the top panel.
Figure 9
Figure 9 Evolution of a train of solitons for (a) h = 1.482, (b) h = 2.682 and (c) h = 5.682. The panels depict the evolution (bottom) and final profile (top) of the absolute value of the field u inside the cavity. Other parameters are θ = 3.8, u0 = 2.6, c = 3, σ = 0.2727 and τ0 = tR/2.

Equations (4)

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t R E t = ( α + i δ 0 ) E i L β 2 2 2 E τ 2 + i γ L | E | 2 E + T E 0 ( τ ) ,
u ( t , τ ) t = ( 1 + i θ ) u ( t , τ ) + i | u ( t , τ ) | 2 u ( t , τ ) + i 2 u ( t , τ ) τ 2 + u 0 ( τ ) ,
u 0 ( τ ) = u 0 + b ( τ ) = u 0 + h exp ( ( τ τ 0 σ ) 2 ) .
u t = ( 1 + i θ ) u + i | u | 2 u c u τ + i 2 u τ 2 + u 0 ( τ ) .

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