Abstract

Temporal cavity solitons (CSs) are pulses of light that can persist in coherently driven passive resonators, such as fiber ring resonators and monolithic microresonators. It has been theoretically predicted that they can exhibit rich instability dynamics, yet experimental observations have remained scarce. Here, we report on the observations of complex spatiotemporal instabilities of temporal CSs in a synchronously driven fiber ring resonator. Through continuous variation of a single control parameter, we observe a string of predicted instabilities, including irregular oscillations (breathing) and chaotic collapses. Beyond a critical point, we find behavior reminiscent of a phase transition: CSs trigger localized domains of spatiotemporal chaos that invade the surrounding continuous wave background. Our findings directly confirm a number of theoretical predictions, and they highlight that complex CS instabilities can play a role in experimental systems.

© 2016 Optical Society of America

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References

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2016 (3)

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

F. Copie, M. Conforti, A. Kudlinski, A. Mussot, and S. Trillo, Phys. Rev. Lett. 116, 143901 (2016).
[Crossref]

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, Opt. Lett. 41, 2565 (2016).
[Crossref]

2015 (3)

2014 (2)

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, Phys. Rev. A 89, 063814 (2014).
[Crossref]

2013 (3)

2010 (1)

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[Crossref]

2009 (1)

M. G. Clerc, S. Coulibaly, N. Mujica, R. Navarro, and T. Sauma, Philos. Trans. R. Soc. London Ser. A 367, 3213 (2009).
[Crossref]

2005 (1)

D. Gomila, M. A. Matías, and P. Colet, Phys. Rev. Lett. 94, 063905 (2005).
[Crossref]

1998 (1)

F. Mitschke and A. Schwache, J. Opt. B 10, 779 (1998).

1997 (1)

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[Crossref]

1996 (2)

F. Mitschke, G. Steinmeyer, and A. Schwache, Physica D 96, 251 (1996).
[Crossref]

I. V. Barashenkov and Y. S. Smirnov, Phys. Rev. E 54, 5707 (1996).
[Crossref]

1995 (2)

M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
[Crossref]

S. Longhi, Opt. Lett. 20, 695 (1995).
[Crossref]

1992 (1)

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[Crossref]

1987 (1)

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[Crossref]

1985 (1)

K. Nozaki and N. Bekki, J. Phys. Soc. Jpn. 54, 2363 (1985).
[Crossref]

Balakireva, I. V.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, Phys. Rev. A 89, 063814 (2014).
[Crossref]

Bao, C.

C. Bao, J. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence in an on-chip optical microresonator,” arXiv:1606.06788 (2016).

Barashenkov, I. V.

I. V. Barashenkov and Y. S. Smirnov, Phys. Rev. E 54, 5707 (1996).
[Crossref]

M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
[Crossref]

Bekki, N.

K. Nozaki and N. Bekki, J. Phys. Soc. Jpn. 54, 2363 (1985).
[Crossref]

Bogdan, M. M.

M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
[Crossref]

Bondila, M.

M. Bondila, I. V. Barashenkov, and M. M. Bogdan, Physica D 87, 314 (1995).
[Crossref]

Brasch, V.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

Chembo, Y. K.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, Phys. Rev. A 89, 063814 (2014).
[Crossref]

Y. K. Chembo and C. R. Menyuk, Phys. Rev. A 87, 053852 (2013).
[Crossref]

Clerc, M. G.

M. G. Clerc, S. Coulibaly, N. Mujica, R. Navarro, and T. Sauma, Philos. Trans. R. Soc. London Ser. A 367, 3213 (2009).
[Crossref]

Coen, S.

K. Luo, J. K. Jang, S. Coen, S. G. Murdoch, and M. Erkintalo, Opt. Lett. 40, 3735 (2015).
[Crossref]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, Nat. Commun. 6, 7370 (2015).
[Crossref]

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, Opt. Express 21, 9180 (2013).
[Crossref]

S. Coen, H. G. Randle, T. Sylvestre, and M. Erkintalo, Opt. Lett. 38, 37 (2013).
[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[Crossref]

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[Crossref]

Coillet, A.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, Phys. Rev. A 89, 063814 (2014).
[Crossref]

Colet, P.

D. Gomila, M. A. Matías, and P. Colet, Phys. Rev. Lett. 94, 063905 (2005).
[Crossref]

Conforti, M.

F. Copie, M. Conforti, A. Kudlinski, A. Mussot, and S. Trillo, Phys. Rev. Lett. 116, 143901 (2016).
[Crossref]

Copie, F.

F. Copie, M. Conforti, A. Kudlinski, A. Mussot, and S. Trillo, Phys. Rev. Lett. 116, 143901 (2016).
[Crossref]

Coulibaly, S.

M. G. Clerc, S. Coulibaly, N. Mujica, R. Navarro, and T. Sauma, Philos. Trans. R. Soc. London Ser. A 367, 3213 (2009).
[Crossref]

Emplit, Ph.

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, Opt. Express 21, 9180 (2013).
[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[Crossref]

Erkintalo, M.

Gaeta, A. L.

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, Opt. Lett. 41, 2565 (2016).
[Crossref]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FM2A.8.

Geiselmann, M.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

Gelens, L.

Godey, C.

C. Godey, I. V. Balakireva, A. Coillet, and Y. K. Chembo, Phys. Rev. A 89, 063814 (2014).
[Crossref]

Gomila, D.

D. Gomila, M. A. Matías, and P. Colet, Phys. Rev. Lett. 94, 063905 (2005).
[Crossref]

Gorodetsky, M. L.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

M. Karpov, H. Guo, E. Lucas, A. Kordts, M. H. P. Pfeiffer, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and controlled switching of dissipative Kerr solitons in optical microresonators,” arXiv:1601.05036 (2016).

Gorza, S.-P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[Crossref]

Griffith, A. G.

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FM2A.8.

Guo, H.

M. Karpov, H. Guo, E. Lucas, A. Kordts, M. H. P. Pfeiffer, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and controlled switching of dissipative Kerr solitons in optical microresonators,” arXiv:1601.05036 (2016).

Haelterman, M.

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, Opt. Express 21, 9180 (2013).
[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[Crossref]

S. Coen and M. Haelterman, Phys. Rev. Lett. 79, 4139 (1997).
[Crossref]

M. Haelterman, S. Trillo, and S. Wabnitz, Opt. Commun. 91, 401 (1992).
[Crossref]

Herr, T.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

Jang, J. K.

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, Opt. Lett. 41, 2565 (2016).
[Crossref]

K. Luo, J. K. Jang, S. Coen, S. G. Murdoch, and M. Erkintalo, Opt. Lett. 40, 3735 (2015).
[Crossref]

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, Nat. Commun. 6, 7370 (2015).
[Crossref]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FM2A.8.

Jaramillo-Villegas, J.

C. Bao, J. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence in an on-chip optical microresonator,” arXiv:1606.06788 (2016).

Ji, X.

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, Opt. Lett. 41, 2565 (2016).
[Crossref]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FM2A.8.

Joshi, C.

Jost, J. D.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

Karpov, M.

M. Karpov, H. Guo, E. Lucas, A. Kordts, M. H. P. Pfeiffer, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and controlled switching of dissipative Kerr solitons in optical microresonators,” arXiv:1601.05036 (2016).

Kippenberg, T. J.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

M. Karpov, H. Guo, E. Lucas, A. Kordts, M. H. P. Pfeiffer, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and controlled switching of dissipative Kerr solitons in optical microresonators,” arXiv:1601.05036 (2016).

Klenner, A.

Kockaert, P.

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[Crossref]

Kondratiev, N. M.

T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L. Gorodetsky, and T. J. Kippenberg, Nat. Photonics 8, 145 (2014).
[Crossref]

Kordts, A.

M. Karpov, H. Guo, E. Lucas, A. Kordts, M. H. P. Pfeiffer, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and controlled switching of dissipative Kerr solitons in optical microresonators,” arXiv:1601.05036 (2016).

Kudlinski, A.

F. Copie, M. Conforti, A. Kudlinski, A. Mussot, and S. Trillo, Phys. Rev. Lett. 116, 143901 (2016).
[Crossref]

Leaird, D. E.

C. Bao, J. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, and A. M. Weiner, “Observation of Fermi-Pasta-Ulam recurrence in an on-chip optical microresonator,” arXiv:1606.06788 (2016).

Lefever, R.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[Crossref]

Leo, F.

F. Leo, L. Gelens, Ph. Emplit, M. Haelterman, and S. Coen, Opt. Express 21, 9180 (2013).
[Crossref]

F. Leo, S. Coen, P. Kockaert, S.-P. Gorza, Ph. Emplit, and M. Haelterman, Nat. Photonics 4, 471 (2010).
[Crossref]

Lihachev, G.

V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, Science 351, 357 (2016).
[Crossref]

M. Karpov, H. Guo, E. Lucas, A. Kordts, M. H. P. Pfeiffer, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and controlled switching of dissipative Kerr solitons in optical microresonators,” arXiv:1601.05036 (2016).

Lipson, M.

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, Opt. Lett. 41, 2565 (2016).
[Crossref]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FM2A.8.

Lobanov, V. E.

M. Karpov, H. Guo, E. Lucas, A. Kordts, M. H. P. Pfeiffer, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and controlled switching of dissipative Kerr solitons in optical microresonators,” arXiv:1601.05036 (2016).

Longhi, S.

Lucas, E.

M. Karpov, H. Guo, E. Lucas, A. Kordts, M. H. P. Pfeiffer, G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, and T. J. Kippenberg, “Universal dynamics and controlled switching of dissipative Kerr solitons in optical microresonators,” arXiv:1601.05036 (2016).

Lugiato, L. A.

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[Crossref]

Luke, K.

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, Opt. Lett. 41, 2565 (2016).
[Crossref]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FM2A.8.

Luo, K.

Matías, M. A.

D. Gomila, M. A. Matías, and P. Colet, Phys. Rev. Lett. 94, 063905 (2005).
[Crossref]

Menyuk, C. R.

Y. K. Chembo and C. R. Menyuk, Phys. Rev. A 87, 053852 (2013).
[Crossref]

Miller, S. A.

C. Joshi, J. K. Jang, K. Luke, X. Ji, S. A. Miller, A. Klenner, Y. Okawachi, M. Lipson, and A. L. Gaeta, Opt. Lett. 41, 2565 (2016).
[Crossref]

M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X. Ji, M. Lipson, and A. L. Gaeta, in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2016), paper FM2A.8.

Mitschke, F.

F. Mitschke and A. Schwache, J. Opt. B 10, 779 (1998).

F. Mitschke, G. Steinmeyer, and A. Schwache, Physica D 96, 251 (1996).
[Crossref]

Mujica, N.

M. G. Clerc, S. Coulibaly, N. Mujica, R. Navarro, and T. Sauma, Philos. Trans. R. Soc. London Ser. A 367, 3213 (2009).
[Crossref]

Murdoch, S. G.

J. K. Jang, M. Erkintalo, S. Coen, and S. G. Murdoch, Nat. Commun. 6, 7370 (2015).
[Crossref]

K. Luo, J. K. Jang, S. Coen, S. G. Murdoch, and M. Erkintalo, Opt. Lett. 40, 3735 (2015).
[Crossref]

Mussot, A.

F. Copie, M. Conforti, A. Kudlinski, A. Mussot, and S. Trillo, Phys. Rev. Lett. 116, 143901 (2016).
[Crossref]

Navarro, R.

M. G. Clerc, S. Coulibaly, N. Mujica, R. Navarro, and T. Sauma, Philos. Trans. R. Soc. London Ser. A 367, 3213 (2009).
[Crossref]

Nozaki, K.

K. Nozaki and N. Bekki, J. Phys. Soc. Jpn. 54, 2363 (1985).
[Crossref]

Okawachi, Y.

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Figures (4)

Fig. 1.
Fig. 1.

(a) CS (red curves) and cw (black curves) solutions for X=30. Solid curves, stable solutions; dotted curves, unstable solutions diverging to one of the other solutions; dashed lines, unstable solutions with more complex dynamics. Inset highlights the different dynamical CS regimes: perpetually oscillating CSs (I); oscillating CSs that eventually decay to a cw state (II); CSs that trigger spatiotemporal chaos (III). (b–d) Examples of numerically simulated dynamics for different regimes. (b) Regime I, Δ=8; (c) Regime II, Δ=7.45; (d) Regime III, Δ=6.

Fig. 2.
Fig. 2.

Schematic illustration of the experimental setup. PC, polarization controller; PD, photodetector; SMF, single-mode fiber; MZM, Mach–Zehnder modulator. Top left inset shows a typical pump pulse profile.

Fig. 3.
Fig. 3.

Experimentally measured spatiotemporal evolution inside the fiber ring resonator as Δ is continuously reduced. The different panels show snapshots around different Δ regions of interest, extracted from a single long measurement. Line plots on the right show the evolution of the integrated energy for a particular CS (highlighted by dashed white lines).

Fig. 4.
Fig. 4.

(a) Experimentally measured intracavity field evolution over the full 20 ns field profile as Δ is slowly reduced around Δ6. Arrows highlight CSs. (b) Zoom on a particular region (highlighted by a white arrow) where a CS triggers an expanding domain of spatiotemporal chaos. Corresponding simulations are shown in (c).

Equations (1)

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E(t,τ)t=[1+i(|E|2Δ)+i2τ2]E+S.

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