Dissipative Kerr solitons in optical microresonators combine nonlinear optical physics with photonic-integrated technologies. They are promising for a number of applications ranging from optical coherent communications to astrophysical spectrometer calibration, and are also of fundamental interest to the physical sciences. Dissipative Kerr solitons can form a variety of stable states, including breathers and multiple-soliton formations. Among these states, soliton crystals stand out: temporally ordered ensembles of soliton pulses, which are regularly arranged by a modulation of the continuous-wave intracavity driving field. To date, however, the dynamics of soliton crystals and their defect-free generation remain unexplored. Here, we show that the chaotic operating regimes of driven optical microresonators significantly impact the dynamics of soliton crystals. We realize deterministic generation of perfect soliton crystal states, which correspond to a stable, defect-free lattice of intracavity optical pulses. We reveal a critical pump power, below which the stochastic process of soliton excitation abruptly becomes deterministic, which enables faultless, device-independent access to perfect soliton crystals. We also demonstrate the switching of these states and its relation to the regime of transient chaos. Finally, we report on other dynamical phenomena observed in soliton crystals including the formation of breathers, transitions between perfect soliton crystals, their melting and recrystallization.
Subscribe to Journal
Get full journal access for 1 year
only $4.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data used to produce the plots within this paper are available at https://doi.org/10.5281/zenodo.2809645. All other data used in this study are available from the corresponding authors on reasonable request.
The code used to produce the plots within this paper is available at https://doi.org/10.5281/zenodo.2809645.
Haelterman, M., Trillo, S. & Wabnitz, S. Dissipative modulation instability in a nonlinear dispersive ring cavity. Opt. Commun. 91, 401–407 (1992).
Akhmediev, N. N. & Ankiewicz, A. Solitons Around Us: Integrable, Hamiltonian and Dissipative Systems 105–126 (Springer, 2003).
Kippenberg, T. J., Gaeta, A. L., Lipson, M. & Gorodetsky, M. L. Dissipative Kerr solitons in optical microresonators. Science 361, eaan8083 (2018).
Herr, T. et al. Temporal solitons in optical microresonators. Nat. Photon. 8, 145–152 (2014).
Brasch, V. et al. Photonic chip–based optical frequency comb using soliton Cherenkov radiation. Science 351, 357–360 (2016).
Raja, A. S. et al. Electrically pumped photonic integrated soliton microcomb. Nat. Commun. 10, 680–687 (2019).
Stern, B., Ji, X., Okawachi, Y., Gaeta, A. L. & Lipson, M. Battery-operated integrated frequency comb generator. Nature 562, 401–405 (2018).
Marin-Palomo, P. et al. Microresonator-based solitons for massively parallel coherent optical communications. Nature 546, 274–279 (2017).
Jost, J. D. et al. Counting the cycles of light using a self-referenced optical microresonator. Optica 2, 706–711 (2015).
Suh, M.-G., Yang, Q.-F., Yang, K. Y., Yi, X. & Vahala, K. J. Microresonator soliton dual-comb spectroscopy. Science 354, 600–603 (2016).
Yu, M. et al. Silicon-chip-based mid-infrared dual-comb spectroscopy. Nat. Commun. 9, 1869–1876 (2018).
Trocha, P. et al. Ultrafast optical ranging using microresonator soliton frequency combs. Science 359, 887–891 (2018).
Suh, M.-G. & Vahala, K. J. Soliton microcomb range measurement. Science 359, 884–887 (2018).
Liang, W. et al. High spectral purity Kerr frequency comb radio frequency photonic oscillator. Nat. Commun. 6, 7957 (2015).
Spencer, D. T. et al. An optical-frequency synthesizer using integrated photonics. Nature 557, 81–85 (2018).
Obrzud, E. et al. A microphotonic astrocomb. Nat. Photon. 13, 31–36 (2019).
Suh, M.-G. et al. Searching for exoplanets using a microresonator astrocomb. Nat. Photon. 13, 25–30 (2019).
Cole, D. C., Lamb, E. S., Del’Haye, P., Diddams, S. A. & Papp, S. B. Soliton crystals in Kerr resonators. Nat. Photon. 11, 671–677 (2017).
Wang, Y. et al. Universal mechanism for the binding of temporal cavity solitons. Optica 4, 855–863 (2017).
Taheri, H., Matsko, A. B. & Maleki, L. Optical lattice trap for Kerr solitons. Eur. Phys. J. D 71, 153–165 (2017).
Wang, W. et al. Robust soliton crystals in a thermally controlled microresonator. Opt. Lett. 43, 2002–2005 (2018).
Karpov, M. et al. Dynamics of soliton crystals in optical microresonators. In Conference on Lasers and Electro-Optics FTu1D.2 (Optical Society of America, 2017).
Lu, Z. et al. Raman self-frequency-shift of soliton crystal in a high index doped silica micro-ring resonator. Opt. Mater. Express 8, 2662–2669 (2018).
Luke, K., Dutt, A., Poitras, C. B. & Lipson, M. Overcoming Si3N4 film stress limitations for high quality factor ring resonators. Opt. Express 21, 22829–22833 (2013).
Pfeiffer, M. H. P. et al. Photonic Damascene process for integrated high-Q microresonator based nonlinear photonics. Optica 3, 20–25 (2016).
Kordts, A., Pfeiffer, M. H. P., Guo, H., Brasch, V. & Kippenberg, T. J. Higher order mode suppression in high-Q anomalous dispersion SiN microresonators for temporal dissipative Kerr soliton formation. Opt. Lett. 41, 452–455 (2016).
Grudinin, I. S. et al. High-contrast Kerr frequency combs. Optica 4, 434–437 (2017).
Lugiato, L. A. & Lefever, R. Spatial dissipative structures in passive optical systems. Phys. Rev. Lett. 58, 2209–2211 (1987).
Guo, H. et al. Universal dynamics and deterministic switching of dissipative Kerr solitons in optical microresonators. Nat. Phys. 13, 94–102 (2017).
Anderson, M., Leo, F., Coen, S., Erkintalo, M. & Murdoch, S. G. Observations of spatiotemporal instabilities of temporal cavity solitons. Optica 3, 1071–1074 (2016).
Lu, Z. et al. Deterministic generation and switching of dissipative Kerr soliton in a thermally controlled micro-resonator. AIP Adv. 9, 025314–025319 (2019).
Xue, X. et al. Mode-locked dark pulse Kerr combs in normal-dispersion microresonators. Nat. Photon. 9, 594–600 (2015).
Xue, X. et al. Normal-dispersion microcombs enabled by controllable mode interactions. Laser Photon. Rev. 9, L23–L28 (2015).
Lucas, E., Karpov, M., Guo, H., Gorodetsky, M. & Kippenberg, T. Breathing dissipative solitons in optical microresonators. Nat. Commun. 8, 736–746 (2017).
Joshi, C. et al. Thermally controlled comb generation and soliton modelocking in microresonators. Opt. Lett. 41, 2565–2568 (2016).
Sun, C., Askham, T. & Kutz, J. N. Stability and dynamics of microring combs: elliptic function solutions of the Lugiato–Lefever equation. J. Opt. Soc. Am. B 35, 1341–1353 (2018).
Del’Haye, P., Arcizet, O., Gorodetsky, M. L., Holzwarth, R. & Kippenberg, T. J. Frequency comb assisted diode laser spectroscopy for measurement of microcavity dispersion. Nat. Photon. 3, 529–533 (2009).
Herr, T. et al. Mode spectrum and temporal soliton formation in optical microresonators. Phys. Rev. Lett. 113, 123901–123906 (2014).
We gratefully acknowledge fruitful discussions with E. Lucas and M. Anderson. This publication was supported by the Air Force Office of Scientific Research, Air Force Material Command, USAF under award no. FA9550-15-1-0099 and by funding from the European Union’s Horizon 2020 Marie Sklodowska-Curie IF grant agreement no. 753749 (SOLISYNTH). This publication was supported by contract D18AC00032 (DRINQS) from the Defense Advanced Research Projects Agency, Defense Sciences Office. M.K. acknowledges the support from the European Space Technology Centre with ESA contract no. 4000116145/16/NL/MH/GM. Si3N4 samples were fabricated and grown in the Center of MicroNanoTechnology (CMi) at EPFL.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Karpov, M., Pfeiffer, M.H.P., Guo, H. et al. Dynamics of soliton crystals in optical microresonators. Nat. Phys. 15, 1071–1077 (2019). https://doi.org/10.1038/s41567-019-0635-0
Physical Review Letters (2021)
Nature Physics (2021)
Physical Review A (2021)
Physical Review A (2021)
Nature Communications (2021)