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Soliton crystals in Kerr resonators

Nature Photonics volume 11, pages 671–676 (2017)Cite this article

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Abstract

Self-organized solitons confined to an optical resonator would offer unique capabilities for experiments in communication, computation and sensing with light. Here, we report the observation of soliton crystals in monolithic Kerr microresonators—spontaneously and collectively ordered ensembles of co-propagating solitons whose interactions discretize their allowed temporal separations. We unambiguously identify and characterize soliton crystals through analysis of their ‘fingerprint’ optical spectra, which arise from spectral interference between the solitons. We identify a rich space of soliton crystals exhibiting crystallographic defects and we perform time-domain measurements to directly confirm our inference of their crystal structure. Soliton crystallization is explained by long-range soliton interactions mediated by resonator mode degeneracies, and we probe the qualitative difference between soliton crystals and the disorganized soliton liquid that would form in the absence of these interactions. Our work explores the physics of monolithic Kerr resonators in a regime of dense soliton occupation and offers a way to increase the efficiency of Kerr combs. Furthermore, the extreme degeneracy of the configuration space of soliton crystals suggests an implementation for an on-chip optical buffer.

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Fig. 1: Generation of a soliton crystal using the Kerr nonlinearity in a χ (3)-nonlinear medium (here silica).
Fig. 2: Investigation of a superstructured crystal.
Fig. 3: A taxonomy of soliton crystals.
Fig. 4: Intensity cross-correlation measurements of crystal j from Fig. 3.

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References

  1. Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Microresonator-based optical frequency combs. Science 332, 555–559 (2011).

    Article  ADS  Google Scholar 

  2. Diddams, S. A. The evolving optical frequency comb. J. Opt. Soc. Am. B 27, B51–B62 (2010).

    Article  ADS  Google Scholar 

  3. Herr, T. et al. Temporal solitons in optical microresonators. Nat. Photon. 8, 145–152 (2014).

    Article  ADS  Google Scholar 

  4. Herr, T. et al. Mode spectrum and temporal soliton formation in optical microresonators. Phys. Rev. Lett. 113, 123901 (2014).

    Article  ADS  Google Scholar 

  5. Joshi, C. et al. Thermally controlled comb generation and soliton modelocking in microresonators. Opt. Lett. 41, 2565–2568 (2016).

    Article  ADS  Google Scholar 

  6. Yi, X., Yang, Q.-F., Yang, K. Y., Suh, M.-G. & Vahala, K. Soliton frequency comb at microwave rates in a high-Q silica microresonator. Optica 2, 1078–1085 (2015).

    Article  Google Scholar 

  7. Drake, T. E. et al. An octave-bandwidth Kerr optical frequency comb on a silicon chip. Adv. Opt. Photon. STu3Q.4 (2016).

  8. Godey, C., Balakireva, I. V., Coillet, A. & Chembo, Y. K. 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Coen, S. & Erkintalo, M. Universal scaling laws of Kerr frequency combs. Opt. Lett. 38, 1790–1792 (2013).

    Article  ADS  Google Scholar 

  11. Yang, K. Y. et al. Broadband dispersion-engineered microresonator on a chip. Nat. Photon. 10, 316–320 (2016).

    Article  ADS  Google Scholar 

  12. Okawachi, Y. et al. Bandwidth shaping of microresonator-based frequency combs via dispersion engineering. Opt. Lett. 39, 3535–3538 (2014).

    Article  ADS  Google Scholar 

  13. Jang, J. K., Erkintalo, M., Coen, S. & Murdoch, S. G. Temporal tweezing of light through the trapping and manipulation of temporal cavity solitons. Nat. Commun. 6, 7370 (2015).

    Article  ADS  Google Scholar 

  14. Leo, F. et al. Temporal cavity solitons in one-dimensional Kerr media as bits in an all-optical buffer. Nat. Photon. 4, 471–476 (2010).

    Article  ADS  Google Scholar 

  15. Jang, J. K. et al. All-optical buffer based on temporal cavity solitons operating at 10 Gb/s. Opt. Lett. 41, 4526–4529 (2016).

    Article  ADS  Google Scholar 

  16. Jang, J. K., Erkintalo, M., Murdoch, S. G. & Coen, S. Ultraweak long-range interactions of solitons observed over astronomical distances. Nat. Photon. 7, 657–663 (2013).

    Article  ADS  Google Scholar 

  17. Coillet, A. et al. Azimuthal Turing patterns, bright and dark cavity solitons in Kerr combs generated with whispering-gallery-mode resonators. IEEE Photon. J. 5, 6100409 (2013).

    Article  Google Scholar 

  18. Renninger, W. H. & Rakich, P. T. Closed-form solutions and scaling laws for Kerr frequency combs. Sci. Rep. 6, 24742 (2016).

    Article  ADS  Google Scholar 

  19. Qi, Z., D’Aguanno, G. & Menyuk, C. R. Nonlinear frequency combs generated by cnoidal waves in microring resonators. J. Opt. Soc. Am. B 34, 785–794 (2017).

    Article  ADS  Google Scholar 

  20. Malomed, B. A., Schwache, A. & Mitschke, F. Soliton lattice and gas in passive fiber-ring resonators. Fiber Integr. Opt. 17, 267–277 (1998).

    Article  Google Scholar 

  21. Mitschke, F. & Schwache, A. Soliton ensembles in a nonlinear resonator. J. Opt. B 10, 779–788 (1998).

    Google Scholar 

  22. Schwache, A. & Mitschke, F. Properties of an optical soliton gas. Phys. Rev. E 55, 7720–7725 (1997).

    Article  ADS  Google Scholar 

  23. Zajnulina, M. et al. Characteristics and stability of soliton crystals in optical fibres for the purpose of optical frequency comb generation. Opt. Commun. 393, 95–102 (2017).

    Article  ADS  Google Scholar 

  24. Haboucha, A., Leblond, H., Salhi, M., Komarov, A. & Sanchez, F. Coherent soliton pattern formation in a fiber laser. Opt. Lett. 33, 524–526 (2008).

    Article  ADS  Google Scholar 

  25. Amrani, F., Salhi, M., Grelu, P., Leblond, H. & Sanchez, F. Universal soliton pattern formations in passively mode-locked fiber lasers. Opt. Lett. 36, 1545–1547 (2011).

    Article  ADS  Google Scholar 

  26. Haboucha, A., Leblond, H., Salhi, M., Komarov, A. & Sanchez, F. Analysis of soliton pattern formation in passively mode-locked fiber lasers. Phys. Rev. A 78, 043806 (2008).

    Article  ADS  Google Scholar 

  27. Ashcroft, N. W. & Mermin, D. N. Solid State Physics (Brooks Cole, Belmont, USA, 1976).

  28. Herr, T. et al. Universal formation dynamics and noise of Kerr-frequency combs in microresonators. Nat. Photon. 6, 480–487 (2012).

    Article  ADS  Google Scholar 

  29. McDonald, G. S. & Firth, W. Spatial solitary wave optical memory. J. Opt. Soc. Am. B 7, 1328–1335 (1990).

    Article  ADS  Google Scholar 

  30. Luo, K., Jang, J. K., Coen, S., Murdoch, S. G. & Erkintalo, M. Spontaneous creation and annihilation of temporal cavity solitons in a coherently driven passive fiber resonator. Opt. Lett. 40, 3735–3738 (2015).

    Article  ADS  Google Scholar 

  31. Del’Haye, P., Beha, K., Papp, S. B. & Diddams, S. A. Self-injection locking and phase-locked states in microresonator-based optical frequency combs. Phys. Rev. Lett. 112, 043905 (2014).

    Article  ADS  Google Scholar 

  32. Del’Haye, P. et al. Phase steps and resonator detuning measurements in microresonator frequency combs. Nat. Commun. 6, 5668 (2015).

    Article  Google Scholar 

  33. Del’Haye, P., Diddams, S. A. & Papp, S. B. Laser-machined ultra-high-Q microrod resonators for nonlinear optics. Appl. Phys. Lett. 102, 221119 (2013).

    Article  ADS  Google Scholar 

  34. Lee, H. et al. Chemically etched ultrahigh-Q wedge-resonator on a silicon chip. Nat. Photon. 6, 369–373 (2012).

    Article  ADS  Google Scholar 

  35. Silver, J. M., Guo, C., Del Bino, L. & Del’Haye, P. Kerr superoscillator model for microresonator frequency combs. Phys. Rev. A 95, 033835 (2017).

    Article  ADS  Google Scholar 

  36. Carmon, T., Yang, L. & Vahala, K. J. Dynamical thermal behavior and thermal self-stability of microcavities. Opt. Express 12, 4742–4750 (2004).

    Article  ADS  Google Scholar 

  37. Liu, Y. et al. Investigation of mode coupling in normal-dispersion silicon nitride microresonators for Kerr frequency comb generation. Optica 1, 137–144 (2014).

    Article  Google Scholar 

  38. Hansson, T. & Wabnitz, S. Bichromatically pumped microresonator frequency combs. Phys. Rev. A 90, 013811 (2014).

    Article  ADS  Google Scholar 

  39. Skryabin, D. V. & Firth, W. J. Interaction of cavity solitons in degenerate optical parametric oscillators. Opt. Lett. 24, 1056–1058 (1999).

    Article  ADS  Google Scholar 

  40. Wabnitz, S. Control of soliton train transmission, storage, and clock recovery by CW light injection. J. Opt. Soc. Am. B 13, 2739–2749 (1996).

    Article  ADS  Google Scholar 

  41. Haus, H. A. & Huang, W. Coupled-mode theory. Proc. IEEE 79, 1505–1518 (1991).

    Article  Google Scholar 

  42. Barker, J. A. & Henderson, D. What is ‘liquid’? Understanding the states of matter. Rev. Mod. Phys. 48, 587–671 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  43. Egami, T. & Billinge, S. Underneath the Bragg Peaks (Elsevier, Oxford, UK, 2012).

  44. Weiner, A. Ultrafast Optics (Wiley, Hoboken, USA, 2009).

  45. Pang, M., He, W., Jiang, X. & Russell, P. S. J. All-optical bit storage in a fibre laser by optomechanically bound states of solitons. Nat. Photon. 10, 454–458 (2016).

    Article  ADS  Google Scholar 

  46. Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).

    Article  ADS  Google Scholar 

  47. Spillane, S. M., Kippenberg, T. J., Painter, O. J. & Vahala, K. J. Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics. Phys. Rev. Lett. 91, 043902 (2003).

    Article  ADS  Google Scholar 

  48. Beha, K. et al. Electronic synthesis of light. Optica 4, 406–411 (2017).

    Article  Google Scholar 

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Acknowledgements

The authors thank D. Hickstein and K. Beloy for comments on the manuscript and K.Y. Yang and K. Vahala for providing the 16 GHz wedge resonators. This material is based on work supported by the Air Force Office of Scientific Research under award no. FA9550-16-1-0016. Additional support was provided by the NIST-on-a-Chip programme and the DARPA QuASAR and PULSE programmes. D.C.C. acknowledges support from the NSF GRFP under grant no. DGE 1144083.

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Author notes

  1. Pascal Del’Haye

    Present address: National Physical Laboratory (NPL), Teddington, TW11 0LW, UK

Authors and Affiliations

  1. National Institute of Standards and Technology (NIST), Boulder, CO, 80305, USA

    Daniel C. Cole, Erin S. Lamb, Pascal Del’Haye, Scott A. Diddams & Scott B. Papp

  2. Department of Physics, University of Colorado, Boulder, CO, 80309, USA

    Daniel C. Cole

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Contributions

E.S.L., D.C.C., P.D.’H. and S.B.P. performed the crystal generation experiments. D.C.C. analysed the data, developed the model, and performed the numerical simulations. E.S.L. performed the cross-correlation experiments. D.C.C. wrote the manuscript. All authors discussed the experiments and the model and contributed to revision of the manuscript.

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Correspondence to Daniel C. Cole.

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Soliton crystals in Kerr resonators

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Cole, D.C., Lamb, E.S., Del’Haye, P. et al. Soliton crystals in Kerr resonators. Nature Photon 11, 671–676 (2017). https://doi.org/10.1038/s41566-017-0009-z

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