Skip to main content
Log in

Soliton-comb structures in ring-shaped optical microresonators: generation, reconstruction and stability

  • Regular Article
  • Optical Phenomena and Photonics
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

Characteristic features of soliton-comb structures in optical microresonators are investigated in normal and anomalous dispersion regimes, when the detuning parameter is varied over a broad range of values. The study rests on the assumption that soliton combs are self-organized ensemble of co-propagating coherently entangled states of light, and depending on the group-velocity dispersion they can result from space-division multiplexing of single-bright and single-dark solitons. Their analytical and numerical reconstruction schemes are discussed, while a linear-stability analysis leads to a 2 × 2 Lamé eigenvalue problem whose boundstate spectrum is composed of a Goldstone-type translation mode and stable internal modes, as well as unstable decaying modes and growing modes. A power-spectral analysis of the three distinct possible soliton crystals enables us probe their inner structures in the frequency domain, and unveil the existence of structural defects in their power spectra.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. T.W. Hänsch, Rev. Mod. Phys. 78, 1297 (2006)

    Article  ADS  Google Scholar 

  2. S.A. Diddams, J. Opt. Soc. Am. B 27, 51 (2010)

    Article  Google Scholar 

  3. Y. Chembo, Nanophotonics 5, 214(2016)

    Article  Google Scholar 

  4. T. Hansson, D. Modotto, S. Wabnitz, Opt. Commun. 312, 134 (2014)

    Article  ADS  Google Scholar 

  5. J. Ye, S.T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation and Applications. 1st edn. (Springer, Boston, 2005)

  6. T.W. Hänsch, N. Picqué, J. Phys.: Conf. Ser. 467, 012001 (2013)

    Google Scholar 

  7. D.J. Jones, S.A. Diddams, J.K. Ranka, A. Stentz, R.S. Windeler, J.L. Hall, S.T. Cundiff, Science 288, 635 (2000)

    Article  ADS  Google Scholar 

  8. T. Wilken, G. Curto, R. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. Hernandez, R. Rebolo, T. Hansch, T. Udem, R. Holzwarth, Nature 485, 611 (2012)

    Article  ADS  Google Scholar 

  9. M.T. Murphy, T. Udem, R. Holzwarth, A. Sizmann, L. Pasquini, C. Araujo-Hauck, Mon. Not. R. Astron. Soc. 380, 839 (2007)

    Article  ADS  Google Scholar 

  10. A.L. Gaeta, M. Lipson, T.J. Kippenberg, Nat. Photonics 13, 158 (2019)

    Article  ADS  Google Scholar 

  11. M. Bagheri, C. Frez, L.A. Sterczewski, I. Gruidin, M. Fradet, I. Vurgaftman, C.L. Canedy, W.W. Bewley, C.D. Merritt, C.S. Kim, M. Kim, J.R. Meyer, Sci. Rep. 8, 3322 (2018)

    Article  ADS  Google Scholar 

  12. S. Stutz, D. Auth, C. Weber, O. Nikiforov, L.F. Lester, T. Walther, S. Breuer, Proc. SPIE 10682, 1068222 (2018)

    Google Scholar 

  13. T.J. Kippenberg, R. Holzwarth, S.A. Diddams, Science 332, 555 (2011)

    Article  ADS  Google Scholar 

  14. T.J. Kippenberg, A. Gaeta, M. Lipson, M. Gorodetsky, Science 361, 6402 (2018)

    Article  Google Scholar 

  15. X. Yi, Q.F. Yang, K.Y. Yang, M.G. Suh, K. Vahala, Optica 2, 1078 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. T. Herr, V. Brash, J.D. Jost, I. Mirgorodskiy, G. Lihachev, M.L. Gorodetsky, T.J. Kipenberg, Phys. Rev. Lett. 113, 123901 (2014)

    Article  ADS  Google Scholar 

  18. D. Jr. F. Jubgang, A.M. Dikandé, A. Sunda-Meya, Phys. Rev. A 92, 053850 (2015)

    Article  ADS  Google Scholar 

  19. A. Haboucha, H. Leblond, M. Salhi, A. Komarov, F. Sanchez, Phys. Rev. A 78, 043806 (2008)

    Article  ADS  Google Scholar 

  20. D.C. Cole, E.S. Lamb, P. Del’Haye, S.A. Diddams, P.B. Scott, Nat. Photonics 11, 671 (2017)

    Article  ADS  Google Scholar 

  21. R.D. Dikandé, A.M. Dikandé, Phy. Rev. A 97, 033813 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  22. L.A. Lugiato, R. Lefever, Phys. Rev. Lett. 58, 2209 (1987)

    Article  ADS  Google Scholar 

  23. A.M. Dikandé, Phys. Rev. A 81, 013821 (2010)

    Article  ADS  Google Scholar 

  24. Y. He, S. Wang, X. Zeng, IEEE Photon J. 8, 7102508 (2016)

    Google Scholar 

  25. P. Parra-Rivas, D. Gomila, L. Gelens, Phys. Rev. A 95, 053863 (2017)

    Article  ADS  Google Scholar 

  26. A. Pasquazi, M. Peccianti, L. Razzari, D.J. Moss, S. Coen, M. Erkintalo, Y.K. Chembo, T. Hansson, S. Wabnitz, P. Del’Haye, X. Xue, Phys. Rep. 729, 1 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  27. A.B. Matsko, A.A. Savchenkov, W. Liang, V.S. Ilchenko, D. Seidel, L. Maleki, Opt. Lett. 36, 2845 (2011)

    Article  ADS  Google Scholar 

  28. A.M. Dikandé, J. Opt. 13, 035203 (2011)

    Article  ADS  Google Scholar 

  29. Z. Qi, G. D’Aguanno, C.R. Menyuk, J. Opt. Soc. Am. B 4, 785 (2017)

    Article  ADS  Google Scholar 

  30. S. Wabnitz, Opt. Lett. 18, 601 (1993)

    Article  ADS  Google Scholar 

  31. Y.S. Kivshar, D.E. Pelinovsky, T. Cretegny, M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998)

    Article  ADS  Google Scholar 

  32. J.M. Soto-Crespo, N. Devine, N. Akhmediev, Phys. Rev. A 96, 023825 (2017)

    Article  ADS  Google Scholar 

  33. Y.S. Kivshar, B.A. Malomed, Rev. Mod. Phys. 61, 763 (1989)

    Article  ADS  Google Scholar 

  34. Z. Qi, D. Giuseppe, C.R. Menyuk, J. Opt. Soc. Am. B 34, 785 (2017)

    Article  ADS  Google Scholar 

  35. T. Hansson, S. Wabnitz, J. Opt. Soc. Am. B 32, 1259 (2015)

    Article  ADS  Google Scholar 

  36. X. Hu, W. Wang, L. Wang, W. Zhang, Y. Wang, W. Zhao, Photon. Res. 5, 207 (2017)

    Article  Google Scholar 

  37. W. Loh, P. Del’Haye, S.B. Papp, S.A. Diddams, Phys. Rev. A 89, 053810 (2014)

    Article  ADS  Google Scholar 

  38. D.C. Cole, S.B. Papp, S.A. Diddams, J. Opt. Soc. Am. B 35, 1666 (2018)

    Article  ADS  Google Scholar 

  39. P. Trocha, M. Karpov, D. Ganin, M.H.P. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude, T.J. Kippenberg, C. Koos, Science 359, 887 (2018)

    Article  ADS  Google Scholar 

  40. H. Bao, A. Cooper, S.T. Chu, D.J. Moss, R. Morandotti, B.E. Little, M. Peccianti, A. Pasquazi, Photon. Res. 6, B67 (2018)

    Article  Google Scholar 

  41. Y. Chembo, C. Menyuk, Phys. Rev. A 87, 053852 (2013)

    Article  ADS  Google Scholar 

  42. N. Cong, Comput. Math. Appl. 31, 111 (1996)

    Article  MathSciNet  Google Scholar 

  43. K. Luo, J. Jang, S. Coen, S. Murdoch, M. Erkintalo, Opt. Lett. 40, 3735 (2015)

    Article  ADS  Google Scholar 

  44. Y. Chembo, N. Yu, Phys. Rev. A 82, 033801 (2010)

    Article  ADS  Google Scholar 

  45. I. Coddington, W.C. Swann, N.R. Newbury, Phys. Rev. Lett. 100, 013902 (2008)

    Article  ADS  Google Scholar 

  46. Y. Chembo, D.V. Strekalov, N. Yu, Phys. Rev. Lett. 104, 103902 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alain M. Dikandé.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dikandé Bitha, R.D., Dikandé, A.M. Soliton-comb structures in ring-shaped optical microresonators: generation, reconstruction and stability. Eur. Phys. J. D 73, 152 (2019). https://doi.org/10.1140/epjd/e2019-100052-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/e2019-100052-y

Navigation