Izvestiya of Saratov University.

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Razumkov V. A., Melnikov L. A. Numerical Modeling of the Opposite Waves Spatio-Temporal Dynamics in a Ring Fibre Nonlinear Microcavity. //Izvestiya of Saratov University. New series. Series: Physics. , 2020, vol. 20, iss. 1, pp. 64-71. DOI:

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Numerical Modeling of the Opposite Waves Spatio-Temporal Dynamics in a Ring Fibre Nonlinear Microcavity

Razumkov Vadim Alekseevich, Saratov State Technical University named after Yuri Gagarin
Melnikov Leonid Arkad'evich, Saratov State Technical University named after Yuri Gagarin

Background and Objectives: Optical frequency combs have a significant impact in the terabit communications area. Kerr frequency comb generation in the nonlinear microcavities is especially promising because it allows for creation of the combs with spacings of tens of gigahertz between the frequencies. However, such combs can also spawn strong phase noises, what, in turn, leads to the problems with the high-speed data transmission. Results of the already conducted experiments show that it is Kerr combs that allow for serious demands of the coherent communications and thus are a very effective way to create microsized transmission receivers that are capable of supporting terabit per second rates of data flow. Thus, it is apparent that the ability to predict electromagnetic field behavior within the microcavities has a huge practical value. Since the operating regime of such cavities corresponds to strong nonlinearity, then proper research of its dynamics is possible right now only based on the numerical methods. It should be noted that the models used ought to give an adequate representation of the occurring process and do not require long calculation times. Materials and Methods: Since the equations used are the transport equation, we use in our numerical model an effective finite differences model of the second order known as “Cabaret”. To check for the algorithm stability, we have calculated full pulse energy during a round trip, and it was shown that there is less than 1% of the numerical losses after two million steps, which is about one thousand of the cavity round trips. Results: We have achieved conclusive results in several modes of the model, getting frequency soliton combs, following each other with a period roughly equal to that of a cavity roundtrip, as well as chaotic modes and overlaps of the combs. Conclusion: Summarizing, we can conclude that using the second order finite differences model “Cabaret” allows to simulate long temporal dynamics of the fibre microcavities, with GVD, crossand self phase modulation taken into consideration, displaying good fit to the theoretical expectations. The proposed scheme and model allow to investigate cavity dynamics with two counter-propagatating pulse trains with second order dispersion and modulation instability, Rayleigh scattering and other effects and linear wave interfaces.

  1. Hillerkuss D., Schmogrow R., Schellinger T., Jordan M., Winter M., Huber G., Vallaitis T., Bonk R., Kleinow P., Frey F., Roeger M., Koenig S., Ludwig A., Marculescu A., Li J., Hoh M., Dreschmann M., Meyer J., Ben Ezra S., Narkiss N., Nebendahl B., Parmigiani F., Petropoulos P., Resan B., Oehler A., Weingarten K., Ellermeyer T., Lutz J., Moeller M., Huebner M., Becker J., Koos C., Freude W., Leuthold J. 26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing. Nature Photonics, 2011, vol. 5, iss. 6, pp. 364–371. DOI:
  2. Del’Haye P., Schliesser A., Arcizet O., Wilken T., Holzwarth R., Kippenberg T. J. Optical frequency comb generation from a monolithic microresonator. Nature, 2007, vol. 450, pp. 1214–1217. DOI:
  3. Levy J. S., Saha K., Okawachi Y., Foster M. A., Gaeta A. L., Lipson M. High-Performance Silicon-Nitride-Based Multiple-Wavelength Source. IEEE Photonics Technology Letters, 2012 Aug.15, vol. 24, no. 16, pp. 1375–1377. DOI:
  4. Herr T., Hartinger K., Riemensberger J., Wang C. Y., Gavartin E., Holzwarth R., Gorodetsky M. L., Kippenberg T. J. Universal formation dynamics and noise of Kerr-frequency combs in microresonators. Nature Photonics, 2012, vol. 6, iss. 7, pp. 480–487. DOI:
  5. Pfeifl e J., Weimann C., Bach F., Riemensberger J., Hartinger K., Hillerkuss D., Jordan M., Holtzwarth R., Kippenberg T. J., Leuthold J., Freude W., Koos C. Microresonator-Based Optical Frequency Combs for High-Bitrate WDM Data Transmission. Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OW1C.4.
  6. Wang P.-H., Ferdous F., Miao H., Wang J., Leaird D. E., Srinivasan K., Chen L., Aksyuk V., Weiner A. M. Observation of correlation between route to formation, coherence, noise, and communication performance of Kerr combs. Opt. Express, 2012, vol. 20, pp. 29284–29295.
  7. Pfeifl e J., Brasch V., Lauermann M., Yu Y., Wegner D., Herr T., Hartinger K., Schindler P., Li J., Hillerkuss D., Schmogrow R., Weimann C., Holzwarth R., Freude W., Leuthold J., Kippenberg T. J., Koos C. Coherent terabit communications with microresonator Kerr frequency combs. Nature Photonics, 2014, vol. 8, iss. 5, pp. 375–380. DOI:
  8. Herr T., Brasch V., Jost J. D., Wang C. Y., Kondratiev N. M., Gorodetsky M. L., Kippenberg T. J. Temporal solitons in optical microresonators. Nature Photonics, 2014, vol. 8, iss. 2, pp. 145–152. DOI:
  9. Miller D. A. B. Device Requirements for Optical Interconnects to Silicon Chips. Proceedings of the IEEE, 2009 July, vol. 97, no. 7, pp. 1166–1185. DOI:
  10. Qian D., Huang M.-F., Ip E., Huang Y.-K., Shao Y., Hu J., Wang T. 101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM Transmission over 3×55-km SSMF using Pilot-based Phase Noise Mitigation. Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPB5. DOI:
  11. Witzens J., Baehr-Jones T., Hochberg M. On-chip OPOs. Nature Photonics, 2010, vol. 4, iss. 1, pp. 10–12. DOI:
  12. Hillerkuss D., Schmogrow R., Meyer M., Wolf S., Jordan M., Kleinow P., Lindenmann N., Schindler P. C., Melikyan A., Yang X., Ben-Ezra S., Nebendahl B., Dreschmann M., Meyer J., Parmigiani F., Petropoulos P., Resan B., Oehler A., Weingarten K., Altenhain L., Ellermeyer T., Moeller M., Huebner M., Becker J., Koos C., Freude W., Leuthold J. Single-laser 32.5 Tbit/s Nyquist WDM transmission. IEEE/OSA Journal of Optical Communications and Networking, 2012 Oct., vol. 4, no. 10, pp. 715–723. DOI:
  13. Wu R., Supradeepa V. R., Long C. M., Leaird D. E., Weiner A. M. Generation of very fl at optical frequency combs from continuous-wave lasers using cascaded intensity and phase modulators driven by tailored radio frequency waveforms. Opt. Lett., 2010, vol. 35, pp. 3234–3236. DOI:
  14. Chembo Y. K. K., Yu N. Modal expansion approach to optical-frequency-comb generation with monolithic whispering gallery-mode resonators. Phys. Rev. A, 2010, vol. 82, 33801.
  15. Maleki L., Ilchenko V. S., Savchenkov A. A., Liang W., Seidel D., Matsko A. B. High performance, miniature hyper-parametric microwave photonic oscillator. 2010 IEEE International Frequency Control Symposium (FCS), IEEE Xplore, 2010, pp. 558–563.
  16. Matsko A. B., Savchenkov A. A., Liang W., Ilchenko V. S., Seidel D., Maleki L. Mode-locked Kerr frequency combs. Opt. Lett., 2011, vol. 36, pp. 2845–2847.
  17. Chembo Y. K., Menyuk C. R. Spatiotemporal Lugiato-Lefever formalism for Kerr-comb generation in whispering gallery-mode resonators. Phys. Rev. A, 2013, vol. 87, 053852.
  18. Rosales R., Merghem K., Martinez A., Akrout A., Tourrenc J.-P., Accard A., Lelarge F., Ramdane A. InAs/InP Quantum-Dot Passively Mode-Locked Lasers for 1.55-μ m Applications. IEEE Journal of Selected Topics in Quantum Electronics, 2011 Sept.–Oct., vol. 17, no. 5, pp. 1292–1301. DOI:
  19. Herr T., Brasch V., Jost J. D., Wang C. Y., Kondratiev N. M., Gorodetsky M. L., Kippenberg T. J. Supplementary information to Temporal solitons in optical microresonators. Nature Photonics, 2014, vol. 8, iss. 2, pp. 145–152. DOI:
  20. Gorodetsky M. L. Opticheskiye Microrezonatory s gigantskoy dobrotnostyu [Optical Microresonators with Huge Quality]. Moscow, PHIZMATLIT Publ., 2011. 416 p. (in Russian).
  21. Razukov V. A., Melnikov L. A. Short pulse dynamics in a linear cavity fi ber laser. Proc. SPIE. Saratov Fall Meeting 2015: Third International Symposium on Optics and Biophotonics and Seventh Finnish-Russian Photonics and Laser Symposium (PALS), 2016, vol. 9917, pp. 788–792. DOI:
  22. Razukov V. A., Melnikov L. A., Mazhirina Yu. A., Sukhanov S. V. Numerical modeling of space-temporal dynamics in fi ber lasers. J. Appl. Spectr., 2016, vol. 83, no. 6–16, pp. 344–345.
  23. Melnikov L. A., Mazhirina Yu. A. Dynamics and instabilities in long SRS fi bre lasers with linear and ring cavities. Quantum Electronics, 2017, vol. 47, iss. 12, pp. 1083–1090. DOI:
  24. Agraval G. P. Nonlinear Fiber Optics. Academic Press, 2007. 529 p.
  25. Mazhirina Yu. A., Melnikov L. A., Turitsyn S. K., Churkin D. V., Tarasov N. S. Nonlinear Dynamics of Long mirrorless SRS fi bre laser. Izvestiya VUZ, Applied Nonlinear Dynamics, 2014, vol. 22, no. 5, pp. 73–82 (in Russian).
  26. Goloviznin V. M., Samarskii A. A. Finite difference approximation of convective transport equation with space splitting time derivative. Matematicheskoe Modelirovanie [Matem. Mod.], 1998, vol. 10, no. 1, pp. 86–100 (in Russian).
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