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[EN] Dynamical radiation pressure effects in cavity optomechanical systems give rise to self-sustained oscillations or 'phonon lasing' behavior, producing stable oscillators up to GHz frequencies in nanoscale devices. Like in photonic lasers, phonon lasing normally occurs in a single mechanical mode. We show here that mode-locked, multimode phonon lasing can be established in a multimode optomechanical system through Floquet dynamics induced by a temporally modulated laser drive. We demonstrate this concept in a suitably engineered silicon photonic nanocavity coupled to multiple GHz-frequency mechanical modes. We find that the long-term frequency stability is significantly improved in the multimode lasing state as a result of the mode locking. These results provide a path toward highly stable ultracompact oscillators, pulsed phonon lasing, coherent waveform synthesis, and emergent many-mode phenomena in oscillator arrays. ; The authors thank Javier del Pino for useful discussions. This work is supported by the European Union's Horizon 2020 research and innovation program under Grant Agreements No. 732894 (FET Proactive HOT), 713450 (FET-Open PHENOMEN), and 945915 (SIOMO), the Spanish State Research Agency (PGC2018-094490-BC21) and by the Juilan Schwinger Foundation project grant No. JSF-16-03-0000 (TOM). It is part of the research program of the Netherlands Organisation for Scientific Research (NWO). A. M. acknowledges funding from Generalitat Valenciana under Grants No. PROMETEO/2019/123, BEST/2020/178, and IDIFEDER/2018/033. E. V. acknowledges support from the European Research Council (ERC Starting Grant No. 759644-TOPP). ; Mercadé-Morales, L.; Pelka, K.; Burgwal, R.; Xuereb, A.; Martínez, A.; Verhagen, E. (2021). Floquet Phonon Lasing in Multimode Optomechanical Systems. Physical Review Letters. 127(7):1-7. https://doi.org/10.1103/PhysRevLett.127.073601 ; S ; 1 ; 7 ; 127 ; 7

9829 9839 26 8 ; S ; Navarro-Urrios, D.; Capuj, N.; Maire, J.; Colombano, M.; Jaramillo-Fernandez, J.; Chavez-Angel, E.; Martín-Rodríguez, LL. (2018). Nanocrystalline silicon optomechanical cavities. Optics Express. 26(8):9829-9839. https://doi.org/10.1364/OE.26.009829 ; "© 2018 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited" [EN] Silicon on insulator photonics has offered a versatile platform for the recent development of integrated optomechanical circuits. However, there are some constraints such as the high cost of the wafers and limitation to a single physical device level. In the present work we investigate nanocrystalline silicon as an alternative material for optomechanical devices. In particular we demonstrate that optomechanical crystal cavities fabricated of nanocrystalline silicon have optical and mechanical properties enabling non-linear dynamical behaviour and effects such as thermo-optic/free-carrier-dispersion self-pulsing, phonon lasing and chaos, all at low input laser power and with typical frequencies as high as 0.3 GHz. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement European Commission project PHENOMEN (H2020-EU-713450), MINECO Severo Ochoa Excellence program (SEV-2013-0295), MINECO (FIS2015-70862-P, RYC-2014-15392) and CERCA Programme/Generalitat de Catalunya. Kippenberg, T. J., & Vahala, K. J. (2008). Cavity Optomechanics: Back-Action at the Mesoscale. Science, 321(5893), 1172-1176. doi:10.1126/science.1156032 Aspelmeyer, M., Kippenberg, T. J., & Marquardt, F. (2014). Cavity optomechanics. Reviews of Modern Physics, 86(4), 1391-1452. doi:10.1103/revmodphys.86.1391 Navarro-Urrios, D., Capuj, N. E., Gomis-Bresco, J., Alzina, F., Pitanti, A., Griol, A., … Sotomayor Torres, C. M. (2015). A self-stabilized coherent ...