Giant injection-locking bandwidth of a self-pulsing limit-cycle in an optomechanical cavity

[EN] Locking of oscillators to ultra-stable external sources is of paramount importance for improving close-to-carrier phase noise in free running oscillators. In most of them, such as Micro-Electro-Mechanical-Systems or LC circuit-based oscillators, the locking frequency range is limited by the robustness of their natural frequency, which comes explicitly related with intrinsic parameters of the system. In this work we report the synchronization of an optically-driven self-pulsing limit-cycle taking place in a silicon optomechanical crystal cavity to an external harmonic signal that modulates the driving laser. Because of the extreme ductility of the natural self-pulsing frequency (several tens of MHz), the injection-locking mechanism is highly efficient and displays giant relative bandwidths exceeding 60%. The external modulation reveals itself as a knob to explore dynamical attractors that are otherwise elusive and, in particular, as a means to initialize a mechanical resonator into a state of self-sustained oscillations driven by radiation pressure forces. Moreover, we exploit the large anharmonicity of the studied limit-cycle to induce injection-locking to integer multiples and fractions of the frequency of the external reference, which can be used for frequency conversion purposes in nano-electro-opto-mechanical systems. This work was supported by the MICINN project ALLEGRO (PID2021-124618NB-C21 and PID2021-124618NB-C22). Navarro-Urrios, D.; Arregui, G.; Colombano, MF.; Jaramillo-Fernández, J.; Pitanti, A.; Griol Barres, A.; Mercadé, L... (2022). Giant injection-locking bandwidth of a self-pulsing limit-cycle in an optomechanical cavity. Communications Physics. 5(1):1-12. https://doi.org/10.1038/s42005-022-01113-9 Pikovsky, A., Kurths, J., Rosenblum, M. & Kurths, J. Synchronization: a universal concept in nonlinear sciences (Cambridge University Press, 2003). Balanov, A., Janson, N., Postnov, D. & Sosnovtseva, O. Synchronization: from simple to complex (Springer Science & Business Media, 2008). Adler, R. A study of locking phenomena in oscillators. Proc. IEEE 61, 1380–1385 (1973). Kurokawa, K. Injection locking of microwave solid-state oscillators. Proc. IEEE 61, 1386–1410 (1973). Paciorek, L. J. Injection locking of oscillators. Proc. IEEE 53, 1723–1727 (1965). Stover, H. L. Theoretical explanation for the output spectra of unlocked driven oscillators. Proc. IEEE 54, 310–311 (1966). Armand, M. On the output spectrum of unlocked driven oscillators. P